nb07-advi.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "05080d5f-640d-4a95-bba4-f0dadda33ce5",
   "metadata": {},
   "source": [
    "# `nb07`: Variational inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "493ac96c-00ac-4587-a2f6-d0dbf59eb703",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import jax.scipy as jsc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fe3855f7-12b8-40be-9131-1060fa96e542",
   "metadata": {},
   "outputs": [],
   "source": [
    "import wandb\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f2a306b-c9a5-478c-bfe1-ee061702441f",
   "metadata": {},
   "source": [
    "# The pitcher's example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bcf09449-1829-4273-9567-4decd0f73817",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gaussian mean-field variational parameterization\n",
    "def vp_init(size):\n",
    "    mu = np.random.randn(size)\n",
    "    log_s = np.random.randn(size)  # omega\n",
    "    return jnp.array([mu, log_s])\n",
    "\n",
    "def eps_rvs(size, n=1):\n",
    "    return np.random.randn(n, size)\n",
    "\n",
    "def zeta(vp, eps):\n",
    "    mu = vp[0]\n",
    "    s = jnp.exp(vp[1])\n",
    "    return mu + s * eps   \n",
    "\n",
    "def entropy_q(vp):\n",
    "    K = len(vp[0])\n",
    "    return K / 2. * (1. + np.log(2 * np.pi)) + jnp.sum(vp[1]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5e5eb1b1-c4a0-422b-bd1e-2c80556fbcab",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Transformation from bounded to real\n",
    "def sigmoid(x):\n",
    "    return 1. / (1. + jnp.exp(-x))\n",
    "    \n",
    "def T(z, a, b):\n",
    "    zeta = jsc.special.logit((z - a) / (b - a))\n",
    "    return zeta\n",
    "\n",
    "def T_inv(zeta, a, b):\n",
    "    z = a + (b - a) * sigmoid(zeta)\n",
    "    return z\n",
    "    \n",
    "def det_jac_T_inv(zeta, a, b):\n",
    "    return (b - a) * sigmoid(zeta) * (1 - sigmoid(zeta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c372cdea-3a08-458e-86e1-fc5d41636489",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prior\n",
    "def log_prior_v(v):\n",
    "    return jnp.log(1. / 10)\n",
    "\n",
    "def log_prior_alpha(alpha):\n",
    "    return jnp.log(2. / np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1fc29d0e-644e-4242-946e-3d739ea81992",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Likelihood\n",
    "def _trajectory(v, alpha, dt=0.1, G=9.81):\n",
    "    v_x = v * jnp.cos(alpha)  # x velocity m/s\n",
    "    v_y = v * jnp.sin(alpha)  # y velocity m/s\n",
    "    \n",
    "    x = 0.0  # initial position\n",
    "    y = 1.5  # initial height\n",
    "\n",
    "    while y > 0:  # simulate until ball hits floor\n",
    "        v_y += dt * -G  # acceleration due to gravity\n",
    "        x += dt * v_x\n",
    "        y += dt * v_y\n",
    "        \n",
    "    return x, y\n",
    "\n",
    "def log_likelihood(x_obs, v, alpha, sigma=0.5):\n",
    "    mu, _ = _trajectory(v, alpha)\n",
    "    return -0.5 * ((x_obs - mu) / sigma) ** 2 - jnp.log(sigma * (2. * np.pi) ** 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "72cc4bae-ff12-4b57-8676-521c3a52e39f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def elbo(vp, x_obs, eps):\n",
    "    _zeta = zeta(vp, eps)\n",
    "    out = 0.0\n",
    "    \n",
    "    # log p(v)\n",
    "    v = T_inv(_zeta[0], 0., 10.)\n",
    "    out += log_prior_v(v)\n",
    "    out += jnp.log(det_jac_T_inv(_zeta[0], 0., 10.))\n",
    "    \n",
    "    # log p(alpha)\n",
    "    alpha = T_inv(_zeta[1], 0., np.pi / 2)\n",
    "    out += log_prior_alpha(alpha)\n",
    "    out += jnp.log(det_jac_T_inv(_zeta[1], 0., np.pi / 2.))\n",
    "    \n",
    "    # log p(x|v, alpha)\n",
    "    out += log_likelihood(x_obs, v, alpha)\n",
    "    \n",
    "    # entropy q\n",
    "    out += entropy_q(vp)\n",
    "    \n",
    "    return jnp.sum(out) \n",
    "\n",
    "grad_elbo = jax.grad(elbo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d44003da-31c2-4085-8903-a76830daf6ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: All log messages before absl::InitializeLog() is called are written to STDERR\n",
      "I0000 00:00:1701026145.818482  139325 tfrt_cpu_pjrt_client.cc:349] TfrtCpuClient created.\n",
      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n",
      "Failed to detect the name of this notebook, you can set it manually with the WANDB_NOTEBOOK_NAME environment variable to enable code saving.\n",
      "\u001b[34m\u001b[1mwandb\u001b[0m: Currently logged in as: \u001b[33mglouppe\u001b[0m. Use \u001b[1m`wandb login --relogin`\u001b[0m to force relogin\n"
     ]
    },
    {
     "data": {
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       "Tracking run with wandb version 0.16.0"
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     "data": {
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       "Run data is saved locally in <code>/home/glouppe/Documents/teaching/DATS0001 - Foundations of Data Science/2023-2024/course/wandb/run-20231126_201546-o1xlpdlm</code>"
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      "text/html": [
       "Syncing run <strong><a href='https://wandb.ai/glouppe/nb08-advi/runs/o1xlpdlm' target=\"_blank\">generous-armadillo-13</a></strong> to <a href='https://wandb.ai/glouppe/nb08-advi' target=\"_blank\">Weights & Biases</a> (<a href='https://wandb.me/run' target=\"_blank\">docs</a>)<br/>"
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       " View project at <a href='https://wandb.ai/glouppe/nb08-advi' target=\"_blank\">https://wandb.ai/glouppe/nb08-advi</a>"
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       " View run at <a href='https://wandb.ai/glouppe/nb08-advi/runs/o1xlpdlm' target=\"_blank\">https://wandb.ai/glouppe/nb08-advi/runs/o1xlpdlm</a>"
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   ],
   "source": [
    "v_true = 7.5\n",
    "alpha_true = np.pi / 4\n",
    "mu, _ = _trajectory(v_true, alpha_true)\n",
    "x_obs = np.random.randn(1) * 0.5 + mu\n",
    "x_obs = x_obs[0]\n",
    "\n",
    "vp = vp_init(2)\n",
    "batchsize = 25\n",
    "lr = 0.02\n",
    "n_epochs = 50\n",
    "\n",
    "wandb.init(project=\"nb08-advi\")\n",
    "wandb.config.update({\n",
    "    \"v_true\": v_true, \"alpha_true\": alpha_true, \"x_obs\": x_obs,\n",
    "    \"lr\": lr, \"batchsize\": batchsize\n",
    "})"
   ]
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  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "64ce1e24-05f2-4353-9c98-2360a27daa7d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [01:12<00:00,  1.46s/it]\n"
     ]
    }
   ],
   "source": [
    "test = eps_rvs(2, 100)\n",
    "g = grad_elbo(vp, x_obs, test[0])\n",
    "\n",
    "for epoch in tqdm(range(n_epochs)):\n",
    "    # Log\n",
    "    elbo_test = np.mean([elbo(vp, x_obs, eps) for eps in test])\n",
    "    wandb.log({\"ELBO\": elbo_test})\n",
    "    \n",
    "    # Update            \n",
    "    g = jnp.zeros_like(g)\n",
    "    \n",
    "    for eps in eps_rvs(2, batchsize):\n",
    "        g += grad_elbo(vp, x_obs, eps)\n",
    "    \n",
    "    vp += lr * g / batchsize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "74a344c9-2d2b-4077-8227-683259315fa9",
   "metadata": {},
   "outputs": [],
   "source": [
    "_zeta = zeta(vp, eps_rvs(2, 10000))\n",
    "v = T_inv(_zeta[:, 0], 0., 10.)\n",
    "alpha = T_inv(_zeta[:, 1], 0., np.pi / 2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "075d8fba-520e-49e2-a71d-bb5e7129f01a",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import corner\n",
    "thetas = np.array([v, alpha]).T\n",
    "labels = [\"v\", \"alpha\"]\n",
    "fig = corner.corner(thetas, labels=labels, truths=[v_true, alpha_true])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5fa1220f-127e-4591-8035-b2a43c1dc580",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# p(x | x_obs)\n",
    "xs = []\n",
    "    \n",
    "for v, alpha in thetas[:5000]:\n",
    "    mu, _ = _trajectory(v, alpha)   \n",
    "    x = np.random.randn(1) * 0.5 + mu\n",
    "    xs.append(x[0])\n",
    "\n",
    "plt.hist(xs, density=True, bins=30, color=\"orange\")\n",
    "plt.scatter([x_obs], [0.])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}