binning.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import annotations\n",
    "\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "from jax.random import PRNGKey\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import relaxed\n",
    "from jaxopt import OptaxSolver\n",
    "from optax import adam\n",
    "from functools import partial\n",
    "import jax.scipy as jsp\n",
    "from plothelp import autogrid\n",
    "import pyhf\n",
    "from celluloid import Camera\n",
    "\n",
    "pyhf.set_backend(\"jax\", default=True)\n",
    "\n",
    "# matplotlib settings\n",
    "plt.rc(\"figure\", figsize=(6, 2), dpi=150, facecolor=\"w\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binning optimisation with `relaxed` and gradient descent\n",
    "\n",
    "Normally, when we choose a binning, we pick something with uniform widths. It's easy, convenient, and can often aid in reasoning. However, if you wanted to squeeze every last drop of sensitivity out of an analysis, this binning (i.e. the location of the bin edges) can be further optimised for the best significance. That's what we'll be exploring below.\n",
    "\n",
    "To start, we'll generate some toy signal and background data to play with."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate background data from an exponential distribution with a little noise\n",
    "def generate_background(key, n_samples, n_features, noise_std):\n",
    "    key, subkey = jax.random.split(key, 2)\n",
    "    data = jax.random.exponential(subkey, (n_samples, n_features))\n",
    "    key, subkey = jax.random.split(key, 2)\n",
    "    data += jax.random.normal(subkey, (n_samples, n_features)) * noise_std\n",
    "    return data\n",
    "\n",
    "\n",
    "# generate signal data from a normal distribution close to the background\n",
    "def generate_signal(key, n_samples, n_features):\n",
    "    key, subkey = jax.random.split(key, 2)\n",
    "    data = jax.random.normal(subkey, (n_samples, n_features)) / 2 + 2\n",
    "    return data\n",
    "\n",
    "\n",
    "# get 1000 samples from the background and 100 samples from the signal\n",
    "bkg = generate_background(PRNGKey(0), 1000, 1, 0.1).ravel()\n",
    "sig = generate_signal(PRNGKey(1), 100, 1).ravel()\n",
    "\n",
    "plt.hist(\n",
    "    [bkg, sig], stacked=True, bins=30, histtype=\"step\", label=[\"background\", \"signal\"]\n",
    ")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we've just used an arbitrary binning for display purposes, but now we'll seek to find something more optimal. We can come up with a criteria for this using the infamous formula for median discovery significance in the case of known background:\n",
    "\n",
    "$$\n",
    "Z_A = 2 \\sum_{i=0}^{\\mathrm{num~bins-1}}(s_i + b_i)\\log(1 + s_i / b_i) - s_i\n",
    "$$\n",
    "\n",
    "We can then seek to minimise 1/$Z_A$ (since there are far more minimisation than maximisation routines) using gradient descent. One optimisation step will then involve constructing the histogram with our current binning, calculating the significance of that histogram, then updating the bin edges with the gradient of the significance. For the last step, we'll use the `jaxopt` library for minimisation, and the `adam` optimiser from `optax`.\n",
    "\n",
    "There is one important caveat though -- this workflow contains histograms, which are not a differentiable operation. To circumvent this issue, we'll be using `relaxed.hist`, which is a surrogate for the traditional histogram calculated via kernel density estimation. The main difference is that `relaxed.hist` has a parameter called the *bandwidth*, where lower bandwidth = less approximation [but more unstable gradients]. (see section 2.1 of https://arxiv.org/abs/2203.05570 for more info). Note that after optimisation, we'd use this binning for a true histogram, so we should calculate that significance too as our main performance measure.\n",
    "\n",
    "Below, we set this all up, then perform the optimisation!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# differentiable significance pipeline\n",
    "def asimov_pipe(bins, s, b, bandwidth=1e-2):\n",
    "    # restrict bin edges so they don't overlap during optimisation\n",
    "    bins_new = jnp.concatenate(\n",
    "        (\n",
    "            jnp.array([bins[0]]),\n",
    "            jnp.where(bins[1:] > bins[:-1], bins[1:], bins[:-1] + 1e-4),\n",
    "        ),\n",
    "        axis=0,\n",
    "    )\n",
    "    # make differentiable histograms for each dataset\n",
    "    s_hist = relaxed.hist(s, bins=bins_new, bandwidth=bandwidth) + 1e-4\n",
    "    b_hist = relaxed.hist(b, bins=bins_new, bandwidth=bandwidth) + 1e-4\n",
    "    # 1/significance because we want to minimise this function\n",
    "    return 1 / relaxed.metrics.asimov_sig(s_hist, b_hist)\n",
    "\n",
    "\n",
    "# significance with true histograms for comparison\n",
    "def hard_asimov_pipe(bins, s, b):\n",
    "    s_hist = jnp.histogram(s, bins=bins)[0] + 1e-4\n",
    "    b_hist = jnp.histogram(b, bins=bins)[0] + 1e-4\n",
    "    return relaxed.metrics.asimov_sig(s_hist, b_hist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# optimisation!\n",
    "def run(num_bins):\n",
    "    bins = jnp.linspace(0, 8, num_bins + 1)\n",
    "    loss = partial(asimov_pipe, s=sig, b=bkg, bandwidth=1e-1)\n",
    "    solver = OptaxSolver(loss, adam(learning_rate=1e-3), maxiter=10000, tol=1e-6)\n",
    "    opt = solver.run(bins).params\n",
    "    return opt\n",
    "\n",
    "\n",
    "# scan over a range of bin numbers to find the best significance\n",
    "bin_number_range_to_scan = [2, 4, 6, 8]  # add more bins here as you like\n",
    "results = [run(i) for i in bin_number_range_to_scan]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x240 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib as mpl\n",
    "\n",
    "\n",
    "def plot_bins(ax, bins_opt, i, title=True) -> None:\n",
    "    a = ax.hist(\n",
    "        [bkg, sig],\n",
    "        stacked=True,\n",
    "        bins=bins_opt,\n",
    "        histtype=\"step\",\n",
    "        label=[\"background\", \"signal\"],\n",
    "        color=[\"C0\", \"C1\"],\n",
    "    )\n",
    "    handles = [\n",
    "        mpl.patches.Patch(edgecolor=\"C0\", facecolor=\"w\", label=\"background\"),\n",
    "        mpl.patches.Patch(edgecolor=\"C1\", facecolor=\"w\", label=\"signal\"),\n",
    "    ]\n",
    "    labels = [\"background\", \"signal\"]\n",
    "    # add legend\n",
    "    ax.legend(handles, labels, loc=\"upper right\")\n",
    "    significance = hard_asimov_pipe(bins_opt, sig, bkg)\n",
    "    if title:\n",
    "        ax.set_title(f\"#bins={len(bins_opt)-1}, sig={significance:.3f}\")\n",
    "    else:\n",
    "        ax.text(\n",
    "            0.6,\n",
    "            0.45,\n",
    "            f\"#bins={len(bins_opt)-1}, significance={significance:.3f}\",\n",
    "            ha=\"center\",\n",
    "            va=\"center\",\n",
    "            transform=ax.transAxes,\n",
    "        )\n",
    "\n",
    "\n",
    "# plot helper function I wrote for automatic grids\n",
    "# see github.com/phinate/plothelp\n",
    "_ = autogrid(\n",
    "    data=results,\n",
    "    subplot_kwargs={\"sharex\": True, \"sharey\": True},\n",
    "    plot_func=plot_bins,\n",
    "    title=\"optimised bins (stat-only)\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the same calculation, but producing an animation of how the bin edges (and significance) change during training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/phinate/code/examples/venv/lib/python3.9/site-packages/matplotlib/animation.py:887: UserWarning: Animation was deleted without rendering anything. This is most likely not intended. To prevent deletion, assign the Animation to a variable, e.g. `anim`, that exists until you have outputted the Animation using `plt.show()` or `anim.save()`.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
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       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 750x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_bins = 5\n",
    "pars = jnp.linspace(0, 8, num_bins + 1)\n",
    "\n",
    "# differentiable significance pipeline\n",
    "def asimov_pipe(bins, s, b, bandwidth=1e-2):\n",
    "    # restrict bin edges so they don't overlap during optimisation\n",
    "    bins_new = jnp.concatenate(\n",
    "        (\n",
    "            jnp.array([bins[0]]),\n",
    "            jnp.where(bins[1:] > bins[:-1], bins[1:], bins[:-1] + 1e-4),\n",
    "        ),\n",
    "        axis=0,\n",
    "    )\n",
    "    # make differentiable histograms for each dataset\n",
    "    s_hist = relaxed.hist(s, bins=bins_new, bandwidth=bandwidth) + 1e-4\n",
    "    b_hist = relaxed.hist(b, bins=bins_new, bandwidth=bandwidth) + 1e-4\n",
    "\n",
    "    # 1/significance because we want to minimise this function\n",
    "    return 1 / relaxed.metrics.asimov_sig(s_hist, b_hist)\n",
    "\n",
    "\n",
    "loss = partial(asimov_pipe, s=sig, b=bkg, bandwidth=1e-1)\n",
    "solver = OptaxSolver(loss, adam(learning_rate=5e-3), maxiter=10000, tol=1e-6)\n",
    "state = solver.init_state(pars)  # we're doing init, update steps instead of .run()\n",
    "\n",
    "fig, ax = plt.subplots(figsize=[5,2])\n",
    "cam = Camera(fig)\n",
    "steps = 200  # increase me for better results! (100ish works well)\n",
    "for i in range(steps):\n",
    "    pars, state = solver.update(pars, state)\n",
    "    s_hist = jnp.histogram(sig, bins=pars)[0] + 1e-4\n",
    "    b_hist = jnp.histogram(bkg, bins=pars)[0] + 1e-4\n",
    "    significance = relaxed.metrics.asimov_sig(s_hist, b_hist)\n",
    "    plot_bins(ax, pars, 0, False)\n",
    "    cam.snap()\n",
    "\n",
    "ani = cam.animate()\n",
    "from IPython.display import HTML\n",
    "HTML(ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Systematic-aware binning (prototype)\n",
    "\n",
    "The above code concerns the problem of optimising with known background. A more realistic scenario would be that we have some kind of uncertainty on this background, which would strongly affect the significance if it isn't negligible.\n",
    "\n",
    "Not to worry -- we can still optimise while accounting for this uncertainty! The issue is that we're now forced to describe in detail our statistical modelling step, as this will let us calculate the significance in a way that includes the treatment of nuisance parameters that model the background uncertainty.\n",
    "\n",
    "We'll look at the case of a simple three-point systematic, which contains a nominal estimation of the background histogram at the best estimate of some physical parameter, e.g. the jet energy scale (JES), but also two variations of the background that correspond to simulating physics at+-1 standard deviations away from that estimate. Here, we're just going to transpose the background data to the right and the left by a shift value.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "shift = 0.4\n",
    "bup = bkg + shift\n",
    "bdown = bkg - shift\n",
    "\n",
    "from copy import deepcopy\n",
    "\n",
    "# specify the workspace for a simple model with a three-point background systematic\n",
    "def correlated_background(signal, bkg, bkg_up, bkg_down):\n",
    "    spec = {\n",
    "        \"channels\": [\n",
    "            {\n",
    "                \"name\": \"single_channel\",\n",
    "                \"samples\": [\n",
    "                    {\n",
    "                        \"name\": \"signal\",\n",
    "                        \"data\": signal,\n",
    "                        \"modifiers\": [\n",
    "                            {\"name\": \"mu\", \"type\": \"normfactor\", \"data\": None}\n",
    "                        ],\n",
    "                    },\n",
    "                    {\n",
    "                        \"name\": \"background\",\n",
    "                        \"data\": bkg,\n",
    "                        \"modifiers\": [\n",
    "                            {\n",
    "                                \"name\": \"correlated_bkg_uncertainty\",\n",
    "                                \"type\": \"histosys\",\n",
    "                                \"data\": {\"hi_data\": bkg_up, \"lo_data\": bkg_down},\n",
    "                            }\n",
    "                        ],\n",
    "                    },\n",
    "                ],\n",
    "            }\n",
    "        ]\n",
    "    }\n",
    "    return pyhf.Model(\n",
    "        spec, validate=False\n",
    "    )  # false validation enables the use of jax arrays\n",
    "\n",
    "\n",
    "from pyhf import interpolators\n",
    "\n",
    "# pipeline to calculate the full CLs for the model, given a number of bins\n",
    "def pipe(num_bins):\n",
    "    def cls_pipe(bins, s, b, bup, bdown, bandwidth=1e-2, skeleton_model=None):\n",
    "        # restrict bin edges so they don't overlap\n",
    "        bins_new = jnp.concatenate(\n",
    "            (\n",
    "                jnp.array([bins[0]]),\n",
    "                jnp.where(bins[1:] > bins[:-1], bins[1:], bins[:-1] + 1e-3),\n",
    "            ),\n",
    "            axis=0,\n",
    "        )\n",
    "        # make differentiable histograms for each dataset\n",
    "        s_hist = relaxed.hist(s, bins=bins_new, bandwidth=bandwidth) + 1e-4\n",
    "        b_hist = relaxed.hist(b, bins=bins_new, bandwidth=bandwidth) + 1e-4\n",
    "        bup_hist = relaxed.hist(bup, bins=bins_new, bandwidth=bandwidth) + 1e-4\n",
    "        bdown_hist = relaxed.hist(bdown, bins=bins_new, bandwidth=bandwidth) + 1e-4\n",
    "\n",
    "        # we hack our new values into the model since we already have the structure\n",
    "        # NB: this only approximates the model (there's other metadata to edit somewhere)\n",
    "        # but it's good enough for a loose optimisation, and it's super fast!\n",
    "        # make a dummy model with unit yields\n",
    "        model = deepcopy(skeleton_model)\n",
    "        interpcode = model.main_model.modifiers_appliers[\"histosys\"].interpcode\n",
    "\n",
    "        def update_model(new_nominal, new_histoset):\n",
    "            model.main_model.nominal_rates = new_nominal\n",
    "            interpolator = getattr(interpolators, interpcode)(new_histoset)\n",
    "            model.main_model.modifiers_appliers[\"histosys\"].interpolator = interpolator\n",
    "\n",
    "        nominal_rates = jnp.stack([b_hist, s_hist]).reshape(\n",
    "            model.main_model.nominal_rates.shape\n",
    "        )\n",
    "        histoset = [[[bdown_hist, b_hist, bup_hist], [s_hist] * 3]]\n",
    "\n",
    "        update_model(nominal_rates, histoset)\n",
    "        # differentiabe cls calculation\n",
    "        nominal = (\n",
    "            jnp.array(model.config.suggested_init()).at[model.config.poi_index].set(0.0)\n",
    "        )\n",
    "        data = model.expected_data(nominal)\n",
    "        pval = relaxed.infer.hypotest(\n",
    "            1, lr=1e-3, model=model, data=data, test_stat=\"q\", expected_pars=nominal\n",
    "        )\n",
    "        return pval\n",
    "\n",
    "    return cls_pipe\n",
    "\n",
    "\n",
    "# use true histograms to calculate the CLs for a given binning\n",
    "def pipe_uncert_hard(bins, s, b):\n",
    "    s_hist = jnp.histogram(s, bins=bins)[0] + 1e-4\n",
    "    b_hist = jnp.histogram(b, bins=bins)[0] + 1e-4\n",
    "    bup_hist = jnp.histogram(bup, bins=bins)[0] + 1e-4\n",
    "    bdown_hist = jnp.histogram(bdown, bins=bins)[0] + 1e-4\n",
    "    uncert = jnp.abs(bup_hist - bdown_hist) + 1e-4\n",
    "    model = correlated_background(s_hist, b_hist, bup_hist, bdown_hist)\n",
    "    nominal = model.config.suggested_init()\n",
    "    data = model.expected_data(nominal)\n",
    "    pval = pyhf.infer.hypotest(0, pdf=model, data=data, test_stat=\"q0\")\n",
    "    return jsp.stats.norm.ppf(1 - pval), [s_hist, b_hist, uncert]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/phinate/code/relaxed/venv/lib/python3.9/site-packages/jax/_src/tree_util.py:188: FutureWarning: jax.tree_util.tree_multimap() is deprecated. Please use jax.tree_util.tree_map() instead as a drop-in replacement.\n",
      "  warnings.warn('jax.tree_util.tree_multimap() is deprecated. Please use jax.tree_util.tree_map() '\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(DeviceArray(0.00171969, dtype=float64),\n",
       " DeviceArray([-0.00830832,  0.01676664, -0.00397049,  0.00054664,\n",
       "               0.        ], dtype=float64))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bins = jnp.linspace(0, 8, num_bins + 1)\n",
    "cls_pipe = pipe(num_bins)\n",
    "loss = partial(\n",
    "    cls_pipe,\n",
    "    s=sig,\n",
    "    b=bkg,\n",
    "    bup=bup,\n",
    "    bdown=bdown,\n",
    "    bandwidth=1e-2,\n",
    "    skeleton_model=correlated_background(*[jnp.ones(num_bins)] * 4),\n",
    ")\n",
    "jax.value_and_grad(loss)(bins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/phinate/code/relaxed/venv/lib/python3.9/site-packages/jax/_src/tree_util.py:188: FutureWarning: jax.tree_util.tree_multimap() is deprecated. Please use jax.tree_util.tree_map() instead as a drop-in replacement.\n",
      "  warnings.warn('jax.tree_util.tree_multimap() is deprecated. Please use jax.tree_util.tree_map() '\n"
     ]
    }
   ],
   "source": [
    "# optimisation!\n",
    "def run_uncert(num_bins):\n",
    "    bins = jnp.linspace(0, 8, num_bins + 1)\n",
    "    cls_pipe = pipe(num_bins)\n",
    "    skeleton = correlated_background(*[jnp.ones(num_bins)] * 4)\n",
    "    loss = partial(\n",
    "        cls_pipe,\n",
    "        s=sig,\n",
    "        b=bkg,\n",
    "        bup=bup,\n",
    "        bdown=bdown,\n",
    "        bandwidth=1e-2,\n",
    "        skeleton_model=skeleton,\n",
    "    )\n",
    "    solver = OptaxSolver(\n",
    "        loss, adam(learning_rate=1e-3), maxiter=10000, tol=1e-6, jit=True\n",
    "    )\n",
    "    opt = solver.run(bins).params\n",
    "    return opt  # , pipe_uncert_hard(opt, sig, bkg)\n",
    "\n",
    "\n",
    "# slower than before, since we're doing a full CLs calculation\n",
    "bin_number_range_to_scan = [2, 3, 6]  # add more bins here as you like\n",
    "many = [run_uncert(i) for i in bin_number_range_to_scan]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x240 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_bins(ax, bins_opt, i) -> None:\n",
    "    ax.hist(\n",
    "        [bkg, sig],\n",
    "        stacked=True,\n",
    "        bins=bins_opt,\n",
    "        histtype=\"step\",\n",
    "        label=[\"background\", \"signal\"],\n",
    "    )\n",
    "    ax.hist(\n",
    "        bdown.tolist(),\n",
    "        bins=bins_opt,\n",
    "        histtype=\"step\",\n",
    "        label=\"bdown\",\n",
    "        alpha=0.5,\n",
    "        linestyle=\"--\",\n",
    "    )\n",
    "    ax.hist(\n",
    "        bup.tolist(),\n",
    "        bins=bins_opt,\n",
    "        histtype=\"step\",\n",
    "        label=\"bup\",\n",
    "        alpha=0.5,\n",
    "        linestyle=\"--\",\n",
    "    )\n",
    "    ax.legend()\n",
    "    significance, _ = pipe_uncert_hard(bins_opt, sig, bkg)\n",
    "    ax.set_title(f\"#bins={len(bins_opt)-1}, sig={significance:.3f}\")\n",
    "\n",
    "\n",
    "_ = autogrid(\n",
    "    data=many,\n",
    "    subplot_kwargs={\"sharex\": True, \"sharey\": True},\n",
    "    plot_func=plot_bins,\n",
    "    title=\"optimised bins (including systematic uncertainty)\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x240 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# comparison to stat-only:\n",
    "_ = autogrid(\n",
    "    data=results,\n",
    "    subplot_kwargs={\"sharex\": True, \"sharey\": True},\n",
    "    plot_func=plot_bins,\n",
    "    title=\"optimised bins\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/phinate/code/relaxed/venv/lib/python3.9/site-packages/jax/_src/tree_util.py:188: FutureWarning: jax.tree_util.tree_multimap() is deprecated. Please use jax.tree_util.tree_map() instead as a drop-in replacement.\n",
      "  warnings.warn('jax.tree_util.tree_multimap() is deprecated. Please use jax.tree_util.tree_map() '\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "DeviceArray(0.00130859, dtype=float64)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class A:\n",
    "    x: float\n",
    "    y: float\n",
    "\n",
    "    def __init__(self, x, y):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "\n",
    "    def logpdf(self):\n",
    "        return self.x**2 + self.y * 2\n",
    "\n",
    "\n",
    "model = A(1, 2)\n",
    "\n",
    "\n",
    "def function(pars):\n",
    "    a, b = pars\n",
    "    model.x = a\n",
    "    model.y = b\n",
    "    return abs(model.logpdf() - 5)\n",
    "\n",
    "\n",
    "solver = OptaxSolver(\n",
    "    function, adam(learning_rate=1e-2), maxiter=10000, tol=1e-6, jit=True\n",
    ")\n",
    "function(solver.run((3.0, 4.0)).params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "22d6333b89854cd01c2018f3ca2f5a59a2cde2765fbca789ff36cfad48ca629b"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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