API
Part of the API of DynamicPPL is defined in the more lightweight interface package AbstractPPL.jl and reexported here.
Model
Macros
A core component of DynamicPPL is the @model macro. It can be used to define probabilistic models in an intuitive way by specifying random variables and their distributions with ~ statements. These statements are rewritten by @model as calls of internal functions for sampling the variables and computing their log densities.
DynamicPPL.@model — Macro@model(expr[, warn = false])Macro to specify a probabilistic model.
If warn is true, a warning is displayed if internal variable names are used in the model definition.
Examples
Model definition:
@model function model(x, y = 42)
+ ...
+endTo generate a Model, call model(xvalue) or model(xvalue, yvalue).
One can nest models and call another model inside the model function with @submodel.
DynamicPPL.@submodel — Macro@submodel model
+@submodel ... = modelRun a Turing model nested inside of a Turing model.
Examples
julia> @model function demo1(x)
+ x ~ Normal()
+ return 1 + abs(x)
+ end;
+
+julia> @model function demo2(x, y)
+ @submodel a = demo1(x)
+ return y ~ Uniform(0, a)
+ end;When we sample from the model demo2(missing, 0.4) random variable x will be sampled:
julia> vi = VarInfo(demo2(missing, 0.4));
+
+julia> @varname(x) in keys(vi)
+trueVariable a is not tracked since it can be computed from the random variable x that was tracked when running demo1:
julia> @varname(a) in keys(vi)
+falseWe can check that the log joint probability of the model accumulated in vi is correct:
julia> x = vi[@varname(x)];
+
+julia> getlogp(vi) ≈ logpdf(Normal(), x) + logpdf(Uniform(0, 1 + abs(x)), 0.4)
+true@submodel prefix=... model
+@submodel prefix=... ... = modelRun a Turing model nested inside of a Turing model and add "prefix." as a prefix to all random variables inside of the model.
Valid expressions for prefix=... are:
prefix=false: no prefix is used.prefix=true: attempt to automatically determine the prefix from the left-hand side... = modelby first converting into aVarName, and then callingSymbolon this.prefix=expression: results in the prefixSymbol(expression).
The prefix makes it possible to run the same Turing model multiple times while keeping track of all random variables correctly.
Examples
Example models
julia> @model function demo1(x)
+ x ~ Normal()
+ return 1 + abs(x)
+ end;
+
+julia> @model function demo2(x, y, z)
+ @submodel prefix="sub1" a = demo1(x)
+ @submodel prefix="sub2" b = demo1(y)
+ return z ~ Uniform(-a, b)
+ end;When we sample from the model demo2(missing, missing, 0.4) random variables sub1.x and sub2.x will be sampled:
julia> vi = VarInfo(demo2(missing, missing, 0.4));
+
+julia> @varname(var"sub1.x") in keys(vi)
+true
+
+julia> @varname(var"sub2.x") in keys(vi)
+trueVariables a and b are not tracked since they can be computed from the random variables sub1.x and sub2.x that were tracked when running demo1:
julia> @varname(a) in keys(vi)
+false
+
+julia> @varname(b) in keys(vi)
+falseWe can check that the log joint probability of the model accumulated in vi is correct:
julia> sub1_x = vi[@varname(var"sub1.x")];
+
+julia> sub2_x = vi[@varname(var"sub2.x")];
+
+julia> logprior = logpdf(Normal(), sub1_x) + logpdf(Normal(), sub2_x);
+
+julia> loglikelihood = logpdf(Uniform(-1 - abs(sub1_x), 1 + abs(sub2_x)), 0.4);
+
+julia> getlogp(vi) ≈ logprior + loglikelihood
+trueDifferent ways of setting the prefix
julia> @model inner() = x ~ Normal()
+inner (generic function with 2 methods)
+
+julia> # When `prefix` is unspecified, no prefix is used.
+ @model submodel_noprefix() = @submodel a = inner()
+submodel_noprefix (generic function with 2 methods)
+
+julia> @varname(x) in keys(VarInfo(submodel_noprefix()))
+true
+
+julia> # Explicitely don't use any prefix.
+ @model submodel_prefix_false() = @submodel prefix=false a = inner()
+submodel_prefix_false (generic function with 2 methods)
+
+julia> @varname(x) in keys(VarInfo(submodel_prefix_false()))
+true
+
+julia> # Automatically determined from `a`.
+ @model submodel_prefix_true() = @submodel prefix=true a = inner()
+submodel_prefix_true (generic function with 2 methods)
+
+julia> @varname(var"a.x") in keys(VarInfo(submodel_prefix_true()))
+true
+
+julia> # Using a static string.
+ @model submodel_prefix_string() = @submodel prefix="my prefix" a = inner()
+submodel_prefix_string (generic function with 2 methods)
+
+julia> @varname(var"my prefix.x") in keys(VarInfo(submodel_prefix_string()))
+true
+
+julia> # Using string interpolation.
+ @model submodel_prefix_interpolation() = @submodel prefix="$(nameof(inner()))" a = inner()
+submodel_prefix_interpolation (generic function with 2 methods)
+
+julia> @varname(var"inner.x") in keys(VarInfo(submodel_prefix_interpolation()))
+true
+
+julia> # Or using some arbitrary expression.
+ @model submodel_prefix_expr() = @submodel prefix=1 + 2 a = inner()
+submodel_prefix_expr (generic function with 2 methods)
+
+julia> @varname(var"3.x") in keys(VarInfo(submodel_prefix_expr()))
+true
+
+julia> # (×) Automatic prefixing without a left-hand side expression does not work!
+ @model submodel_prefix_error() = @submodel prefix=true inner()
+ERROR: LoadError: cannot automatically prefix with no left-hand side
+[...]Notes
- The choice
prefix=expressionmeans that the prefixing will incur a runtime cost. This is also the case forprefix=true, depending on whether the expression on the the right-hand side of... = modelrequires runtime-information or not, e.g.x = modelwill result in the static prefixx, whilex[i] = modelwill be resolved at runtime.
Type
A Model can be created by calling the model function, as defined by @model.
DynamicPPL.Model — Typestruct Model{F,argnames,defaultnames,missings,Targs,Tdefaults}
+ f::F
+ args::NamedTuple{argnames,Targs}
+ defaults::NamedTuple{defaultnames,Tdefaults}
+endA Model struct with model evaluation function of type F, arguments of names argnames types Targs, default arguments of names defaultnames with types Tdefaults, and missing arguments missings.
Here argnames, defaultargnames, and missings are tuples of symbols, e.g. (:a, :b).
An argument with a type of Missing will be in missings by default. However, in non-traditional use-cases missings can be defined differently. All variables in missings are treated as random variables rather than observations.
The default arguments are used internally when constructing instances of the same model with different arguments.
Examples
julia> Model(f, (x = 1.0, y = 2.0))
+Model{typeof(f),(:x, :y),(),(),Tuple{Float64,Float64},Tuple{}}(f, (x = 1.0, y = 2.0), NamedTuple())
+
+julia> Model(f, (x = 1.0, y = 2.0), (x = 42,))
+Model{typeof(f),(:x, :y),(:x,),(),Tuple{Float64,Float64},Tuple{Int64}}(f, (x = 1.0, y = 2.0), (x = 42,))
+
+julia> Model{(:y,)}(f, (x = 1.0, y = 2.0), (x = 42,)) # with special definition of missings
+Model{typeof(f),(:x, :y),(:x,),(:y,),Tuple{Float64,Float64},Tuple{Int64}}(f, (x = 1.0, y = 2.0), (x = 42,))Models are callable structs.
DynamicPPL.Model — Method(model::Model)([rng, varinfo, sampler, context])Sample from the model using the sampler with random number generator rng and the context, and store the sample and log joint probability in varinfo.
The method resets the log joint probability of varinfo and increases the evaluation number of sampler.
Basic properties of a model can be accessed with getargnames, getmissings, and nameof.
Base.nameof — Methodnameof(model::Model)Get the name of the model as Symbol.
DynamicPPL.getargnames — Functiongetargnames(model::Model)Get a tuple of the argument names of the model.
DynamicPPL.getmissings — Functiongetmissings(model::Model)Get a tuple of the names of the missing arguments of the model.
Evaluation
With rand one can draw samples from the prior distribution of a Model.
Base.rand — Functionrand([rng=Random.default_rng()], [T=NamedTuple], model::Model)Generate a sample of type T from the prior distribution of the model.
One can also evaluate the log prior, log likelihood, and log joint probability.
DynamicPPL.logprior — Functionlogprior(model::Model, varinfo::AbstractVarInfo)Return the log prior probability of variables varinfo for the probabilistic model.
See also logjoint and loglikelihood.
logprior(model::Model, chain::AbstractMCMC.AbstractChains)Return an array of log prior probabilities evaluated at each sample in an MCMC chain.
Examples
julia> using MCMCChains, Distributions
+
+julia> @model function demo_model(x)
+ s ~ InverseGamma(2, 3)
+ m ~ Normal(0, sqrt(s))
+ for i in eachindex(x)
+ x[i] ~ Normal(m, sqrt(s))
+ end
+ end;
+
+julia> # construct a chain of samples using MCMCChains
+ chain = Chains(rand(10, 2, 3), [:s, :m]);
+
+julia> logprior(demo_model([1., 2.]), chain);logprior(model::Model, θ)Return the log prior probability of variables θ for the probabilistic model.
See also logjoint and loglikelihood.
Examples
julia> @model function demo(x)
+ m ~ Normal()
+ for i in eachindex(x)
+ x[i] ~ Normal(m, 1.0)
+ end
+ end
+demo (generic function with 2 methods)
+
+julia> # Using a `NamedTuple`.
+ logprior(demo([1.0]), (m = 100.0, ))
+-5000.918938533205
+
+julia> # Using a `OrderedDict`.
+ logprior(demo([1.0]), OrderedDict(@varname(m) => 100.0))
+-5000.918938533205
+
+julia> # Truth.
+ logpdf(Normal(), 100.0)
+-5000.918938533205StatsAPI.loglikelihood — Functionloglikelihood(model::Model, varinfo::AbstractVarInfo)Return the log likelihood of variables varinfo for the probabilistic model.
loglikelihood(model::Model, chain::AbstractMCMC.AbstractChains)Return an array of log likelihoods evaluated at each sample in an MCMC chain.
Examples
julia> using MCMCChains, Distributions
+
+julia> @model function demo_model(x)
+ s ~ InverseGamma(2, 3)
+ m ~ Normal(0, sqrt(s))
+ for i in eachindex(x)
+ x[i] ~ Normal(m, sqrt(s))
+ end
+ end;
+
+julia> # construct a chain of samples using MCMCChains
+ chain = Chains(rand(10, 2, 3), [:s, :m]);
+
+julia> loglikelihood(demo_model([1., 2.]), chain);loglikelihood(model::Model, θ)Return the log likelihood of variables θ for the probabilistic model.
See also logjoint and logprior.
Examples
julia> @model function demo(x)
+ m ~ Normal()
+ for i in eachindex(x)
+ x[i] ~ Normal(m, 1.0)
+ end
+ end
+demo (generic function with 2 methods)
+
+julia> # Using a `NamedTuple`.
+ loglikelihood(demo([1.0]), (m = 100.0, ))
+-4901.418938533205
+
+julia> # Using a `OrderedDict`.
+ loglikelihood(demo([1.0]), OrderedDict(@varname(m) => 100.0))
+-4901.418938533205
+
+julia> # Truth.
+ logpdf(Normal(100.0, 1.0), 1.0)
+-4901.418938533205DynamicPPL.logjoint — Functionlogjoint(model::Model, varinfo::AbstractVarInfo)Return the log joint probability of variables varinfo for the probabilistic model.
See logprior and loglikelihood.
logjoint(model::Model, chain::AbstractMCMC.AbstractChains)Return an array of log joint probabilities evaluated at each sample in an MCMC chain.
Examples
julia> using MCMCChains, Distributions
+
+julia> @model function demo_model(x)
+ s ~ InverseGamma(2, 3)
+ m ~ Normal(0, sqrt(s))
+ for i in eachindex(x)
+ x[i] ~ Normal(m, sqrt(s))
+ end
+ end;
+
+julia> # construct a chain of samples using MCMCChains
+ chain = Chains(rand(10, 2, 3), [:s, :m]);
+
+julia> logjoint(demo_model([1., 2.]), chain);logjoint(model::Model, θ)Return the log joint probability of variables θ for the probabilistic model.
See logprior and loglikelihood.
Examples
julia> @model function demo(x)
+ m ~ Normal()
+ for i in eachindex(x)
+ x[i] ~ Normal(m, 1.0)
+ end
+ end
+demo (generic function with 2 methods)
+
+julia> # Using a `NamedTuple`.
+ logjoint(demo([1.0]), (m = 100.0, ))
+-9902.33787706641
+
+julia> # Using a `OrderedDict`.
+ logjoint(demo([1.0]), OrderedDict(@varname(m) => 100.0))
+-9902.33787706641
+
+julia> # Truth.
+ logpdf(Normal(100.0, 1.0), 1.0) + logpdf(Normal(), 100.0)
+-9902.33787706641LogDensityProblems.jl interface
The LogDensityProblems.jl interface is also supported by simply wrapping a Model in a DynamicPPL.LogDensityFunction:
DynamicPPL.LogDensityFunction — TypeLogDensityFunctionA callable representing a log density function of a model.
Fields
varinfo: varinfo used for evaluationmodel: model used for evaluationcontext: context used for evaluation; ifnothing,leafcontext(model.context)will be used when applicable
Examples
julia> using Distributions
+
+julia> using DynamicPPL: LogDensityFunction, contextualize
+
+julia> @model function demo(x)
+ m ~ Normal()
+ x ~ Normal(m, 1)
+ end
+demo (generic function with 2 methods)
+
+julia> model = demo(1.0);
+
+julia> f = LogDensityFunction(model);
+
+julia> # It implements the interface of LogDensityProblems.jl.
+ using LogDensityProblems
+
+julia> LogDensityProblems.logdensity(f, [0.0])
+-2.3378770664093453
+
+julia> LogDensityProblems.dimension(f)
+1
+
+julia> # By default it uses `VarInfo` under the hood, but this is not necessary.
+ f = LogDensityFunction(model, SimpleVarInfo(model));
+
+julia> LogDensityProblems.logdensity(f, [0.0])
+-2.3378770664093453
+
+julia> # This also respects the context in `model`.
+ f_prior = LogDensityFunction(contextualize(model, DynamicPPL.PriorContext()), VarInfo(model));
+
+julia> LogDensityProblems.logdensity(f_prior, [0.0]) == logpdf(Normal(), 0.0)
+trueCondition and decondition
A Model can be conditioned on a set of observations with AbstractPPL.condition or its alias |.
Base.:| — Methodmodel | (x = 1.0, ...)Return a Model which now treats variables on the right-hand side as observations.
See condition for more information and examples.
AbstractPPL.condition — Functioncondition(model::Model; values...)
+condition(model::Model, values::NamedTuple)Return a Model which now treats the variables in values as observations.
See also: decondition, conditioned
Limitations
This does currently not work with variables that are provided to the model as arguments, e.g. @model function demo(x) ... end means that condition will not affect the variable x.
Therefore if one wants to make use of condition and decondition one should not be specifying any random variables as arguments.
This is done for the sake of backwards compatibility.
Examples
Simple univariate model
julia> using Distributions
+
+julia> @model function demo()
+ m ~ Normal()
+ x ~ Normal(m, 1)
+ return (; m=m, x=x)
+ end
+demo (generic function with 2 methods)
+
+julia> model = demo();
+
+julia> m, x = model(); (m ≠ 1.0 && x ≠ 100.0)
+true
+
+julia> # Create a new instance which treats `x` as observed
+ # with value `100.0`, and similarly for `m=1.0`.
+ conditioned_model = condition(model, x=100.0, m=1.0);
+
+julia> m, x = conditioned_model(); (m == 1.0 && x == 100.0)
+true
+
+julia> # Let's only condition on `x = 100.0`.
+ conditioned_model = condition(model, x = 100.0);
+
+julia> m, x =conditioned_model(); (m ≠ 1.0 && x == 100.0)
+true
+
+julia> # We can also use the nicer `|` syntax.
+ conditioned_model = model | (x = 100.0, );
+
+julia> m, x = conditioned_model(); (m ≠ 1.0 && x == 100.0)
+trueThe above uses a NamedTuple to hold the conditioning variables, which allows us to perform some additional optimizations; in many cases, the above has zero runtime-overhead.
But we can also use a Dict, which offers more flexibility in the conditioning (see examples further below) but generally has worse performance than the NamedTuple approach:
julia> conditioned_model_dict = condition(model, Dict(@varname(x) => 100.0));
+
+julia> m, x = conditioned_model_dict(); (m ≠ 1.0 && x == 100.0)
+true
+
+julia> # There's also an option using `|` by letting the right-hand side be a tuple
+ # with elements of type `Pair{<:VarName}`, i.e. `vn => value` with `vn isa VarName`.
+ conditioned_model_dict = model | (@varname(x) => 100.0, );
+
+julia> m, x = conditioned_model_dict(); (m ≠ 1.0 && x == 100.0)
+trueCondition only a part of a multivariate variable
Not only can be condition on multivariate random variables, but we can also use the standard mechanism of setting something to missing in the call to condition to only condition on a part of the variable.
julia> @model function demo_mv(::Type{TV}=Float64) where {TV}
+ m = Vector{TV}(undef, 2)
+ m[1] ~ Normal()
+ m[2] ~ Normal()
+ return m
+ end
+demo_mv (generic function with 4 methods)
+
+julia> model = demo_mv();
+
+julia> conditioned_model = condition(model, m = [missing, 1.0]);
+
+julia> # (✓) `m[1]` sampled while `m[2]` is fixed
+ m = conditioned_model(); (m[1] ≠ 1.0 && m[2] == 1.0)
+trueIntuitively one might also expect to be able to write model | (m[1] = 1.0, ). Unfortunately this is not supported as it has the potential of increasing compilation times but without offering any benefit with respect to runtime:
julia> # (×) `m[2]` is not set to 1.0.
+ m = condition(model, var"m[2]" = 1.0)(); m[2] == 1.0
+falseBut you can do this if you use a Dict as the underlying storage instead:
julia> # Alternatives:
+ # - `model | (@varname(m[2]) => 1.0,)`
+ # - `condition(model, Dict(@varname(m[2] => 1.0)))`
+ # (✓) `m[2]` is set to 1.0.
+ m = condition(model, @varname(m[2]) => 1.0)(); (m[1] ≠ 1.0 && m[2] == 1.0)
+trueNested models
condition of course also supports the use of nested models through the use of @submodel.
julia> @model demo_inner() = m ~ Normal()
+demo_inner (generic function with 2 methods)
+
+julia> @model function demo_outer()
+ @submodel m = demo_inner()
+ return m
+ end
+demo_outer (generic function with 2 methods)
+
+julia> model = demo_outer();
+
+julia> model() ≠ 1.0
+true
+
+julia> conditioned_model = model | (m = 1.0, );
+
+julia> conditioned_model()
+1.0But one needs to be careful when prefixing variables in the nested models:
julia> @model function demo_outer_prefix()
+ @submodel prefix="inner" m = demo_inner()
+ return m
+ end
+demo_outer_prefix (generic function with 2 methods)
+
+julia> # (×) This doesn't work now!
+ conditioned_model = demo_outer_prefix() | (m = 1.0, );
+
+julia> conditioned_model() == 1.0
+false
+
+julia> # (✓) `m` in `demo_inner` is referred to as `inner.m` internally, so we do:
+ conditioned_model = demo_outer_prefix() | (var"inner.m" = 1.0, );
+
+julia> conditioned_model()
+1.0
+
+julia> # Note that the above `var"..."` is just standard Julia syntax:
+ keys((var"inner.m" = 1.0, ))
+(Symbol("inner.m"),)And similarly when using Dict:
julia> conditioned_model_dict = demo_outer_prefix() | (@varname(var"inner.m") => 1.0);
+
+julia> conditioned_model_dict()
+1.0The difference is maybe more obvious once we look at how these different in their trace/VarInfo:
julia> keys(VarInfo(demo_outer()))
+1-element Vector{VarName{:m, typeof(identity)}}:
+ m
+
+julia> keys(VarInfo(demo_outer_prefix()))
+1-element Vector{VarName{Symbol("inner.m"), typeof(identity)}}:
+ inner.mFrom this we can tell what the correct way to condition m within demo_inner is in the two different models.
condition([context::AbstractContext,] values::NamedTuple)
+condition([context::AbstractContext]; values...)Return ConditionContext with values and context if values is non-empty, otherwise return context which is DefaultContext by default.
See also: decondition
DynamicPPL.conditioned — Functionconditioned(model::Model)Return the conditioned values in model.
Examples
julia> using Distributions
+
+julia> using DynamicPPL: conditioned, contextualize
+
+julia> @model function demo()
+ m ~ Normal()
+ x ~ Normal(m, 1)
+ end
+demo (generic function with 2 methods)
+
+julia> m = demo();
+
+julia> # Returns all the variables we have conditioned on + their values.
+ conditioned(condition(m, x=100.0, m=1.0))
+(x = 100.0, m = 1.0)
+
+julia> # Nested ones also work (note that `PrefixContext` does nothing to the result).
+ cm = condition(contextualize(m, PrefixContext{:a}(condition(m=1.0))), x=100.0);
+
+julia> conditioned(cm)
+(x = 100.0, m = 1.0)
+
+julia> # Since we conditioned on `m`, not `a.m` as it will appear after prefixed,
+ # `a.m` is treated as a random variable.
+ keys(VarInfo(cm))
+1-element Vector{VarName{Symbol("a.m"), typeof(identity)}}:
+ a.m
+
+julia> # If we instead condition on `a.m`, `m` in the model will be considered an observation.
+ cm = condition(contextualize(m, PrefixContext{:a}(condition(var"a.m"=1.0))), x=100.0);
+
+julia> conditioned(cm).x
+100.0
+
+julia> conditioned(cm).var"a.m"
+1.0
+
+julia> keys(VarInfo(cm)) # <= no variables are sampled
+VarName[]conditioned(context::AbstractContext)Return NamedTuple of values that are conditioned on under context`.
Note that this will recursively traverse the context stack and return a merged version of the condition values.
Similarly, one can specify with AbstractPPL.decondition that certain, or all, random variables are not observed.
AbstractPPL.decondition — Functiondecondition(model::Model)
+decondition(model::Model, variables...)Return a Model for which variables... are not considered observations. If no variables are provided, then all variables currently considered observations will no longer be.
This is essentially the inverse of condition. This also means that it suffers from the same limitiations.
Note that currently we only support variables to take on explicit values provided to condition.
Examples
julia> using Distributions
+
+julia> @model function demo()
+ m ~ Normal()
+ x ~ Normal(m, 1)
+ return (; m=m, x=x)
+ end
+demo (generic function with 2 methods)
+
+julia> conditioned_model = condition(demo(), m = 1.0, x = 10.0);
+
+julia> conditioned_model()
+(m = 1.0, x = 10.0)
+
+julia> # By specifying the `VarName` to `decondition`.
+ model = decondition(conditioned_model, @varname(m));
+
+julia> (m, x) = model(); (m ≠ 1.0 && x == 10.0)
+true
+
+julia> # When `NamedTuple` is used as the underlying, you can also provide
+ # the symbol directly (though the `@varname` approach is preferable if
+ # if the variable is known at compile-time).
+ model = decondition(conditioned_model, :m);
+
+julia> (m, x) = model(); (m ≠ 1.0 && x == 10.0)
+true
+
+julia> # `decondition` multiple at once:
+ (m, x) = decondition(model, :m, :x)(); (m ≠ 1.0 && x ≠ 10.0)
+true
+
+julia> # `decondition` without any symbols will `decondition` all variables.
+ (m, x) = decondition(model)(); (m ≠ 1.0 && x ≠ 10.0)
+true
+
+julia> # Usage of `Val` to perform `decondition` at compile-time if possible
+ # is also supported.
+ model = decondition(conditioned_model, Val{:m}());
+
+julia> (m, x) = model(); (m ≠ 1.0 && x == 10.0)
+trueSimilarly when using a Dict:
julia> conditioned_model_dict = condition(demo(), @varname(m) => 1.0, @varname(x) => 10.0);
+
+julia> conditioned_model_dict()
+(m = 1.0, x = 10.0)
+
+julia> deconditioned_model_dict = decondition(conditioned_model_dict, @varname(m));
+
+julia> (m, x) = deconditioned_model_dict(); m ≠ 1.0 && x == 10.0
+trueBut, as mentioned, decondition is only supported for variables explicitly provided to condition earlier;
julia> @model function demo_mv(::Type{TV}=Float64) where {TV}
+ m = Vector{TV}(undef, 2)
+ m[1] ~ Normal()
+ m[2] ~ Normal()
+ return m
+ end
+demo_mv (generic function with 4 methods)
+
+julia> model = demo_mv();
+
+julia> conditioned_model = condition(model, @varname(m) => [1.0, 2.0]);
+
+julia> conditioned_model()
+2-element Vector{Float64}:
+ 1.0
+ 2.0
+
+julia> deconditioned_model = decondition(conditioned_model, @varname(m[1]));
+
+julia> deconditioned_model() # (×) `m[1]` is still conditioned
+2-element Vector{Float64}:
+ 1.0
+ 2.0
+
+julia> # (✓) this works though
+ deconditioned_model_2 = deconditioned_model | (@varname(m[1]) => missing);
+
+julia> m = deconditioned_model_2(); (m[1] ≠ 1.0 && m[2] == 2.0)
+truedecondition(context::AbstractContext, syms...)Return context but with syms no longer conditioned on.
Note that this recursively traverses contexts, deconditioning all along the way.
See also: condition
Fixing and unfixing
We can also fix a collection of variables in a Model to certain using fix.
This might seem quite similar to the aforementioned condition and its siblings, but they are indeed different operations:
conditioned variables are considered to be observations, and are thus included in the computationlogjointandloglikelihood, but not inlogprior.fixed variables are considered to be constant, and are thus not included in any log-probability computations.
The differences are more clearly spelled out in the docstring of fix below.
DynamicPPL.fix — Functionfix(model::Model; values...)
+fix(model::Model, values::NamedTuple)Return a Model which now treats the variables in values as fixed.
Examples
Simple univariate model
julia> using Distributions
+
+julia> @model function demo()
+ m ~ Normal()
+ x ~ Normal(m, 1)
+ return (; m=m, x=x)
+ end
+demo (generic function with 2 methods)
+
+julia> model = demo();
+
+julia> m, x = model(); (m ≠ 1.0 && x ≠ 100.0)
+true
+
+julia> # Create a new instance which treats `x` as observed
+ # with value `100.0`, and similarly for `m=1.0`.
+ fixed_model = fix(model, x=100.0, m=1.0);
+
+julia> m, x = fixed_model(); (m == 1.0 && x == 100.0)
+true
+
+julia> # Let's only fix on `x = 100.0`.
+ fixed_model = fix(model, x = 100.0);
+
+julia> m, x = fixed_model(); (m ≠ 1.0 && x == 100.0)
+trueThe above uses a NamedTuple to hold the fixed variables, which allows us to perform some additional optimizations; in many cases, the above has zero runtime-overhead.
But we can also use a Dict, which offers more flexibility in the fixing (see examples further below) but generally has worse performance than the NamedTuple approach:
julia> fixed_model_dict = fix(model, Dict(@varname(x) => 100.0));
+
+julia> m, x = fixed_model_dict(); (m ≠ 1.0 && x == 100.0)
+true
+
+julia> # Alternative: pass `Pair{<:VarName}` as positional argument.
+ fixed_model_dict = fix(model, @varname(x) => 100.0, );
+
+julia> m, x = fixed_model_dict(); (m ≠ 1.0 && x == 100.0)
+trueFix only a part of a multivariate variable
We can not only fix multivariate random variables, but we can also use the standard mechanism of setting something to missing in the call to fix to only fix a part of the variable.
julia> @model function demo_mv(::Type{TV}=Float64) where {TV}
+ m = Vector{TV}(undef, 2)
+ m[1] ~ Normal()
+ m[2] ~ Normal()
+ return m
+ end
+demo_mv (generic function with 4 methods)
+
+julia> model = demo_mv();
+
+julia> fixed_model = fix(model, m = [missing, 1.0]);
+
+julia> # (✓) `m[1]` sampled while `m[2]` is fixed
+ m = fixed_model(); (m[1] ≠ 1.0 && m[2] == 1.0)
+trueIntuitively one might also expect to be able to write something like fix(model, var"m[1]" = 1.0, ). Unfortunately this is not supported as it has the potential of increasing compilation times but without offering any benefit with respect to runtime:
julia> # (×) `m[2]` is not set to 1.0.
+ m = fix(model, var"m[2]" = 1.0)(); m[2] == 1.0
+falseBut you can do this if you use a Dict as the underlying storage instead:
julia> # Alternative: `fix(model, Dict(@varname(m[2] => 1.0)))`
+ # (✓) `m[2]` is set to 1.0.
+ m = fix(model, @varname(m[2]) => 1.0)(); (m[1] ≠ 1.0 && m[2] == 1.0)
+trueNested models
fix of course also supports the use of nested models through the use of @submodel.
julia> @model demo_inner() = m ~ Normal()
+demo_inner (generic function with 2 methods)
+
+julia> @model function demo_outer()
+ @submodel m = demo_inner()
+ return m
+ end
+demo_outer (generic function with 2 methods)
+
+julia> model = demo_outer();
+
+julia> model() ≠ 1.0
+true
+
+julia> fixed_model = model | (m = 1.0, );
+
+julia> fixed_model()
+1.0But one needs to be careful when prefixing variables in the nested models:
julia> @model function demo_outer_prefix()
+ @submodel prefix="inner" m = demo_inner()
+ return m
+ end
+demo_outer_prefix (generic function with 2 methods)
+
+julia> # (×) This doesn't work now!
+ fixed_model = demo_outer_prefix() | (m = 1.0, );
+
+julia> fixed_model() == 1.0
+false
+
+julia> # (✓) `m` in `demo_inner` is referred to as `inner.m` internally, so we do:
+ fixed_model = demo_outer_prefix() | (var"inner.m" = 1.0, );
+
+julia> fixed_model()
+1.0
+
+julia> # Note that the above `var"..."` is just standard Julia syntax:
+ keys((var"inner.m" = 1.0, ))
+(Symbol("inner.m"),)And similarly when using Dict:
julia> fixed_model_dict = demo_outer_prefix() | (@varname(var"inner.m") => 1.0);
+
+julia> fixed_model_dict()
+1.0The difference is maybe more obvious once we look at how these different in their trace/VarInfo:
julia> keys(VarInfo(demo_outer()))
+1-element Vector{VarName{:m, typeof(identity)}}:
+ m
+
+julia> keys(VarInfo(demo_outer_prefix()))
+1-element Vector{VarName{Symbol("inner.m"), typeof(identity)}}:
+ inner.mFrom this we can tell what the correct way to fix m within demo_inner is in the two different models.
Difference from condition
A very similar functionality is also provided by condition which, not surprisingly, conditions variables instead of fixing them. The only difference between fixing and conditioning is as follows:
conditioned variables are considered to be observations, and are thus included in the computationlogjointandloglikelihood, but not inlogprior.fixed variables are considered to be constant, and are thus not included in any log-probability computations.
julia> @model function demo()
+ m ~ Normal()
+ x ~ Normal(m, 1)
+ return (; m=m, x=x)
+ end
+demo (generic function with 2 methods)
+
+julia> model = demo();
+
+julia> model_fixed = fix(model, m = 1.0);
+
+julia> model_conditioned = condition(model, m = 1.0);
+
+julia> logjoint(model_fixed, (x=1.0,))
+-0.9189385332046728
+
+julia> # Different!
+ logjoint(model_conditioned, (x=1.0,))
+-2.3378770664093453
+
+julia> # And the difference is the missing log-probability of `m`:
+ logjoint(model_fixed, (x=1.0,)) + logpdf(Normal(), 1.0) == logjoint(model_conditioned, (x=1.0,))
+truefix([context::AbstractContext,] values::NamedTuple)
+fix([context::AbstractContext]; values...)Return FixedContext with values and context if values is non-empty, otherwise return context which is DefaultContext by default.
See also: unfix
DynamicPPL.fixed — Functionfixed(model::Model)Return the fixed values in model.
Examples
julia> using Distributions
+
+julia> using DynamicPPL: fixed, contextualize
+
+julia> @model function demo()
+ m ~ Normal()
+ x ~ Normal(m, 1)
+ end
+demo (generic function with 2 methods)
+
+julia> m = demo();
+
+julia> # Returns all the variables we have fixed on + their values.
+ fixed(fix(m, x=100.0, m=1.0))
+(x = 100.0, m = 1.0)
+
+julia> # Nested ones also work (note that `PrefixContext` does nothing to the result).
+ cm = fix(contextualize(m, PrefixContext{:a}(fix(m=1.0))), x=100.0);
+
+julia> fixed(cm)
+(x = 100.0, m = 1.0)
+
+julia> # Since we fixed on `m`, not `a.m` as it will appear after prefixed,
+ # `a.m` is treated as a random variable.
+ keys(VarInfo(cm))
+1-element Vector{VarName{Symbol("a.m"), typeof(identity)}}:
+ a.m
+
+julia> # If we instead fix on `a.m`, `m` in the model will be considered an observation.
+ cm = fix(contextualize(m, PrefixContext{:a}(fix(var"a.m"=1.0))), x=100.0);
+
+julia> fixed(cm).x
+100.0
+
+julia> fixed(cm).var"a.m"
+1.0
+
+julia> keys(VarInfo(cm)) # <= no variables are sampled
+VarName[]fixed(context::AbstractContext)Return the values that are fixed under context.
Note that this will recursively traverse the context stack and return a merged version of the fix values.
The difference between fix and condition is described in the docstring of fix above.
Similarly, we can unfix variables, i.e. return them to their original meaning:
DynamicPPL.unfix — Functionunfix(model::Model)
+unfix(model::Model, variables...)Return a Model for which variables... are not considered fixed. If no variables are provided, then all variables currently considered fixed will no longer be.
This is essentially the inverse of fix. This also means that it suffers from the same limitiations.
Note that currently we only support variables to take on explicit values provided to fix.
Examples
julia> using Distributions
+
+julia> @model function demo()
+ m ~ Normal()
+ x ~ Normal(m, 1)
+ return (; m=m, x=x)
+ end
+demo (generic function with 2 methods)
+
+julia> fixed_model = fix(demo(), m = 1.0, x = 10.0);
+
+julia> fixed_model()
+(m = 1.0, x = 10.0)
+
+julia> # By specifying the `VarName` to `unfix`.
+ model = unfix(fixed_model, @varname(m));
+
+julia> (m, x) = model(); (m ≠ 1.0 && x == 10.0)
+true
+
+julia> # When `NamedTuple` is used as the underlying, you can also provide
+ # the symbol directly (though the `@varname` approach is preferable if
+ # if the variable is known at compile-time).
+ model = unfix(fixed_model, :m);
+
+julia> (m, x) = model(); (m ≠ 1.0 && x == 10.0)
+true
+
+julia> # `unfix` multiple at once:
+ (m, x) = unfix(model, :m, :x)(); (m ≠ 1.0 && x ≠ 10.0)
+true
+
+julia> # `unfix` without any symbols will `unfix` all variables.
+ (m, x) = unfix(model)(); (m ≠ 1.0 && x ≠ 10.0)
+true
+
+julia> # Usage of `Val` to perform `unfix` at compile-time if possible
+ # is also supported.
+ model = unfix(fixed_model, Val{:m}());
+
+julia> (m, x) = model(); (m ≠ 1.0 && x == 10.0)
+trueSimilarly when using a Dict:
julia> fixed_model_dict = fix(demo(), @varname(m) => 1.0, @varname(x) => 10.0);
+
+julia> fixed_model_dict()
+(m = 1.0, x = 10.0)
+
+julia> unfixed_model_dict = unfix(fixed_model_dict, @varname(m));
+
+julia> (m, x) = unfixed_model_dict(); m ≠ 1.0 && x == 10.0
+trueBut, as mentioned, unfix is only supported for variables explicitly provided to fix earlier:
julia> @model function demo_mv(::Type{TV}=Float64) where {TV}
+ m = Vector{TV}(undef, 2)
+ m[1] ~ Normal()
+ m[2] ~ Normal()
+ return m
+ end
+demo_mv (generic function with 4 methods)
+
+julia> model = demo_mv();
+
+julia> fixed_model = fix(model, @varname(m) => [1.0, 2.0]);
+
+julia> fixed_model()
+2-element Vector{Float64}:
+ 1.0
+ 2.0
+
+julia> unfixed_model = unfix(fixed_model, @varname(m[1]));
+
+julia> unfixed_model() # (×) `m[1]` is still fixed
+2-element Vector{Float64}:
+ 1.0
+ 2.0
+
+julia> # (✓) this works though
+ unfixed_model_2 = fix(unfixed_model, @varname(m[1]) => missing);
+
+julia> m = unfixed_model_2(); (m[1] ≠ 1.0 && m[2] == 2.0)
+trueunfix(context::AbstractContext, syms...)Return context but with syms no longer fixed.
Note that this recursively traverses contexts, unfixing all along the way.
See also: fix
Utilities
It is possible to manually increase (or decrease) the accumulated log density from within a model function.
DynamicPPL.@addlogprob! — Macro@addlogprob!(ex)Add the result of the evaluation of ex to the joint log probability.
Examples
This macro allows you to include arbitrary terms in the likelihood
julia> myloglikelihood(x, μ) = loglikelihood(Normal(μ, 1), x);
+
+julia> @model function demo(x)
+ μ ~ Normal()
+ @addlogprob! myloglikelihood(x, μ)
+ end;
+
+julia> x = [1.3, -2.1];
+
+julia> loglikelihood(demo(x), (μ=0.2,)) ≈ myloglikelihood(x, 0.2)
+trueand to reject samples:
julia> @model function demo(x)
+ m ~ MvNormal(zero(x), I)
+ if dot(m, x) < 0
+ @addlogprob! -Inf
+ # Exit the model evaluation early
+ return
+ end
+ x ~ MvNormal(m, I)
+ return
+ end;
+
+julia> logjoint(demo([-2.1]), (m=[0.2],)) == -Inf
+trueThe @addlogprob! macro increases the accumulated log probability regardless of the evaluation context, i.e., regardless of whether you evaluate the log prior, the log likelihood or the log joint density. If you would like to avoid this behaviour you should check the evaluation context. It can be accessed with the internal variable __context__. For instance, in the following example the log density is not accumulated when only the log prior is computed:
julia> myloglikelihood(x, μ) = loglikelihood(Normal(μ, 1), x);
+
+julia> @model function demo(x)
+ μ ~ Normal()
+ if DynamicPPL.leafcontext(__context__) !== PriorContext()
+ @addlogprob! myloglikelihood(x, μ)
+ end
+ end;
+
+julia> x = [1.3, -2.1];
+
+julia> logprior(demo(x), (μ=0.2,)) ≈ logpdf(Normal(), 0.2)
+true
+
+julia> loglikelihood(demo(x), (μ=0.2,)) ≈ myloglikelihood(x, 0.2)
+trueReturn values of the model function for a collection of samples can be obtained with generated_quantities.
DynamicPPL.generated_quantities — Functiongenerated_quantities(model::Model, chain::AbstractChains)Execute model for each of the samples in chain and return an array of the values returned by the model for each sample.
Examples
General
Often you might have additional quantities computed inside the model that you want to inspect, e.g.
@model function demo(x)
+ # sample and observe
+ θ ~ Prior()
+ x ~ Likelihood()
+ return interesting_quantity(θ, x)
+end
+m = demo(data)
+chain = sample(m, alg, n)
+# To inspect the `interesting_quantity(θ, x)` where `θ` is replaced by samples
+# from the posterior/`chain`:
+generated_quantities(m, chain) # <= results in a `Vector` of returned values
+ # from `interesting_quantity(θ, x)`Concrete (and simple)
julia> using DynamicPPL, Turing
+
+julia> @model function demo(xs)
+ s ~ InverseGamma(2, 3)
+ m_shifted ~ Normal(10, √s)
+ m = m_shifted - 10
+
+ for i in eachindex(xs)
+ xs[i] ~ Normal(m, √s)
+ end
+
+ return (m, )
+ end
+demo (generic function with 1 method)
+
+julia> model = demo(randn(10));
+
+julia> chain = sample(model, MH(), 10);
+
+julia> generated_quantities(model, chain)
+10×1 Array{Tuple{Float64},2}:
+ (2.1964758025119338,)
+ (2.1964758025119338,)
+ (0.09270081916291417,)
+ (0.09270081916291417,)
+ (0.09270081916291417,)
+ (0.09270081916291417,)
+ (0.09270081916291417,)
+ (0.043088571494005024,)
+ (-0.16489786710222099,)
+ (-0.16489786710222099,)generated_quantities(model::Model, parameters::NamedTuple)
+generated_quantities(model::Model, values, keys)
+generated_quantities(model::Model, values, keys)Execute model with variables keys set to values and return the values returned by the model.
If a NamedTuple is given, keys=keys(parameters) and values=values(parameters).
Example
julia> using DynamicPPL, Distributions
+
+julia> @model function demo(xs)
+ s ~ InverseGamma(2, 3)
+ m_shifted ~ Normal(10, √s)
+ m = m_shifted - 10
+ for i in eachindex(xs)
+ xs[i] ~ Normal(m, √s)
+ end
+ return (m, )
+ end
+demo (generic function with 2 methods)
+
+julia> model = demo(randn(10));
+
+julia> parameters = (; s = 1.0, m_shifted=10);
+
+julia> generated_quantities(model, parameters)
+(0.0,)
+
+julia> generated_quantities(model, values(parameters), keys(parameters))
+(0.0,)For a chain of samples, one can compute the pointwise log-likelihoods of each observed random variable with pointwise_loglikelihoods.
DynamicPPL.pointwise_loglikelihoods — Functionpointwise_loglikelihoods(model::Model, chain::Chains, keytype = String)Runs model on each sample in chain returning a OrderedDict{String, Matrix{Float64}} with keys corresponding to symbols of the observations, and values being matrices of shape (num_chains, num_samples).
keytype specifies what the type of the keys used in the returned OrderedDict are. Currently, only String and VarName are supported.
Notes
Say y is a Vector of n i.i.d. Normal(μ, σ) variables, with μ and σ both being <:Real. Then the observe (i.e. when the left-hand side is an observation) statements can be implemented in three ways:
- using a
forloop:
for i in eachindex(y)
+ y[i] ~ Normal(μ, σ)
+end- using
.~:
y .~ Normal(μ, σ)- using
MvNormal:
y ~ MvNormal(fill(μ, n), σ^2 * I)In (1) and (2), y will be treated as a collection of n i.i.d. 1-dimensional variables, while in (3) y will be treated as a single n-dimensional observation.
This is important to keep in mind, in particular if the computation is used for downstream computations.
Examples
From chain
julia> using DynamicPPL, Turing
+
+julia> @model function demo(xs, y)
+ s ~ InverseGamma(2, 3)
+ m ~ Normal(0, √s)
+ for i in eachindex(xs)
+ xs[i] ~ Normal(m, √s)
+ end
+
+ y ~ Normal(m, √s)
+ end
+demo (generic function with 1 method)
+
+julia> model = demo(randn(3), randn());
+
+julia> chain = sample(model, MH(), 10);
+
+julia> pointwise_loglikelihoods(model, chain)
+OrderedDict{String,Array{Float64,2}} with 4 entries:
+ "xs[1]" => [-1.42932; -2.68123; … ; -1.66333; -1.66333]
+ "xs[2]" => [-1.6724; -0.861339; … ; -1.62359; -1.62359]
+ "xs[3]" => [-1.42862; -2.67573; … ; -1.66251; -1.66251]
+ "y" => [-1.51265; -0.914129; … ; -1.5499; -1.5499]
+
+julia> pointwise_loglikelihoods(model, chain, String)
+OrderedDict{String,Array{Float64,2}} with 4 entries:
+ "xs[1]" => [-1.42932; -2.68123; … ; -1.66333; -1.66333]
+ "xs[2]" => [-1.6724; -0.861339; … ; -1.62359; -1.62359]
+ "xs[3]" => [-1.42862; -2.67573; … ; -1.66251; -1.66251]
+ "y" => [-1.51265; -0.914129; … ; -1.5499; -1.5499]
+
+julia> pointwise_loglikelihoods(model, chain, VarName)
+OrderedDict{VarName,Array{Float64,2}} with 4 entries:
+ xs[1] => [-1.42932; -2.68123; … ; -1.66333; -1.66333]
+ xs[2] => [-1.6724; -0.861339; … ; -1.62359; -1.62359]
+ xs[3] => [-1.42862; -2.67573; … ; -1.66251; -1.66251]
+ y => [-1.51265; -0.914129; … ; -1.5499; -1.5499]Broadcasting
Note that x .~ Dist() will treat x as a collection of independent observations rather than as a single observation.
julia> @model function demo(x)
+ x .~ Normal()
+ end;
+
+julia> m = demo([1.0, ]);
+
+julia> ℓ = pointwise_loglikelihoods(m, VarInfo(m)); first(ℓ[@varname(x[1])])
+-1.4189385332046727
+
+julia> m = demo([1.0; 1.0]);
+
+julia> ℓ = pointwise_loglikelihoods(m, VarInfo(m)); first.((ℓ[@varname(x[1])], ℓ[@varname(x[2])]))
+(-1.4189385332046727, -1.4189385332046727)For converting a chain into a format that can more easily be fed into a Model again, for example using condition, you can use value_iterator_from_chain.
DynamicPPL.value_iterator_from_chain — Functionvalue_iterator_from_chain(model::Model, chain)
+value_iterator_from_chain(varinfo::AbstractVarInfo, chain)Return an iterator over the values in chain for each variable in model/varinfo.
Example
julia> using MCMCChains, DynamicPPL, Distributions, StableRNGs
+
+julia> rng = StableRNG(42);
+
+julia> @model function demo_model(x)
+ s ~ InverseGamma(2, 3)
+ m ~ Normal(0, sqrt(s))
+ for i in eachindex(x)
+ x[i] ~ Normal(m, sqrt(s))
+ end
+
+ return s, m
+ end
+demo_model (generic function with 2 methods)
+
+julia> model = demo_model([1.0, 2.0]);
+
+julia> chain = Chains(rand(rng, 10, 2, 3), [:s, :m]);
+
+julia> iter = value_iterator_from_chain(model, chain);
+
+julia> first(iter)
+OrderedDict{VarName, Any} with 2 entries:
+ s => 0.580515
+ m => 0.739328
+
+julia> collect(iter)
+10×3 Matrix{OrderedDict{VarName, Any}}:
+ OrderedDict(s=>0.580515, m=>0.739328) … OrderedDict(s=>0.186047, m=>0.402423)
+ OrderedDict(s=>0.191241, m=>0.627342) OrderedDict(s=>0.776277, m=>0.166342)
+ OrderedDict(s=>0.971133, m=>0.637584) OrderedDict(s=>0.651655, m=>0.712044)
+ OrderedDict(s=>0.74345, m=>0.110359) OrderedDict(s=>0.469214, m=>0.104502)
+ OrderedDict(s=>0.170969, m=>0.598514) OrderedDict(s=>0.853546, m=>0.185399)
+ OrderedDict(s=>0.704776, m=>0.322111) … OrderedDict(s=>0.638301, m=>0.853802)
+ OrderedDict(s=>0.441044, m=>0.162285) OrderedDict(s=>0.852959, m=>0.0956922)
+ OrderedDict(s=>0.803972, m=>0.643369) OrderedDict(s=>0.245049, m=>0.871985)
+ OrderedDict(s=>0.772384, m=>0.646323) OrderedDict(s=>0.906603, m=>0.385502)
+ OrderedDict(s=>0.70882, m=>0.253105) OrderedDict(s=>0.413222, m=>0.953288)
+
+julia> # This can be used to `condition` a `Model`.
+ conditioned_model = model | first(iter);
+
+julia> conditioned_model() # <= results in same values as the `first(iter)` above
+(0.5805148626851955, 0.7393275279160691)Sometimes it can be useful to extract the priors of a model. This is the possible using extract_priors.
DynamicPPL.extract_priors — Functionextract_priors([rng::Random.AbstractRNG, ]model::Model)Extract the priors from a model.
This is done by sampling from the model and recording the distributions that are used to generate the samples.
Because the extraction is done by execution of the model, there are several caveats:
- If one variable, say,
y ~ Normal(0, x), wherex ~ Normal()is also a random variable, then the extracted prior will have different parameters in every extraction! - If the model does not have static support, say,
n ~ Categorical(1:10); x ~ MvNormmal(zeros(n), I), then the extracted priors themselves will be different between extractions, not just their parameters.
Both of these caveats are demonstrated below.
Examples
Changing parameters
julia> using Distributions, StableRNGs
+
+julia> rng = StableRNG(42);
+
+julia> @model function model_dynamic_parameters()
+ x ~ Normal(0, 1)
+ y ~ Normal(x, 1)
+ end;
+
+julia> model = model_dynamic_parameters();
+
+julia> extract_priors(rng, model)[@varname(y)]
+Normal{Float64}(μ=-0.6702516921145671, σ=1.0)
+
+julia> extract_priors(rng, model)[@varname(y)]
+Normal{Float64}(μ=1.3736306979834252, σ=1.0)Changing support
julia> using LinearAlgebra, Distributions, StableRNGs
+
+julia> rng = StableRNG(42);
+
+julia> @model function model_dynamic_support()
+ n ~ Categorical(ones(10) ./ 10)
+ x ~ MvNormal(zeros(n), I)
+ end;
+
+julia> model = model_dynamic_support();
+
+julia> length(extract_priors(rng, model)[@varname(x)])
+6
+
+julia> length(extract_priors(rng, model)[@varname(x)])
+9Safe extraction of values from a given AbstractVarInfo as they are seen in the model can be done using values_as_in_model.
DynamicPPL.values_as_in_model — Functionvalues_as_in_model(model::Model[, varinfo::AbstractVarInfo, context::AbstractContext])
+values_as_in_model(rng::Random.AbstractRNG, model::Model[, varinfo::AbstractVarInfo, context::AbstractContext])Get the values of varinfo as they would be seen in the model.
If no varinfo is provided, then this is effectively the same as Base.rand(rng::Random.AbstractRNG, model::Model).
More specifically, this method attempts to extract the realization as seen in the model. For example, x[1] ~ truncated(Normal(); lower=0) will result in a realization compatible with truncated(Normal(); lower=0) regardless of whether varinfo is working in unconstrained space.
Hence this method is a "safe" way of obtaining realizations in constrained space at the cost of additional model evaluations.
Arguments
model::Model: model to extract realizations from.varinfo::AbstractVarInfo: variable information to use for the extraction.context::AbstractContext: context to use for the extraction. Ifrngis specified, thencontextwill be wrapped in aSamplingContextwith the providedrng.
Examples
When VarInfo fails
The following demonstrates a common pitfall when working with VarInfo and constrained variables.
julia> using Distributions, StableRNGs
+
+julia> rng = StableRNG(42);
+
+julia> @model function model_changing_support()
+ x ~ Bernoulli(0.5)
+ y ~ x == 1 ? Uniform(0, 1) : Uniform(11, 12)
+ end;
+
+julia> model = model_changing_support();
+
+julia> # Construct initial type-stable `VarInfo`.
+ varinfo = VarInfo(rng, model);
+
+julia> # Link it so it works in unconstrained space.
+ varinfo_linked = DynamicPPL.link(varinfo, model);
+
+julia> # Perform computations in unconstrained space, e.g. changing the values of `θ`.
+ # Flip `x` so we hit the other support of `y`.
+ θ = [!varinfo[@varname(x)], rand(rng)];
+
+julia> # Update the `VarInfo` with the new values.
+ varinfo_linked = DynamicPPL.unflatten(varinfo_linked, θ);
+
+julia> # Determine the expected support of `y`.
+ lb, ub = θ[1] == 1 ? (0, 1) : (11, 12)
+(0, 1)
+
+julia> # Approach 1: Convert back to constrained space using `invlink` and extract.
+ varinfo_invlinked = DynamicPPL.invlink(varinfo_linked, model);
+
+julia> # (×) Fails! Because `VarInfo` _saves_ the original distributions
+ # used in the very first model evaluation, hence the support of `y`
+ # is not updated even though `x` has changed.
+ lb ≤ varinfo_invlinked[@varname(y)] ≤ ub
+false
+
+julia> # Approach 2: Extract realizations using `values_as_in_model`.
+ # (✓) `values_as_in_model` will re-run the model and extract
+ # the correct realization of `y` given the new values of `x`.
+ lb ≤ values_as_in_model(model, varinfo_linked)[@varname(y)] ≤ ub
+trueDynamicPPL.NamedDist — TypeA named distribution that carries the name of the random variable with it.
Testing Utilities
DynamicPPL provides several demo models and helpers for testing samplers in the DynamicPPL.TestUtils submodule.
DynamicPPL.TestUtils.test_sampler — Functiontest_sampler(models, sampler, args...; kwargs...)Test that sampler produces correct marginal posterior means on each model in models.
In short, this method iterates through models, calls AbstractMCMC.sample on the model and sampler to produce a chain, and then checks marginal_mean_of_samples(chain, vn) for every (leaf) varname vn against the corresponding value returned by posterior_mean for each model.
To change how comparison is done for a particular chain type, one can overload marginal_mean_of_samples for the corresponding type.
Arguments
models: A collection of instaces ofDynamicPPL.Modelto test on.sampler: TheAbstractMCMC.AbstractSamplerto test.args...: Arguments forwarded tosample.
Keyword arguments
varnames_filter: A filter to apply tovarnames(model), allowing comparison for only a subset of the varnames.atol=1e-1: Absolute tolerance used in@test.rtol=1e-3: Relative tolerance used in@test.kwargs...: Keyword arguments forwarded tosample.
DynamicPPL.TestUtils.test_sampler_on_demo_models — Functiontest_sampler_on_demo_models(meanfunction, sampler, args...; kwargs...)Test sampler on every model in DEMO_MODELS.
This is just a proxy for test_sampler(meanfunction, DEMO_MODELS, sampler, args...; kwargs...).
DynamicPPL.TestUtils.test_sampler_continuous — Functiontest_sampler_continuous(sampler, args...; kwargs...)Test that sampler produces the correct marginal posterior means on all models in demo_models.
As of right now, this is just an alias for test_sampler_on_demo_models.
DynamicPPL.TestUtils.marginal_mean_of_samples — Functionmarginal_mean_of_samples(chain, varname)Return the mean of variable represented by varname in chain.
DynamicPPL.TestUtils.DEMO_MODELS — ConstantA collection of models corresponding to the posterior distribution defined by the generative process
s ~ InverseGamma(2, 3)
+m ~ Normal(0, √s)
+1.5 ~ Normal(m, √s)
+2.0 ~ Normal(m, √s)or by
s[1] ~ InverseGamma(2, 3)
+s[2] ~ InverseGamma(2, 3)
+m[1] ~ Normal(0, √s)
+m[2] ~ Normal(0, √s)
+1.5 ~ Normal(m[1], √s[1])
+2.0 ~ Normal(m[2], √s[2])These are examples of a Normal-InverseGamma conjugate prior with Normal likelihood, for which the posterior is known in closed form.
In particular, for the univariate model (the former one):
mean(s) == 49 / 24
+mean(m) == 7 / 6And for the multivariate one (the latter one):
mean(s[1]) == 19 / 8
+mean(m[1]) == 3 / 4
+mean(s[2]) == 8 / 3
+mean(m[2]) == 1For every demo model, one can define the true log prior, log likelihood, and log joint probabilities.
DynamicPPL.TestUtils.logprior_true — Functionlogprior_true(model, args...)Return the logprior of model for args.
This should generally be implemented by hand for every specific model.
See also: logjoint_true, loglikelihood_true.
DynamicPPL.TestUtils.loglikelihood_true — Functionloglikelihood_true(model, args...)Return the loglikelihood of model for args.
This should generally be implemented by hand for every specific model.
See also: logjoint_true, logprior_true.
DynamicPPL.TestUtils.logjoint_true — Functionlogjoint_true(model, args...)Return the logjoint of model for args.
Defaults to logprior_true(model, args...) + loglikelihood_true(model, args..).
This should generally be implemented by hand for every specific model so that the returned value can be used as a ground-truth for testing things like:
- Validity of evaluation of
modelusing a particular implementation ofAbstractVarInfo. - Validity of a sampler when combined with DynamicPPL by running the sampler twice: once targeting ground-truth functions, e.g.
logjoint_true, and once targetingmodel.
And more.
See also: logprior_true, loglikelihood_true.
And in the case where the model includes constrained variables, it can also be useful to define
DynamicPPL.TestUtils.logprior_true_with_logabsdet_jacobian — Functionlogprior_true_with_logabsdet_jacobian(model::Model, args...)Return a tuple (args_unconstrained, logprior_unconstrained) of model for args....
Unlike logprior_true, the returned logprior computation includes the log-absdet-jacobian adjustment, thus computing logprior for the unconstrained variables.
Note that args are assumed be in the support of model, while args_unconstrained will be unconstrained.
See also: logprior_true.
DynamicPPL.TestUtils.logjoint_true_with_logabsdet_jacobian — Functionlogjoint_true_with_logabsdet_jacobian(model::Model, args...)Return a tuple (args_unconstrained, logjoint) of model for args.
Unlike logjoint_true, the returned logjoint computation includes the log-absdet-jacobian adjustment, thus computing logjoint for the unconstrained variables.
Note that args are assumed be in the support of model, while args_unconstrained will be unconstrained.
This should generally not be implemented directly, instead one should implement logprior_true_with_logabsdet_jacobian for a given model.
See also: logjoint_true, logprior_true_with_logabsdet_jacobian.
Finally, the following methods can also be of use:
DynamicPPL.TestUtils.varnames — Functionvarnames(model::Model)Return a collection of VarName as they are expected to appear in the model.
Even though it is recommended to implement this by hand for a particular Model, a default implementation using SimpleVarInfo{<:Dict} is provided.
DynamicPPL.TestUtils.posterior_mean — Functionposterior_mean(model::Model)Return a NamedTuple compatible with varnames(model) where the values represent the posterior mean under model.
"Compatible" means that a varname from varnames(model) can be used to extract the corresponding value using get, e.g. get(posterior_mean(model), varname).
DynamicPPL.TestUtils.setup_varinfos — Functionsetup_varinfos(model::Model, example_values::NamedTuple, varnames; include_threadsafe::Bool=false)Return a tuple of instances for different implementations of AbstractVarInfo with each vi, supposedly, satisfying vi[vn] == get(example_values, vn) for vn in varnames.
If include_threadsafe is true, then the returned tuple will also include thread-safe versions of the varinfo instances.
DynamicPPL.update_values!! — Functionupdate_values!!(vi::AbstractVarInfo, vals::NamedTuple, vns)Return instance similar to vi but with vns set to values from vals.
DynamicPPL.TestUtils.test_values — Functiontest_values(vi::AbstractVarInfo, vals::NamedTuple, vns)Test that vi[vn] corresponds to the correct value in vals for every vn in vns.
Debugging Utilities
DynamicPPL provides a few methods for checking validity of a model-definition.
DynamicPPL.DebugUtils.check_model — Functioncheck_model([rng, ]model::Model; kwargs...)Check that model is valid, warning about any potential issues.
See check_model_and_trace for more details on supported keword arguments and details of which types of checks are performed.
Returns
issuccess::Bool: Whether the model check succeeded.
DynamicPPL.DebugUtils.check_model_and_trace — Functioncheck_model_and_trace([rng, ]model::Model; kwargs...)Check that model is valid, warning about any potential issues.
This will check the model for the following issues:
- Repeated usage of the same varname in a model.
- Incorrectly treating a variable as random rather than fixed, and vice versa.
Arguments
rng::Random.AbstractRNG: The random number generator to use when evaluating the model.model::Model: The model to check.
Keyword Arguments
varinfo::VarInfo: The varinfo to use when evaluating the model. Default:VarInfo(model).context::AbstractContext: The context to use when evaluating the model. Default:DefaultContext.error_on_failure::Bool: Whether to throw an error if the model check fails. Default:false.
Returns
issuccess::Bool: Whether the model check succeeded.trace::Vector{Stmt}: The trace of statements executed during the model check.
Examples
Correct model
julia> using StableRNGs
+
+julia> rng = StableRNG(42);
+
+julia> @model demo_correct() = x ~ Normal()
+demo_correct (generic function with 2 methods)
+
+julia> issuccess, trace = check_model_and_trace(rng, demo_correct());
+
+julia> issuccess
+true
+
+julia> print(trace)
+ assume: x ~ Normal{Float64}(μ=0.0, σ=1.0) ⟼ -0.670252 (logprob = -1.14356)
+
+julia> issuccess, trace = check_model_and_trace(rng, demo_correct() | (x = 1.0,));
+
+julia> issuccess
+true
+
+julia> print(trace)
+observe: 1.0 ~ Normal{Float64}(μ=0.0, σ=1.0) (logprob = -1.41894)Incorrect model
julia> @model function demo_incorrect()
+ # (×) Sampling `x` twice will lead to incorrect log-probabilities!
+ x ~ Normal()
+ x ~ Exponential()
+ end
+demo_incorrect (generic function with 2 methods)
+
+julia> issuccess, trace = check_model_and_trace(rng, demo_incorrect(); error_on_failure=true);
+ERROR: varname x used multiple times in modelAnd some which might be useful to determine certain properties of the model based on the debug trace.
DynamicPPL.DebugUtils.has_static_constraints — Functionhas_static_constraints([rng, ]model::Model; num_evals=5, kwargs...)Return true if the model has static constraints, false otherwise.
Note that this is a heuristic check based on sampling from the model multiple times and checking if the model is consistent across runs.
Arguments
rng::Random.AbstractRNG: The random number generator to use when evaluating the model.model::Model: The model to check.
Keyword Arguments
num_evals::Int: The number of evaluations to perform. Default:5.kwargs...: Additional keyword arguments to pass tocheck_model_and_trace.
Advanced
Variable names
Names and possibly nested indices of variables are described with AbstractPPL.VarName. They can be defined with AbstractPPL.@varname. Please see the documentation of AbstractPPL.jl for further information.
Data Structures of Variables
DynamicPPL provides different data structures for samples from the model and their log density. All of them are subtypes of AbstractVarInfo.
DynamicPPL.AbstractVarInfo — TypeAbstractVarInfoAbstract supertype for data structures that capture random variables when executing a probabilistic model and accumulate log densities such as the log likelihood or the log joint probability of the model.
See also: VarInfo, SimpleVarInfo.
Common API
Accumulation of log-probabilities
DynamicPPL.getlogp — Functiongetlogp(vi::AbstractVarInfo)Return the log of the joint probability of the observed data and parameters sampled in vi.
DynamicPPL.setlogp!! — Functionsetlogp!!(vi::AbstractVarInfo, logp)Set the log of the joint probability of the observed data and parameters sampled in vi to logp, mutating if it makes sense.
DynamicPPL.acclogp!! — Functionacclogp!!([context::AbstractContext, ]vi::AbstractVarInfo, logp)Add logp to the value of the log of the joint probability of the observed data and parameters sampled in vi, mutating if it makes sense.
DynamicPPL.resetlogp!! — Functionresetlogp!!(vi::AbstractVarInfo)Reset the value of the log of the joint probability of the observed data and parameters sampled in vi to 0, mutating if it makes sense.
Variables and their realizations
Base.keys — Functionkeys(vi::AbstractVarInfo)Return an iterator over all vns in vi.
Base.getindex — Functiongetindex(vi::AbstractVarInfo, vn::VarName[, dist::Distribution])
+getindex(vi::AbstractVarInfo, vns::Vector{<:VarName}[, dist::Distribution])Return the current value(s) of vn (vns) in vi in the support of its (their) distribution(s).
If dist is specified, the value(s) will be reshaped accordingly.
See also: getindex_raw(vi::AbstractVarInfo, vn::VarName, dist::Distribution)
DynamicPPL.getindex_raw — Functiongetindex_raw(vi::AbstractVarInfo, vn::VarName[, dist::Distribution])
+getindex_raw(vi::AbstractVarInfo, vns::Vector{<:VarName}[, dist::Distribution])Return the current value(s) of vn (vns) in vi.
If dist is specified, the value(s) will be reshaped accordingly.
See also: getindex(vi::AbstractVarInfo, vn::VarName, dist::Distribution)
The difference between getindex(vi, vn, dist) and getindex_raw is that getindex will also transform the value(s) to the support of the distribution(s). This is not the case for getindex_raw.
BangBang.push!! — Functionpush!!(vi::AbstractVarInfo, vn::VarName, r, dist::Distribution)Push a new random variable vn with a sampled value r from a distribution dist to the VarInfo vi, mutating if it makes sense.
push!!(vi::AbstractVarInfo, vn::VarName, r, dist::Distribution, spl::AbstractSampler)Push a new random variable vn with a sampled value r sampled with a sampler spl from a distribution dist to VarInfo vi, if it makes sense.
The sampler is passed here to invalidate its cache where defined.
This method is considered legacy, and is likely to be deprecated in the future.
push!!(vi::AbstractVarInfo, vn::VarName, r, dist::Distribution, gid::Selector)Push a new random variable vn with a sampled value r sampled with a sampler of selector gid from a distribution dist to VarInfo vi.
This method is considered legacy, and is likely to be deprecated in the future.
BangBang.empty!! — Functionempty!!(vi::AbstractVarInfo)Empty the fields of vi.metadata and reset vi.logp[] and vi.num_produce[] to zeros.
This is useful when using a sampling algorithm that assumes an empty vi, e.g. SMC.
Base.isempty — Functionisempty(vi::AbstractVarInfo)Return true if vi is empty and false otherwise.
DynamicPPL.values_as — Functionvalues_as(varinfo[, Type])Return the values/realizations in varinfo as Type, if implemented.
If no Type is provided, return values as stored in varinfo.
Examples
SimpleVarInfo with NamedTuple:
julia> data = (x = 1.0, m = [2.0]);
+
+julia> values_as(SimpleVarInfo(data))
+(x = 1.0, m = [2.0])
+
+julia> values_as(SimpleVarInfo(data), NamedTuple)
+(x = 1.0, m = [2.0])
+
+julia> values_as(SimpleVarInfo(data), OrderedDict)
+OrderedDict{VarName{sym, typeof(identity)} where sym, Any} with 2 entries:
+ x => 1.0
+ m => [2.0]
+
+julia> values_as(SimpleVarInfo(data), Vector)
+2-element Vector{Float64}:
+ 1.0
+ 2.0SimpleVarInfo with OrderedDict:
julia> data = OrderedDict{Any,Any}(@varname(x) => 1.0, @varname(m) => [2.0]);
+
+julia> values_as(SimpleVarInfo(data))
+OrderedDict{Any, Any} with 2 entries:
+ x => 1.0
+ m => [2.0]
+
+julia> values_as(SimpleVarInfo(data), NamedTuple)
+(x = 1.0, m = [2.0])
+
+julia> values_as(SimpleVarInfo(data), OrderedDict)
+OrderedDict{Any, Any} with 2 entries:
+ x => 1.0
+ m => [2.0]
+
+julia> values_as(SimpleVarInfo(data), Vector)
+2-element Vector{Float64}:
+ 1.0
+ 2.0TypedVarInfo:
julia> # Just use an example model to construct the `VarInfo` because we're lazy.
+ vi = VarInfo(DynamicPPL.TestUtils.demo_assume_dot_observe());
+
+julia> vi[@varname(s)] = 1.0; vi[@varname(m)] = 2.0;
+
+julia> # For the sake of brevity, let's just check the type.
+ md = values_as(vi); md.s isa DynamicPPL.Metadata
+true
+
+julia> values_as(vi, NamedTuple)
+(s = 1.0, m = 2.0)
+
+julia> values_as(vi, OrderedDict)
+OrderedDict{VarName{sym, typeof(identity)} where sym, Float64} with 2 entries:
+ s => 1.0
+ m => 2.0
+
+julia> values_as(vi, Vector)
+2-element Vector{Float64}:
+ 1.0
+ 2.0UntypedVarInfo:
julia> # Just use an example model to construct the `VarInfo` because we're lazy.
+ vi = VarInfo(); DynamicPPL.TestUtils.demo_assume_dot_observe()(vi);
+
+julia> vi[@varname(s)] = 1.0; vi[@varname(m)] = 2.0;
+
+julia> # For the sake of brevity, let's just check the type.
+ values_as(vi) isa DynamicPPL.Metadata
+true
+
+julia> values_as(vi, NamedTuple)
+(s = 1.0, m = 2.0)
+
+julia> values_as(vi, OrderedDict)
+OrderedDict{VarName{sym, typeof(identity)} where sym, Float64} with 2 entries:
+ s => 1.0
+ m => 2.0
+
+julia> values_as(vi, Vector)
+2-element Vector{Real}:
+ 1.0
+ 2.0Transformations
DynamicPPL.AbstractTransformation — Typeabstract type AbstractTransformationRepresents a transformation to be used in link!! and invlink!!, amongst others.
A concrete implementation of this should implement the following methods:
link!!: transforms theAbstractVarInfoto the unconstrained space.invlink!!: transforms theAbstractVarInfoto the constrained space.
And potentially:
maybe_invlink_before_eval!!: hook to decide whether to transform before evaluating the model.
See also: link!!, invlink!!, maybe_invlink_before_eval!!.
DynamicPPL.NoTransformation — Typestruct NoTransformation <: DynamicPPL.AbstractTransformationTransformation which applies the identity function.
DynamicPPL.DynamicTransformation — Typestruct DynamicTransformation <: DynamicPPL.AbstractTransformationTransformation which transforms the variables on a per-need-basis in the execution of a given Model.
This is in constrast to StaticTransformation which transforms all variables before the execution of a given Model.
See also: StaticTransformation.
DynamicPPL.StaticTransformation — Typestruct StaticTransformation{F} <: DynamicPPL.AbstractTransformationTransformation which transforms all variables before the execution of a given Model.
This is done through the maybe_invlink_before_eval!! method.
See also: DynamicTransformation, maybe_invlink_before_eval!!.
Fields
bijector::Any: The function, assumed to implement theBijectorsinterface, to be applied to the variables
DynamicPPL.istrans — Functionistrans(vi::AbstractVarInfo[, vns::Union{VarName, AbstractVector{<:Varname}}])Return true if vi is working in unconstrained space, and false if vi is assuming realizations to be in support of the corresponding distributions.
If vns is provided, then only check if this/these varname(s) are transformed.
Not all implementations of AbstractVarInfo support transforming only a subset of the variables.
DynamicPPL.settrans!! — Functionsettrans!!(vi::AbstractVarInfo, trans::Bool[, vn::VarName])Return vi with istrans(vi, vn) evaluating to true.
If vn is not specified, then istrans(vi) evaluates to true for all variables.
DynamicPPL.transformation — Functiontransformation(vi::AbstractVarInfo)Return the AbstractTransformation related to vi.
Bijectors.link — Functionlink([t::AbstractTransformation, ]vi::AbstractVarInfo, model::Model)
+link([t::AbstractTransformation, ]vi::AbstractVarInfo, spl::AbstractSampler, model::Model)Transform the variables in vi to their linked space without mutating vi, using the transformation t.
If t is not provided, default_transformation(model, vi) will be used.
See also: default_transformation, invlink.
Bijectors.invlink — Functioninvlink([t::AbstractTransformation, ]vi::AbstractVarInfo, model::Model)
+invlink([t::AbstractTransformation, ]vi::AbstractVarInfo, spl::AbstractSampler, model::Model)Transform the variables in vi to their constrained space without mutating vi, using the (inverse of) transformation t.
If t is not provided, default_transformation(model, vi) will be used.
See also: default_transformation, link.
DynamicPPL.link!! — Functionlink!!([t::AbstractTransformation, ]vi::AbstractVarInfo, model::Model)
+link!!([t::AbstractTransformation, ]vi::AbstractVarInfo, spl::AbstractSampler, model::Model)Transform the variables in vi to their linked space, using the transformation t, mutating vi if possible.
If t is not provided, default_transformation(model, vi) will be used.
See also: default_transformation, invlink!!.
DynamicPPL.invlink!! — Functioninvlink!!([t::AbstractTransformation, ]vi::AbstractVarInfo, model::Model)
+invlink!!([t::AbstractTransformation, ]vi::AbstractVarInfo, spl::AbstractSampler, model::Model)Transform the variables in vi to their constrained space, using the (inverse of) transformation t, mutating vi if possible.
If t is not provided, default_transformation(model, vi) will be used.
See also: default_transformation, link!!.
DynamicPPL.default_transformation — Functiondefault_transformation(model::Model[, vi::AbstractVarInfo])Return the AbstractTransformation currently related to model and, potentially, vi.
DynamicPPL.maybe_invlink_before_eval!! — Functionmaybe_invlink_before_eval!!([t::Transformation,] vi, context, model)Return a possibly invlinked version of vi.
This will be called prior to model evaluation, allowing one to perform a single invlink!! before evaluation rather than lazyily evaluating the transforms on as-we-need basis as is done with DynamicTransformation.
See also: StaticTransformation, DynamicTransformation.
Examples
julia> using DynamicPPL, Distributions, Bijectors
+
+julia> @model demo() = x ~ Normal()
+demo (generic function with 2 methods)
+
+julia> # By subtyping `Transform`, we inherit the `(inv)link!!`.
+ struct MyBijector <: Bijectors.Transform end
+
+julia> # Define some dummy `inverse` which will be used in the `link!!` call.
+ Bijectors.inverse(f::MyBijector) = identity
+
+julia> # We need to define `with_logabsdet_jacobian` for `MyBijector`
+ # (`identity` already has `with_logabsdet_jacobian` defined)
+ function Bijectors.with_logabsdet_jacobian(::MyBijector, x)
+ # Just using a large number of the logabsdet-jacobian term
+ # for demonstration purposes.
+ return (x, 1000)
+ end
+
+julia> # Change the `default_transformation` for our model to be a
+ # `StaticTransformation` using `MyBijector`.
+ function DynamicPPL.default_transformation(::Model{typeof(demo)})
+ return DynamicPPL.StaticTransformation(MyBijector())
+ end
+
+julia> model = demo();
+
+julia> vi = SimpleVarInfo(x=1.0)
+SimpleVarInfo((x = 1.0,), 0.0)
+
+julia> # Uses the `inverse` of `MyBijector`, which we have defined as `identity`
+ vi_linked = link!!(vi, model)
+Transformed SimpleVarInfo((x = 1.0,), 0.0)
+
+julia> # Now performs a single `invlink!!` before model evaluation.
+ logjoint(model, vi_linked)
+-1001.4189385332047DynamicPPL.reconstruct — Functionreconstruct([f, ]dist, val)Reconstruct val so that it's compatible with dist.
If f is also provided, the reconstruct value will be such that f(reconstruct_val) is compatible with dist.
Utils
Base.merge — Methodmerge(varinfo, other_varinfos...)Merge varinfos into one, giving precedence to the right-most varinfo when sensible.
This is particularly useful when combined with subset(varinfo, vns).
See docstring of subset(varinfo, vns) for examples.
DynamicPPL.subset — Functionsubset(varinfo::AbstractVarInfo, vns::AbstractVector{<:VarName})Subset a varinfo to only contain the variables vns.
The ordering of the variables in the resulting varinfo is not guaranteed to follow the ordering of the variables in varinfo. Hence care must be taken, in particular when used in conjunction with other methods which uses the vector-representation of the varinfo, e.g. getindex(varinfo, sampler).
Examples
julia> @model function demo()
+ s ~ InverseGamma(2, 3)
+ m ~ Normal(0, sqrt(s))
+ x = Vector{Float64}(undef, 2)
+ x[1] ~ Normal(m, sqrt(s))
+ x[2] ~ Normal(m, sqrt(s))
+ end
+demo (generic function with 2 methods)
+
+julia> model = demo();
+
+julia> varinfo = VarInfo(model);
+
+julia> keys(varinfo)
+4-element Vector{VarName}:
+ s
+ m
+ x[1]
+ x[2]
+
+julia> for (i, vn) in enumerate(keys(varinfo))
+ varinfo[vn] = i
+ end
+
+julia> varinfo[[@varname(s), @varname(m), @varname(x[1]), @varname(x[2])]]
+4-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+
+julia> # Extract one with only `m`.
+ varinfo_subset1 = subset(varinfo, [@varname(m),]);
+
+
+julia> keys(varinfo_subset1)
+1-element Vector{VarName{:m, typeof(identity)}}:
+ m
+
+julia> varinfo_subset1[@varname(m)]
+2.0
+
+julia> # Extract one with both `s` and `x[2]`.
+ varinfo_subset2 = subset(varinfo, [@varname(s), @varname(x[2])]);
+
+julia> keys(varinfo_subset2)
+2-element Vector{VarName}:
+ s
+ x[2]
+
+julia> varinfo_subset2[[@varname(s), @varname(x[2])]]
+2-element Vector{Float64}:
+ 1.0
+ 4.0subset is particularly useful when combined with merge(varinfo::AbstractVarInfo)
julia> # Merge the two.
+ varinfo_subset_merged = merge(varinfo_subset1, varinfo_subset2);
+
+julia> keys(varinfo_subset_merged)
+3-element Vector{VarName}:
+ m
+ s
+ x[2]
+
+julia> varinfo_subset_merged[[@varname(s), @varname(m), @varname(x[2])]]
+3-element Vector{Float64}:
+ 1.0
+ 2.0
+ 4.0
+
+julia> # Merge the two with the original.
+ varinfo_merged = merge(varinfo, varinfo_subset_merged);
+
+julia> keys(varinfo_merged)
+4-element Vector{VarName}:
+ s
+ m
+ x[1]
+ x[2]
+
+julia> varinfo_merged[[@varname(s), @varname(m), @varname(x[1]), @varname(x[2])]]
+4-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0Notes
Type-stability
This function is only type-stable when vns contains only varnames with the same symbol. For exmaple, [@varname(m[1]), @varname(m[2])] will be type-stable, but [@varname(m[1]), @varname(x)] will not be.
DynamicPPL.unflatten — Functionunflatten(original, x::AbstractVector)Return instance of original constructed from x.
unflatten(vi::AbstractVarInfo[, context::AbstractContext], x::AbstractVector)Return a new instance of vi with the values of x assigned to the variables.
If context is provided, x is assumed to be realizations only for variables not filtered out by context.
DynamicPPL.varname_leaves — Functionvarname_leaves(vn::VarName, val)Return an iterator over all varnames that are represented by vn on val.
Examples
julia> using DynamicPPL: varname_leaves
+
+julia> foreach(println, varname_leaves(@varname(x), rand(2)))
+x[1]
+x[2]
+
+julia> foreach(println, varname_leaves(@varname(x[1:2]), rand(2)))
+x[1:2][1]
+x[1:2][2]
+
+julia> x = (y = 1, z = [[2.0], [3.0]]);
+
+julia> foreach(println, varname_leaves(@varname(x), x))
+x.y
+x.z[1][1]
+x.z[2][1]DynamicPPL.varname_and_value_leaves — Functionvarname_and_value_leaves(vn::VarName, val)Return an iterator over all varname-value pairs that are represented by vn on val.
Examples
julia> using DynamicPPL: varname_and_value_leaves
+
+julia> foreach(println, varname_and_value_leaves(@varname(x), 1:2))
+(x[1], 1)
+(x[2], 2)
+
+julia> foreach(println, varname_and_value_leaves(@varname(x[1:2]), 1:2))
+(x[1:2][1], 1)
+(x[1:2][2], 2)
+
+julia> x = (y = 1, z = [[2.0], [3.0]]);
+
+julia> foreach(println, varname_and_value_leaves(@varname(x), x))
+(x.y, 1)
+(x.z[1][1], 2.0)
+(x.z[2][1], 3.0)There are also some special handling for certain types:
julia> using LinearAlgebra
+
+julia> x = reshape(1:4, 2, 2);
+
+julia> # `LowerTriangular`
+ foreach(println, varname_and_value_leaves(@varname(x), LowerTriangular(x)))
+(x[1, 1], 1)
+(x[2, 1], 2)
+(x[2, 2], 4)
+
+julia> # `UpperTriangular`
+ foreach(println, varname_and_value_leaves(@varname(x), UpperTriangular(x)))
+(x[1, 1], 1)
+(x[1, 2], 3)
+(x[2, 2], 4)
+
+julia> # `Cholesky` with lower-triangular
+ foreach(println, varname_and_value_leaves(@varname(x), Cholesky([1.0 0.0; 0.0 1.0], 'L', 0)))
+(x.L[1, 1], 1.0)
+(x.L[2, 1], 0.0)
+(x.L[2, 2], 1.0)
+
+julia> # `Cholesky` with upper-triangular
+ foreach(println, varname_and_value_leaves(@varname(x), Cholesky([1.0 0.0; 0.0 1.0], 'U', 0)))
+(x.U[1, 1], 1.0)
+(x.U[1, 2], 0.0)
+(x.U[2, 2], 1.0)SimpleVarInfo
DynamicPPL.SimpleVarInfo — Typestruct SimpleVarInfo{NT, T, C<:DynamicPPL.AbstractTransformation} <: AbstractVarInfoA simple wrapper of the parameters with a logp field for accumulation of the logdensity.
Currently only implemented for NT<:NamedTuple and NT<:AbstractDict.
Fields
values: underlying representation of the realization representedlogp: holds the accumulated log-probabilitytransformation: represents whether it assumes variables to be transformed
Notes
The major differences between this and TypedVarInfo are:
SimpleVarInfodoes not require linearization.SimpleVarInfocan use more efficient bijectors.SimpleVarInfois only type-stable ifNT<:NamedTupleand either a) no indexing is used in tilde-statements, or b) the values have been specified with the correct shapes.
Examples
General usage
julia> using StableRNGs
+
+julia> @model function demo()
+ m ~ Normal()
+ x = Vector{Float64}(undef, 2)
+ for i in eachindex(x)
+ x[i] ~ Normal()
+ end
+ return x
+ end
+demo (generic function with 2 methods)
+
+julia> m = demo();
+
+julia> rng = StableRNG(42);
+
+julia> ### Sampling ###
+ ctx = SamplingContext(rng, SampleFromPrior(), DefaultContext());
+
+julia> # In the `NamedTuple` version we need to provide the place-holder values for
+ # the variables which are using "containers", e.g. `Array`.
+ # In this case, this means that we need to specify `x` but not `m`.
+ _, vi = DynamicPPL.evaluate!!(m, SimpleVarInfo((x = ones(2), )), ctx);
+
+julia> # (✓) Vroom, vroom! FAST!!!
+ vi[@varname(x[1])]
+0.4471218424633827
+
+julia> # We can also access arbitrary varnames pointing to `x`, e.g.
+ vi[@varname(x)]
+2-element Vector{Float64}:
+ 0.4471218424633827
+ 1.3736306979834252
+
+julia> vi[@varname(x[1:2])]
+2-element Vector{Float64}:
+ 0.4471218424633827
+ 1.3736306979834252
+
+julia> # (×) If we don't provide the container...
+ _, vi = DynamicPPL.evaluate!!(m, SimpleVarInfo(), ctx); vi
+ERROR: type NamedTuple has no field x
+[...]
+
+julia> # If one does not know the varnames, we can use a `OrderedDict` instead.
+ _, vi = DynamicPPL.evaluate!!(m, SimpleVarInfo{Float64}(OrderedDict()), ctx);
+
+julia> # (✓) Sort of fast, but only possible at runtime.
+ vi[@varname(x[1])]
+-1.019202452456547
+
+julia> # In addtion, we can only access varnames as they appear in the model!
+ vi[@varname(x)]
+ERROR: KeyError: key x not found
+[...]
+
+julia> vi[@varname(x[1:2])]
+ERROR: KeyError: key x[1:2] not found
+[...]Technically, it's possible to use any implementation of AbstractDict in place of OrderedDict, but OrderedDict ensures that certain operations, e.g. linearization/flattening of the values in the varinfo, are consistent between evaluations. Hence OrderedDict is the preferred implementation of AbstractDict to use here.
You can also sample in transformed space:
julia> @model demo_constrained() = x ~ Exponential()
+demo_constrained (generic function with 2 methods)
+
+julia> m = demo_constrained();
+
+julia> _, vi = DynamicPPL.evaluate!!(m, SimpleVarInfo(), ctx);
+
+julia> vi[@varname(x)] # (✓) 0 ≤ x < ∞
+1.8632965762164932
+
+julia> _, vi = DynamicPPL.evaluate!!(m, DynamicPPL.settrans!!(SimpleVarInfo(), true), ctx);
+
+julia> vi[@varname(x)] # (✓) -∞ < x < ∞
+-0.21080155351918753
+
+julia> xs = [last(DynamicPPL.evaluate!!(m, DynamicPPL.settrans!!(SimpleVarInfo(), true), ctx))[@varname(x)] for i = 1:10];
+
+julia> any(xs .< 0) # (✓) Positive probability mass on negative numbers!
+true
+
+julia> # And with `OrderedDict` of course!
+ _, vi = DynamicPPL.evaluate!!(m, DynamicPPL.settrans!!(SimpleVarInfo(OrderedDict()), true), ctx);
+
+julia> vi[@varname(x)] # (✓) -∞ < x < ∞
+0.6225185067787314
+
+julia> xs = [last(DynamicPPL.evaluate!!(m, DynamicPPL.settrans!!(SimpleVarInfo(), true), ctx))[@varname(x)] for i = 1:10];
+
+julia> any(xs .< 0) # (✓) Positive probability mass on negative numbers!
+trueEvaluation in transformed space of course also works:
julia> vi = DynamicPPL.settrans!!(SimpleVarInfo((x = -1.0,)), true)
+Transformed SimpleVarInfo((x = -1.0,), 0.0)
+
+julia> # (✓) Positive probability mass on negative numbers!
+ getlogp(last(DynamicPPL.evaluate!!(m, vi, DynamicPPL.DefaultContext())))
+-1.3678794411714423
+
+julia> # While if we forget to indicate that it's transformed:
+ vi = DynamicPPL.settrans!!(SimpleVarInfo((x = -1.0,)), false)
+SimpleVarInfo((x = -1.0,), 0.0)
+
+julia> # (✓) No probability mass on negative numbers!
+ getlogp(last(DynamicPPL.evaluate!!(m, vi, DynamicPPL.DefaultContext())))
+-InfIndexing
Using NamedTuple as underlying storage.
julia> svi_nt = SimpleVarInfo((m = (a = [1.0], ), ));
+
+julia> svi_nt[@varname(m)]
+(a = [1.0],)
+
+julia> svi_nt[@varname(m.a)]
+1-element Vector{Float64}:
+ 1.0
+
+julia> svi_nt[@varname(m.a[1])]
+1.0
+
+julia> svi_nt[@varname(m.a[2])]
+ERROR: BoundsError: attempt to access 1-element Vector{Float64} at index [2]
+[...]
+
+julia> svi_nt[@varname(m.b)]
+ERROR: type NamedTuple has no field b
+[...]Using OrderedDict as underlying storage.
julia> svi_dict = SimpleVarInfo(OrderedDict(@varname(m) => (a = [1.0], )));
+
+julia> svi_dict[@varname(m)]
+(a = [1.0],)
+
+julia> svi_dict[@varname(m.a)]
+1-element Vector{Float64}:
+ 1.0
+
+julia> svi_dict[@varname(m.a[1])]
+1.0
+
+julia> svi_dict[@varname(m.a[2])]
+ERROR: BoundsError: attempt to access 1-element Vector{Float64} at index [2]
+[...]
+
+julia> svi_dict[@varname(m.b)]
+ERROR: type NamedTuple has no field b
+[...]VarInfo
Another data structure is VarInfo.
DynamicPPL.VarInfo — Typestruct VarInfo{Tmeta, Tlogp} <: AbstractVarInfo
+ metadata::Tmeta
+ logp::Base.RefValue{Tlogp}
+ num_produce::Base.RefValue{Int}
+endA light wrapper over one or more instances of Metadata. Let vi be an instance of VarInfo. If vi isa VarInfo{<:Metadata}, then only one Metadata instance is used for all the sybmols. VarInfo{<:Metadata} is aliased UntypedVarInfo. If vi isa VarInfo{<:NamedTuple}, then vi.metadata is a NamedTuple that maps each symbol used on the LHS of ~ in the model to its Metadata instance. The latter allows for the type specialization of vi after the first sampling iteration when all the symbols have been observed. VarInfo{<:NamedTuple} is aliased TypedVarInfo.
Note: It is the user's responsibility to ensure that each "symbol" is visited at least once whenever the model is called, regardless of any stochastic branching. Each symbol refers to a Julia variable and can be a hierarchical array of many random variables, e.g. x[1] ~ ... and x[2] ~ ... both have the same symbol x.
DynamicPPL.TypedVarInfo — TypeTypedVarInfo(vi::UntypedVarInfo)This function finds all the unique syms from the instances of VarName{sym} found in vi.metadata.vns. It then extracts the metadata associated with each symbol from the global vi.metadata field. Finally, a new VarInfo is created with a new metadata as a NamedTuple mapping from symbols to type-stable Metadata instances, one for each symbol.
One main characteristic of VarInfo is that samples are stored in a linearized form.
DynamicPPL.link! — Functionlink!(vi::VarInfo, spl::Sampler)Transform the values of the random variables sampled by spl in vi from the support of their distributions to the Euclidean space and set their corresponding "trans" flag values to true.
DynamicPPL.invlink! — Functioninvlink!(vi::VarInfo, spl::AbstractSampler)Transform the values of the random variables sampled by spl in vi from the Euclidean space back to the support of their distributions and sets their corresponding "trans" flag values to false.
DynamicPPL.set_flag! — Functionset_flag!(vi::VarInfo, vn::VarName, flag::String)Set vn's value for flag to true in vi.
DynamicPPL.unset_flag! — Functionunset_flag!(vi::VarInfo, vn::VarName, flag::String)Set vn's value for flag to false in vi.
DynamicPPL.is_flagged — Functionis_flagged(vi::VarInfo, vn::VarName, flag::String)Check whether vn has a true value for flag in vi.
For Gibbs sampling the following functions were added.
DynamicPPL.setgid! — Functionsetgid!(vi::VarInfo, gid::Selector, vn::VarName)Add gid to the set of sampler selectors associated with vn in vi.
DynamicPPL.updategid! — Functionupdategid!(vi::VarInfo, vn::VarName, spl::Sampler)Set vn's gid to Set([spl.selector]), if vn does not have a sampler selector linked and vn's symbol is in the space of spl.
The following functions were used for sequential Monte Carlo methods.
DynamicPPL.get_num_produce — Functionget_num_produce(vi::VarInfo)Return the num_produce of vi.
DynamicPPL.set_num_produce! — Functionset_num_produce!(vi::VarInfo, n::Int)Set the num_produce field of vi to n.
DynamicPPL.increment_num_produce! — Functionincrement_num_produce!(vi::VarInfo)Add 1 to num_produce in vi.
DynamicPPL.reset_num_produce! — Functionreset_num_produce!(vi::VarInfo)Reset the value of num_produce the log of the joint probability of the observed data and parameters sampled in vi to 0.
DynamicPPL.setorder! — Functionsetorder!(vi::VarInfo, vn::VarName, index::Int)Set the order of vn in vi to index, where order is the number of observe statements run before samplingvn`.
DynamicPPL.set_retained_vns_del_by_spl! — Functionset_retained_vns_del_by_spl!(vi::VarInfo, spl::Sampler)Set the "del" flag of variables in vi with order > vi.num_produce[] to true.
Base.empty! — Functionempty!(meta::Metadata)Empty the fields of meta.
This is useful when using a sampling algorithm that assumes an empty meta, e.g. SMC.
Evaluation Contexts
Internally, both sampling and evaluation of log densities are performed with AbstractPPL.evaluate!!.
AbstractPPL.evaluate!! — Functionevaluate!!(model::Model[, rng, varinfo, sampler, context])Sample from the model using the sampler with random number generator rng and the context, and store the sample and log joint probability in varinfo.
Returns both the return-value of the original model, and the resulting varinfo.
The method resets the log joint probability of varinfo and increases the evaluation number of sampler.
The behaviour of a model execution can be changed with evaluation contexts that are passed as additional argument to the model function. Contexts are subtypes of AbstractPPL.AbstractContext.
DynamicPPL.SamplingContext — TypeSamplingContext(
+ [rng::Random.AbstractRNG=Random.default_rng()],
+ [sampler::AbstractSampler=SampleFromPrior()],
+ [context::AbstractContext=DefaultContext()],
+)Create a context that allows you to sample parameters with the sampler when running the model. The context determines how the returned log density is computed when running the model.
See also: DefaultContext, LikelihoodContext, PriorContext
DynamicPPL.DefaultContext — Typestruct DefaultContext <: AbstractContext endThe DefaultContext is used by default to compute log the joint probability of the data and parameters when running the model.
DynamicPPL.LikelihoodContext — Typestruct LikelihoodContext{Tvars} <: AbstractContext
+ vars::Tvars
+endThe LikelihoodContext enables the computation of the log likelihood of the parameters when running the model. vars can be used to evaluate the log likelihood for specific values of the model's parameters. If vars is nothing, the parameter values inside the VarInfo will be used by default.
DynamicPPL.PriorContext — Typestruct PriorContext{Tvars} <: AbstractContext
+ vars::Tvars
+endThe PriorContext enables the computation of the log prior of the parameters vars when running the model.
DynamicPPL.MiniBatchContext — Typestruct MiniBatchContext{Tctx, T} <: AbstractContext
+ context::Tctx
+ loglike_scalar::T
+endThe MiniBatchContext enables the computation of log(prior) + s * log(likelihood of a batch) when running the model, where s is the loglike_scalar field, typically equal to the number of data points / batch size. This is useful in batch-based stochastic gradient descent algorithms to be optimizing log(prior) + log(likelihood of all the data points) in the expectation.
DynamicPPL.PrefixContext — TypePrefixContext{Prefix}(context)Create a context that allows you to use the wrapped context when running the model and adds the Prefix to all parameters.
This context is useful in nested models to ensure that the names of the parameters are unique.
See also: @submodel
Samplers
In DynamicPPL two samplers are defined that are used to initialize unobserved random variables: SampleFromPrior which samples from the prior distribution, and SampleFromUniform which samples from a uniform distribution.
DynamicPPL.SampleFromPrior — TypeSampleFromPriorSampling algorithm that samples unobserved random variables from their prior distribution.
DynamicPPL.SampleFromUniform — TypeSampleFromUniformSampling algorithm that samples unobserved random variables from a uniform distribution.
References
Additionally, a generic sampler for inference is implemented.
DynamicPPL.Sampler — TypeSampler{T}Generic sampler type for inference algorithms of type T in DynamicPPL.
Sampler should implement the AbstractMCMC interface, and in particular AbstractMCMC.step. A default implementation of the initial sampling step is provided that supports resuming sampling from a previous state and setting initial parameter values. It requires to overload loadstate and initialstep for loading previous states and actually performing the initial sampling step, respectively. Additionally, sometimes one might want to implement initialsampler that specifies how the initial parameter values are sampled if they are not provided. By default, values are sampled from the prior.
The default implementation of Sampler uses the following unexported functions.
DynamicPPL.initialstep — Functioninitialstep(rng, model, sampler, varinfo; kwargs...)Perform the initial sampling step of the sampler for the model.
The varinfo contains the initial samples, which can be provided by the user or sampled randomly.
DynamicPPL.loadstate — Functionloadstate(data)Load sampler state from data.
By default, data is returned.
DynamicPPL.initialsampler — Functioninitialsampler(sampler::Sampler)Return the sampler that is used for generating the initial parameters when sampling with sampler.
By default, it returns an instance of SampleFromPrior.
Model-Internal Functions
DynamicPPL.tilde_assume — Functiontilde_assume(context::SamplingContext, right, vn, vi)Handle assumed variables, e.g., x ~ Normal() (where x does occur in the model inputs), accumulate the log probability, and return the sampled value with a context associated with a sampler.
Falls back to
tilde_assume(context.rng, context.context, context.sampler, right, vn, vi)DynamicPPL.dot_tilde_assume — Functiondot_tilde_assume(context::SamplingContext, right, left, vn, vi)Handle broadcasted assumed variables, e.g., x .~ MvNormal() (where x does not occur in the model inputs), accumulate the log probability, and return the sampled value for a context associated with a sampler.
Falls back to
dot_tilde_assume(context.rng, context.context, context.sampler, right, left, vn, vi)DynamicPPL.tilde_observe — Functiontilde_observe(context::SamplingContext, right, left, vi)Handle observed constants with a context associated with a sampler.
Falls back to tilde_observe(context.context, context.sampler, right, left, vi).
DynamicPPL.dot_tilde_observe — Functiondot_tilde_observe(context::SamplingContext, right, left, vi)Handle broadcasted observed constants, e.g., [1.0] .~ MvNormal(), accumulate the log probability, and return the observed value for a context associated with a sampler.
Falls back to dot_tilde_observe(context.context, context.sampler, right, left, vi).