notebooks/2d_classification.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "07d6a47e-96df-40e9-b993-b30169b932f3",
   "metadata": {
    "executionInfo": {
     "elapsed": 5,
     "status": "ok",
     "timestamp": 1686480364678,
     "user": {
      "displayName": "Martin Marek",
      "userId": "04932572550491068578"
     },
     "user_tz": -60
    },
    "id": "kh3BN0GNEm0V",
    "tags": []
   },
   "outputs": [],
   "source": [
    "import os\n",
    "os.chdir(os.path.expanduser('~/My Drive/dirclip-private/core'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "78086589-fe47-422d-aa93-d972c02905cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import operator as op\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.legend_handler import HandlerTuple\n",
    "from scipy.ndimage import gaussian_filter1d\n",
    "from functools import partial\n",
    "from jax import vmap\n",
    "from jax.tree_util import tree_map, tree_leaves, tree_reduce\n",
    "from jax.lax import fori_loop\n",
    "from jax.flatten_util import ravel_pytree\n",
    "import utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2ca004ab-bb7e-4a6f-b8e7-02b0920d10e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60bcfa6b-aef0-488a-9d7c-6a4f36c256f8",
   "metadata": {},
   "source": [
    "# HMC sampler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "54b36902-01c5-4d5d-80e3-6f96bc2d4112",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def r_hat(y, eps=1e-12):\n",
    "    \"\"\"\n",
    "    the R hat metric measures how well an MCMC chain \"mixes\"\n",
    "    Based on the paper \"What Are Bayesian Neural Network Posteriors Really Like? - Appendix B\"\n",
    "    y.shape: [num_chains (M) x num_steps (N) x num_features (B)]\n",
    "    \"\"\"\n",
    "    M, N, B = y.shape\n",
    "\n",
    "    # compute variances\n",
    "    b = (N/(M-1)) * ((y.mean(axis=1, keepdims=True) - y.mean(axis=(0, 1), keepdims=True))**2).sum(axis=(0, 1))\n",
    "    w = 1/(M*(N-1)) * ((y - y.mean(axis=1, keepdims=True))**2).sum(axis=(0, 1))\n",
    "    \n",
    "    # avoid division by zero\n",
    "    b += eps\n",
    "    w += eps\n",
    "    \n",
    "    # get r hat\n",
    "    r_hat = jnp.sqrt((((N-1)/N)*w + (1/N)*b)/w)\n",
    "    \n",
    "    return r_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a28357d7-3edb-4de4-9253-b710a01f54af",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ifelse(cond, val_true, val_false):\n",
    "    return jax.lax.cond(cond, lambda x: x[0], lambda x: x[1], (val_true, val_false))\n",
    "\n",
    "def leapfrog(params, momentum, log_prob_fn, step_size, n_steps):\n",
    "    \"\"\"Approximates Hamiltonian dynamics using the leapfrog algorithm.\"\"\"\n",
    "\n",
    "    # define a single step\n",
    "    def step(i, args):\n",
    "        params, momentum = args\n",
    "\n",
    "        # update momentum\n",
    "        grad = jax.grad(log_prob_fn)(params)\n",
    "        momentum = tree_map(lambda m, g: m + 0.5 * step_size * g, momentum, grad)\n",
    "\n",
    "        # update params\n",
    "        params = tree_map(lambda p, m: p + m * step_size, params, momentum)\n",
    "\n",
    "        # update momentum\n",
    "        grad = jax.grad(log_prob_fn)(params)\n",
    "        momentum = tree_map(lambda m, g: m + 0.5 * step_size * g, momentum, grad)\n",
    "\n",
    "        return params, momentum\n",
    "\n",
    "    # do 'n_steps'\n",
    "    new_params, new_momentum = fori_loop(0, n_steps, step, (params, momentum))\n",
    "\n",
    "    return new_params, new_momentum\n",
    "\n",
    "def hmc_sample(key, params_init, log_prob_fn, step_size, n_leapfrog_steps=10_000, n_steps=100, burn_frac=0.3, n_chains=3):\n",
    "    \"\"\"\n",
    "    Runs HMC and returns the full Markov chain as a list.\n",
    "    - params: array\n",
    "    - log_prob_fn: function that takes params as the only argument and returns a scalar value\n",
    "    \"\"\"\n",
    "\n",
    "    # define a single step\n",
    "    @jax.jit\n",
    "    def step_fn(carry, x):\n",
    "        params, key = carry\n",
    "        key, normal_key, uniform_key = jax.random.split(key, 3)\n",
    "\n",
    "        # generate random momentum\n",
    "        momentum = utils.normal_like_tree(key, params)\n",
    "\n",
    "        # leapfrog\n",
    "        new_params, new_momentum = leapfrog(params, momentum, log_prob_fn, step_size, n_leapfrog_steps)\n",
    "\n",
    "        # MH correction\n",
    "        potentaial_energy_diff = log_prob_fn(new_params) - log_prob_fn(params)\n",
    "        momentum_dot = tree_reduce(op.add, tree_map(lambda x: (x**2).sum(), tree_leaves(momentum)))\n",
    "        new_momentum_dot = tree_reduce(op.add, tree_map(lambda x: (x**2).sum(), tree_leaves(new_momentum)))\n",
    "        kinetic_energy_diff = 0.5*(momentum_dot - new_momentum_dot)\n",
    "        log_accept_prob = potentaial_energy_diff + kinetic_energy_diff\n",
    "        log_accept_prob = jnp.nan_to_num(log_accept_prob, nan=-jnp.inf)\n",
    "        accept_prob = jnp.minimum(1, jnp.exp(log_accept_prob))\n",
    "        accept = jax.random.uniform(uniform_key) < accept_prob\n",
    "        params = ifelse(accept, new_params, params)\n",
    "\n",
    "        return (params, key), (params, accept_prob)\n",
    "\n",
    "    # sample multiple chains\n",
    "    def sample(key):\n",
    "        # do 'n_steps' (compiled)\n",
    "        _, (chain, accept_prob) = jax.lax.scan(step_fn, (params_init, key), xs=None, length=n_steps)\n",
    "        return chain, accept_prob\n",
    "    keys = jax.random.split(key, n_chains)\n",
    "    chains, accept_prob = vmap(sample)(keys)\n",
    "    \n",
    "    # burn-in\n",
    "    n_burn = int(burn_frac*n_steps) # number of burn-in steps\n",
    "    chains = tree_map(lambda leaf: leaf[:, n_burn:], chains)\n",
    "    \n",
    "    # get accuracy\n",
    "    logits = vmap(vmap(lambda params: predict_fn(params, x)))(chains)\n",
    "    y_hat = jax.nn.softmax(logits)\n",
    "    acc = (y_hat.argmax(-1) == y).mean()\n",
    "    \n",
    "    # r-hat\n",
    "    flatten_fn = lambda tree: ravel_pytree(tree)[0]\n",
    "    chain_flat = vmap(vmap(flatten_fn))(chains) # [n_chains, n_steps, n_params]\n",
    "    r_ps = r_hat(chain_flat).mean() # parameter-space\n",
    "    r_fs = r_hat(y_hat[..., 0]).mean() # function-space\n",
    "    \n",
    "    print(f'accept={accept_prob.mean():.2%}, {r_ps=:.2f}, {r_fs=:.2f}, {acc=:.2%}')\n",
    "    return chains"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f54d0bc-5e83-4afa-863a-96d84d9ca971",
   "metadata": {},
   "source": [
    "# Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ebc7dbbf-4dfa-4863-8fc6-b3288e8b621b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "num. params: 492\n"
     ]
    }
   ],
   "source": [
    "# define a simple MLP\n",
    "def make_mlp(key, in_dim: int, out_dim: int, hidden_dims: list[int], init_std: float = 1):\n",
    "    \n",
    "    # initialize parameters\n",
    "    layer_dims = [in_dim, *hidden_dims, out_dim]\n",
    "    ws, bs = [], []\n",
    "    for i in range(1, len(layer_dims)):\n",
    "        key, kw, kb = jax.random.split(key, 3)\n",
    "        in_dim = layer_dims[i-1]\n",
    "        out_dim = layer_dims[i]\n",
    "        ws += [init_std * jax.random.normal(kw, [out_dim, in_dim])]\n",
    "        bs += [init_std * jax.random.normal(kb, [out_dim])]\n",
    "    params = (ws, bs)\n",
    "    \n",
    "    # make forward function\n",
    "    # @jax.jit\n",
    "    @partial(vmap, in_axes=(None, 0))\n",
    "    def forward(params, x):\n",
    "        ws, bs = params\n",
    "        for w, b in zip(ws[:-1], bs[:-1]):\n",
    "            x = jax.nn.relu(w @ x + b)\n",
    "        x = ws[-1] @ x + bs[-1]\n",
    "        return x\n",
    "    \n",
    "    return params, forward\n",
    "\n",
    "key = jax.random.PRNGKey(0)\n",
    "in_dim = 2\n",
    "out_dim = 2\n",
    "hidden_dims = 5*[10]\n",
    "params_init, predict_fn = make_mlp(key, in_dim, out_dim, hidden_dims)\n",
    "print('num. params:', sum(tree_map(jnp.size, tree_leaves(params_init))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b37dc377-bc54-4363-8f9b-67634024ca3a",
   "metadata": {},
   "source": [
    "# dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "55ed22c0-6c51-4c64-b915-47f79eccf9aa",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 274,
       "width": 458
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = jnp.array([[0.15, -0.39], [0.25, -0.23], [0.12, -0.12], [0.38, -0.10], [0.45, -0.38], [0.62, -0.25], [0.83, -0.12], [0.80, -0.37], [0.73, -0.69], [0.18, -0.68], [0.35, -0.58], [0.45, -0.82], [0.51, -0.70], [0.61, -0.60], [0.69, -0.83], [0.87, -0.76], [0.82, -0.59], [0.40, -0.27]])\n",
    "y = jnp.array(9*[0]+9*[1])\n",
    "fig, ax = plt.subplots(figsize=(5, 3))\n",
    "plt.scatter(*x.T, c=y, edgecolors='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54090c2c-8e11-4957-8398-d108b9539bba",
   "metadata": {},
   "source": [
    "# distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0200f835-796f-4aa3-8b2f-e79da32956c9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def log_posterior_fn(params, x, y, std=1, alpha=None, clip_logp=-50, T=1):\n",
    "    log_posterior = 0\n",
    "    \n",
    "    # likelihood\n",
    "    logits = predict_fn(params, x)\n",
    "    _, n_class = logits.shape\n",
    "    y_one_hot = jax.nn.one_hot(y, n_class)\n",
    "    logprobs = jax.nn.log_softmax(logits)\n",
    "    log_posterior += (logprobs * y_one_hot).sum()\n",
    "    \n",
    "    # normal prior\n",
    "    if std is not None:\n",
    "        dx = tree_reduce(op.add, tree_map(lambda x: (x**2).sum(), params))\n",
    "        log_prior = -0.5 * dx / std**2\n",
    "        log_posterior += log_prior\n",
    "    \n",
    "    # dirichlet prior\n",
    "    if alpha is not None:\n",
    "        logprobs_clipped = logprobs.clip(min=clip_logp)\n",
    "        log_prior = ((alpha-1) * logprobs_clipped).sum()\n",
    "        log_posterior += log_prior\n",
    "    \n",
    "    return log_posterior / T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "addc1327-561e-4b35-9625-960e00e428b8",
   "metadata": {},
   "source": [
    "## run HMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cc1abf31-7ca7-4dd4-a38e-6affac0ffa9f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "key = jax.random.PRNGKey(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3d8d39f2-c5b6-44df-8be6-61b32527f12f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accept=96.32%, r_ps=1.00, r_fs=1.00, acc=69.88%\n",
      "CPU times: user 3min 24s, sys: 170 ms, total: 3min 24s\n",
      "Wall time: 3min 24s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "log_prob_fn = partial(log_posterior_fn, x=x, y=y, alpha=1.4)\n",
    "chains_dir_hi = hmc_sample(key, params_init, log_prob_fn, 4e-4, n_steps=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "09fada20-a8b1-45dc-a282-e56b2731ccc7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accept=91.54%, r_ps=1.05, r_fs=1.00, acc=100.00%\n",
      "CPU times: user 3min 24s, sys: 157 ms, total: 3min 24s\n",
      "Wall time: 3min 25s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "log_prob_fn = partial(log_posterior_fn, x=x, y=y, alpha=0.6)\n",
    "chains_dir_lo = hmc_sample(key, params_init, log_prob_fn, 5e-5, n_steps=500)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc3b04e2-7dc0-4edc-a498-aba219a4fc09",
   "metadata": {
    "tags": []
   },
   "source": [
    "# plot predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3fcdc6e7-f151-4ea6-b8af-ee1eae89246f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 33.6 s, sys: 5.53 s, total: 39.1 s\n",
      "Wall time: 14.2 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "%%capture\n",
    "# compute decision boundaries\n",
    "s = 400 # grid size\n",
    "x0_min, x0_max = x[:, 0].min() - 0.1, x[:, 0].max() + 0.1\n",
    "x1_min, x1_max = x[:, 1].min() - 0.1, x[:, 1].max() + 0.1\n",
    "x0 = jnp.linspace(x0_min, x0_max, s)\n",
    "x1 = jnp.linspace(x1_min, x1_max, s)\n",
    "x_ = jnp.stack(jnp.meshgrid(x0, x1), -1)\n",
    "x_ = x_.reshape(s*s, 2)\n",
    "extent = (x0_min, x0_max, x1_min, x1_max)\n",
    "\n",
    "boundaries = []\n",
    "for chains in (chains_dir_hi, chains_dir_lo):\n",
    "    chain = tree_map(jnp.concatenate, chains) # concatenate chains\n",
    "    logits = jax.lax.map(lambda params: predict_fn(params, x_), chain)\n",
    "    probs = jnp.exp(utils.average_predictions(logits))\n",
    "    cs = plt.contour(probs[:, 0].reshape(s, s) > 0.5, extent=extent)\n",
    "    boundaries += [cs.allsegs[0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e0206b23-3d20-47e7-9d16-2d86e6e26fca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 311,
       "width": 511
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(5, 3), layout='compressed')\n",
    "\n",
    "# use same colors as NDG paper\n",
    "# color_class1, color_class2, color_noise = '#ff7f2a', '#aa36c8', '#d30101'\n",
    "# color_smooth, color_flexible = '#d30101', '#013280'\n",
    "\n",
    "# set custom colors\n",
    "color_class1, color_class2, color_noise = 'tab:orange', 'seagreen', 'darkgray'\n",
    "color_smooth, color_flexible = (0.75, 0.02, 0.18), (0.23, 0.3, 0.75) # coolwarm red and blue\n",
    "\n",
    "# plot data\n",
    "ax.scatter(*x[y==0].T, c=8*[color_class1]+[color_noise], s=250, marker='P', edgecolors='black', linewidths=1.2)\n",
    "ax.scatter(*x[y==1].T, c=8*[color_class2]+[color_noise], s=100, marker='o', edgecolors='black', linewidths=1.2)\n",
    "\n",
    "# plot decision boundaries\n",
    "# the decision boundaries are vety slightly smoothened to look less 'rough'\n",
    "for dist_bounds, color in zip(boundaries, (color_smooth, color_flexible)):\n",
    "    for line in dist_bounds:\n",
    "        ax.plot(*gaussian_filter1d(line.T, 12), c=color, ls='--', lw=2.5)\n",
    "\n",
    "# legend\n",
    "# using blank plots to manually control the scatter point size and line width\n",
    "class1_valid = plt.scatter([], [], color=color_class1, s=90, marker='P', edgecolors='black', linewidths=1)\n",
    "class1_noise = plt.scatter([], [], color=color_noise,  s=90, marker='P', edgecolors='black', linewidths=1)\n",
    "class2_valid = plt.scatter([], [], color=color_class2, s=50, marker='o', edgecolors='black', linewidths=1)\n",
    "class2_noise = plt.scatter([], [], color=color_noise,  s=50, marker='o', edgecolors='black', linewidths=1)\n",
    "line1, = ax.plot([], [], c=color_smooth,   ls='--', lw=2.4)\n",
    "line2, = ax.plot([], [], c=color_flexible, ls='--', lw=2.4)\n",
    "legend = ax.legend([(class1_valid, class1_noise), (class2_valid, class2_noise), line1, line2],\n",
    "                   ['class A', 'class B', 'DirClip(1.4)', 'DirClip(0.6)'],\n",
    "                   handler_map={tuple: HandlerTuple(2)}, loc='lower left', framealpha=0.96, fontsize=11)\n",
    "\n",
    "ax.set_xticks([])\n",
    "ax.set_yticks([])\n",
    "ax.set_xlim((x0_min+0.01, x0_max-0.01))\n",
    "ax.set_ylim((x1_min+0.01, x1_max-0.01))\n",
    "# plt.savefig('../plots/dirclip_decision_boundary.pdf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c4fee87f-5e2a-407e-bcf7-2b6ad441aef4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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