moses-scripts

Mapping MOSES models into the AtomSpace

This document contains suggestions to map models, their scores, and their features into AtomSpace hypergraphs.

Usage

scripts to import moses model csv files exported from R moses analyses here:

export_models_and_fitness.sh <MODEL_CSV_FILE> -o <OUTPUT_FILE>

to convert models and their scores into a scheme readily dumpable into the AtomSpace. column headers: "","Sensitivity","Pos Pred Value"

relate_features_and_genes.sh <FEATURE_CSV_FILE> -o <OUTPUT_FILE>

to generate scheme code to relate MOSES features and their corresponding genes. column headers: gene,Freq,level

Models

Models are exported in the following format

EquivalenceLink <1, 1>
  PredicateNode <MODEL_PREDICATE_NAME>
  <MODEL_BODY>

Features

We need to related GeneNodes <GENE_NAME>, used in the GO description, and PredicateNodes <GENE_NAME>, used in the MOSES models. For that I suggest to use the predicate "overexpressed" as follows:

EquivalenceLink <1, 1>
  PredicateNode <GENE_NAME>
  LambdaLink
    VariableNode "$X"
    EvaluationLink
      PredicateNode "overexpressed"
      ListLink
        GeneNode <GENE_NAME>
        VariableNode "$X"

which says that PredicateNode <GENE_NAME> over sample $X is equivalent to "GeneNode <GENE_NAME> is overexpressed in sample $X".

Fitnesses

I'm discussing 4 fitness scores:

1. Accuracy
2. Precision
3. Sensitivity/Recall
4. False Positive Rate

Let's assume we have the following predicates

1. A MOSES model, binary classifier

PredicateNode <MODEL>

2. The target feature, i.e. the real outcome

PredicateNode <OUTCOME>

3. The whole dataset, i.e. containing all inviduals under consideration

PredicateNode <DATA>

Given that we can easily translate the 4 scores into implication links involving combinations of these 4 predicates.

Precision

Precision translates directly into an Implication TV strength. that is

ImplicationLink <TV.strength = PRE, TV.count = POS>
  PredicateNode <MODEL>
  PredicateNode <OUTCOME>

Indeed, According to PLN (assuming all individuals are equiprobable)

TV.s = Sum_x min(p(x), q(x)) / Sum_x p(x)

where p is the indicator function associated to the predicate of a model, x runs over the individuals of the dataset.

This corresponds indeed to the precision

PRE = TP / (TP + FP) = TP / P

where

POS = TP + FP

the number of positive outcomes classified by the model.

One can see that Sum_x p(x) is indeed the number of positively classified individuals POS, and Sum_x min(p(x), q(x)) the number of correctly classified individuals, TP.

Recall

Similarly recall is easily translated into an Implication TV strength. that is

ImplicationLink <TV.strength = REC, TV.count = TRU>
  PredicateNode <OUTCOME>
  PredicateNode <MODEL>

given that

REC = TP / (TP + FN) = TP / TRU

where

TRU = TP + FN

is the number of actual true outcomes.

False Positive Rate

Likewise, the False Positive Rate is translated into the following Implication

ImplicationLink <TV.strength = FPR, TV.count = FAL>
  And
    PredicateNode <DATA>
    Not
      PredicateNode <OUTCOME>
  PredicateNode <MODEL>

given that

FPR = FP / (FP + TN) = FP / FAL

where

FAL = FP + TN

is the number of actual false outcomes.

Note the usage of PredicateNode <DATA> to guaranty that the negation of PredicateNode <OUTCOME> has the cardinality of FAL.

Accuracy

Accuracy also translates into an implication link

ImplicationLink <TV.strength = ACC, TV.count = TOT>
  PredicateNode <DATA>
  Or
    And
      PredicateNode <MODEL>
      PredicateNode <OUTCOME>
    And
      Not PredicateNode <MODEL>
      Not PredicateNode <OUTCOME>

with

ACC = (TP + TN) / (TRU + FAL) = (TP + TN) / TOT

where

TOT = TRU + FAL

is the total size of the population.

As one can see TP is the cardinality of

    And
      PredicateNode <MODEL>
      PredicateNode <OUTCOME>

and TN is the cardinality of

    And
      Not PredicateNode <MODEL>
      Not PredicateNode <OUTCOME>

Since these two sets are disjoint the cardinality of their union is TP + TN.