simple-analysis-optimisation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt\n",
    "import optax\n",
    "from jaxopt import OptaxSolver\n",
    "import relaxed\n",
    "from celluloid import Camera\n",
    "from functools import partial\n",
    "import matplotlib.lines as mlines\n",
    "\n",
    "# matplotlib settings\n",
    "plt.rc(\"figure\", figsize=(6, 2), dpi=150, facecolor=\"w\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimising a simple one-bin analysis with a systematic using `relaxed`\n",
    "\n",
    "Let's define an analysis with a predicted number of signal and background events, with some uncertainty on the background estimate. We'll abstract the analysis configuration into a single parameter $\\phi$ like so:\n",
    "\n",
    "$$s = 15 + \\phi $$\n",
    "$$b = 45 - 2 \\phi $$\n",
    "$$\\sigma_b = 0.5 + 0.1*\\phi^2 $$\n",
    "\n",
    "Note that $s \\propto \\phi$ and $\\propto -2\\phi$, so increasing $\\phi$ corresponds to increasing the signal/backround ratio. However, our uncertainty scales like $\\phi^2$, so we're also going to compromise in our certainty of the background count as we do that. This kind of tradeoff between $s/b$ ratio and uncertainty is important for the discovery of a new signal, so we can't get away with optimising $s/b$ alone.\n",
    "\n",
    "To illustrate this, we'll plot the discovery significance for this model with and without uncertainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# model definition\n",
    "def yields(phi, uncertainty=True):\n",
    "    s = 15 + phi\n",
    "    b = 45 - 2 * phi\n",
    "    db = (\n",
    "        0.5 + 0.1 * phi**2 if uncertainty else jnp.zeros_like(phi) + 0.001\n",
    "    )  # small enough to be negligible\n",
    "    return jnp.asarray([s]), jnp.asarray([b]), jnp.asarray([db])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ce74eb5e02d147c6a0a00e5cf349ad9a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=7.5, description='$\\\\varphi$:', max=10.0, readout_format='.1f'), Outpu…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# just plotting code\n",
    "def yield_plot(phi):\n",
    "    s, b, db = yields(phi)\n",
    "    s, b, db = s.ravel(), b.ravel(), db.ravel()  # everything is [[x]] for pyhf\n",
    "    fig, ax = plt.subplots(figsize=[2,2])\n",
    "    ax.set_ylim((0, 80))\n",
    "    b1 = ax.bar(0.5, b, facecolor=\"C1\", label=\"b\")\n",
    "    b2 = ax.bar(0.5, s, bottom=b, facecolor=\"C9\", label=\"s\")\n",
    "    b3 = ax.bar(\n",
    "        0.5, db, bottom=b - db / 2, facecolor=\"k\", alpha=0.5, label=r\"$\\sigma_b$\"\n",
    "    )\n",
    "    ax.set_xlabel(\"single bin\")\n",
    "    ax.set_ylabel(\"yield\")\n",
    "    ax.set_xticks([])\n",
    "    ax.legend([b1, b2, b3], [\"b\", \"s\", r\"$\\sigma_b$\"], frameon=False, bbox_to_anchor=(1.04, 0.5), loc=\"center left\", borderaxespad=0)\n",
    "import ipywidgets as widgets\n",
    "\n",
    "slider = widgets.FloatSlider(\n",
    "    value=7.5,\n",
    "    min=0,\n",
    "    max=10.0,\n",
    "    step=0.1,\n",
    "    description=r'$\\varphi$:',\n",
    "    disabled=False,\n",
    "    continuous_update=True,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='.1f',\n",
    ")\n",
    "widgets.interactive(yield_plot, phi=slider)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing the discovery $p$-value using `relaxed`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# our analysis pipeline, from phi to p-value\n",
    "def pipeline(phi, return_yields=False, uncertainty=True):\n",
    "    \n",
    "    # grab the yields at the value of phi we want\n",
    "    y = yields(phi, uncertainty=uncertainty)\n",
    "    \n",
    "    # use a dummy version of pyhf for simplicity + compatibility with jax\n",
    "    model = relaxed.dummy_pyhf.uncorrelated_background(*y)\n",
    "    \n",
    "    # calculate expected discovery significance\n",
    "    nominal_pars = jnp.array([1.0, 1.0])  # sets gamma, mu =1 in gamma*b + mu*s\n",
    "    data = model.expected_data(nominal_pars)  # Asimov data\n",
    "    \n",
    "    # do the hypothesis test (and fit model pars with gradient descent)\n",
    "    pvalue = relaxed.infer.hypotest(\n",
    "        0.0,  # value of mu for the alternative hypothesis (background-only)\n",
    "        data,\n",
    "        model,\n",
    "        test_stat=\"q0\",  # discovery significance test\n",
    "        lr=1e-3,  # learning rate for the minimization loop\n",
    "        expected_pars=nominal_pars,  # optionally providing MLE pars in advance\n",
    "    )\n",
    "    if return_yields:\n",
    "        return pvalue, y\n",
    "    else:\n",
    "        return pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we're using proxies for functions we'd normally call using `pyhf` in order to substitute them for differentiable versions. There's an interesting point to make here that \"differentiable version\" does not always refer to \"differentiable surrogate\". The latter is things like `relaxed.cut`, `relaxed.hist` etc. -- which are by definition approximations to the operations they mimic -- but the former may just be something that is the same as the mimicked operation, but written using a framework for automatic differentiation (e.g. `jax`). That's the case for most of `relaxed.infer.hypotest`, but we are using a trick related to the differentiation of fixed points (like those exhibited by optimization loops) to speed up the gradient accumulation.\n",
    "\n",
    "Let's examine the result of the hypothesis test over a range of models (i.e. different values of $\\phi$), both with and without the background uncertainty component:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate p-values for a range of phi values\n",
    "phis = jnp.linspace(0, 10, 100)\n",
    "\n",
    "# with uncertainty\n",
    "pipe = partial(pipeline, return_yields=True, uncertainty=True)\n",
    "pvals, ys = jax.vmap(pipe)(phis)  # map over phi grid\n",
    "\n",
    "# without uncertainty\n",
    "pipe_no_uncertainty = partial(pipeline, uncertainty=False)\n",
    "pvals_no_uncertainty = jax.vmap(pipe_no_uncertainty)(phis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fig, axs = plt.subplots(2, 1, sharex=True, figsize=[4,4])\n",
    "fig, ax = plt.subplots()\n",
    "axs = [ax]\n",
    "axs[0].plot(phis, pvals, label=\"with uncertainty\", color=\"C2\")\n",
    "axs[0].plot(phis, pvals_no_uncertainty, label=\"no uncertainty\", color=\"C4\")\n",
    "axs[0].set_ylabel(\"$p$-value\")\n",
    "# plot vertical dotted line at minimum of p-values + s/b\n",
    "best_phi = phis[jnp.argmin(pvals)]\n",
    "axs[0].axvline(x=best_phi, linestyle=\"dotted\", color=\"C2\", label=\"optimal p-value\")\n",
    "axs[0].axvline(\n",
    "    x=phis[jnp.argmin(pvals_no_uncertainty)],\n",
    "    linestyle=\"dotted\",\n",
    "    color=\"C4\",\n",
    "    label=r\"optimal $s/b$\",\n",
    ")\n",
    "axs[0].legend(loc=\"upper left\", ncol=2)\n",
    "# s, b, db = ys\n",
    "# s, b, db = s.ravel(), b.ravel(), db.ravel()  # everything is [[x]] for pyhf\n",
    "# axs[1].fill_between(phis, s + b, b, color=\"C9\", label=\"signal\")\n",
    "# axs[1].fill_between(phis, b, color=\"C1\", label=\"background\")\n",
    "# axs[1].fill_between(phis, b - db, b + db, facecolor=\"k\", alpha=0.2, label=r\"$\\sigma_b$\")\n",
    "axs[0].set_xlabel(\"$\\phi$\")\n",
    "# axs[1].set_ylabel(\"yield\")\n",
    "# axs[1].legend(loc=\"lower left\")\n",
    "plt.suptitle(\"Discovery p-values, with and without uncertainty\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the different $p$-values significantly diverge as we increase the uncertainty of the background yield. Moreover, the $p$-value without incorporating uncertainty -- which would be the targeted objective if we used Asimov stat-only significance -- has a minimum value at $\\phi = 10$ that totally disregards the high uncertainty induced within the model.\n",
    "\n",
    "However, we can rescue this analysis if we make sure we include the uncertainty in the objective we optimize. Using gradient descent, we can optimise this analysis in an uncertainty-aware way by directly optimising $\\phi$ for the lowest discovery $p$-value. Here's how you do that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "our solution: phi=4.63643\n",
      "true optimum: phi=4.64646\n",
      "best s/b:     phi=10\n",
      "minimization took 1.989s\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "# The fast way!\n",
    "# let's use the OptaxSolver wrapper from jaxopt to perform the minimisation\n",
    "# set a couple of tolerance kwargs to make sure we don't stop too early\n",
    "solver = OptaxSolver(pipeline, opt=optax.adam(1e-3), tol=1e-8, maxiter=10000)\n",
    "pars = 9.0  # random init\n",
    "\n",
    "start = time.perf_counter()\n",
    "result = solver.run(pars).params\n",
    "end = time.perf_counter()\n",
    "\n",
    "print(\n",
    "    f\"our solution: phi={result:.5f}\\ntrue optimum: phi={phis[jnp.argmin(pvals)]:.5f}\\nbest s/b:     phi=10\"\n",
    ")\n",
    "print(f\"minimization took {end-start:.3f}s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 794x450 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The longer way (but with plots) -- takes a minute or two to run!\n",
    "pipe = partial(pipeline, return_yields=True, uncertainty=True)\n",
    "solver = OptaxSolver(pipe, opt=optax.adam(1e-1), has_aux=True)\n",
    "pars = 9.0\n",
    "state = solver.init_state(pars)  # we're doing init, update steps instead of .run()\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=[5.3,3])\n",
    "cam = Camera(fig)\n",
    "steps = 100  # increase me for better results! (100ish works well)\n",
    "for i in range(steps):\n",
    "    pars, state = solver.update(pars, state)\n",
    "    s, b, db = state.aux\n",
    "    val = state.value\n",
    "    ax = axs[0]\n",
    "    cv = ax.plot(phis, pvals, c=\"C0\")\n",
    "    cvs = ax.plot(phis, pvals_no_uncertainty, c=\"green\")\n",
    "    current = ax.scatter(pars, val, c=\"C0\")\n",
    "    ax.set_xlabel(r\"analysis config $\\phi$\")\n",
    "    ax.set_ylabel(\"p-value\")\n",
    "    ax.legend(\n",
    "        [\n",
    "            mlines.Line2D([], [], color=\"C0\"),\n",
    "            mlines.Line2D([], [], color=\"green\"),\n",
    "            current,\n",
    "        ],\n",
    "        [\"p-value (with uncert)\", \"p-value (without uncert)\", \"current value\"],\n",
    "        frameon=False,\n",
    "    )\n",
    "    ax.text(0.3, 0.31, f\"step {i}\", transform=ax.transAxes)\n",
    "    ax = axs[1]\n",
    "    ax.set_ylim((0, 80))\n",
    "    b1 = ax.bar(0.5, b, facecolor=\"C1\", label=\"b\")\n",
    "    b2 = ax.bar(0.5, s, bottom=b, facecolor=\"C9\", label=\"s\")\n",
    "    b3 = ax.bar(\n",
    "        0.5, db, bottom=b - db / 2, facecolor=\"k\", alpha=0.5, label=r\"$\\sigma_b$\"\n",
    "    )\n",
    "    ax.set_ylabel(\"yield\")\n",
    "    ax.set_xticks([])\n",
    "    ax.legend([b1, b2, b3], [\"b\", \"s\", r\"$\\sigma_b$\"], frameon=False)\n",
    "    plt.tight_layout()\n",
    "    cam.snap()\n",
    "\n",
    "ani = cam.animate()\n",
    "from IPython.display import HTML\n",
    "HTML(ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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