03_normalizing_flows.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import partial\n",
    "\n",
    "import jax\n",
    "\n",
    "from jax import config\n",
    "config.update(\"jax_enable_x64\", True)\n",
    "\n",
    "import jax.numpy as np\n",
    "import flax.linen as nn\n",
    "import optax\n",
    "import diffrax as dfx\n",
    "import math\n",
    "from tensorflow_probability.substrates import jax as tfp\n",
    "\n",
    "from sklearn import datasets, preprocessing\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import trange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.0, 2.0)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_samples = 100_000\n",
    "\n",
    "x, _ = datasets.make(n_samples=n_samples, noise=.06)\n",
    "\n",
    "scaler = preprocessing.StandardScaler()\n",
    "x = scaler.fit_transform(x)\n",
    "\n",
    "plt.hist2d(x[:, 0], x[:, 1], bins=100)\n",
    "plt.xlim(-2 ,2)\n",
    "plt.ylim(-2, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MLP(nn.Module):\n",
    "    \"\"\" A simple MLP in Flax.\n",
    "    \"\"\"\n",
    "    hidden_dim: int = 32\n",
    "    out_dim: int = 2\n",
    "    n_layers: int = 3\n",
    "\n",
    "    @nn.compact\n",
    "    def __call__(self, x):\n",
    "        for _ in range(self.n_layers):\n",
    "            x = nn.Dense(features=self.hidden_dim)(x)\n",
    "            x = nn.gelu(x)\n",
    "        x = nn.Dense(features=self.out_dim)(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "class AffineBijector:\n",
    "    def __init__(self, shift_and_log_scale):\n",
    "        self.shift_and_log_scale = shift_and_log_scale\n",
    "\n",
    "    def forward_and_log_det(self, x):\n",
    "        shift, log_scale = np.split(self.shift_and_log_scale, 2, axis=-1)\n",
    "        y = x * np.exp(log_scale) + shift\n",
    "        log_det = log_scale\n",
    "        return y, log_det\n",
    "\n",
    "    def inverse_and_log_det(self, y):\n",
    "        shift, log_scale = np.split(self.shift_and_log_scale, 2, axis=-1)\n",
    "        x = (y - shift) * np.exp(-log_scale)\n",
    "        log_det = -log_scale\n",
    "        return x, log_det\n",
    "\n",
    "class MaskedCoupling:\n",
    "    def __init__(self, mask, conditioner, bijector):\n",
    "        \"\"\"Coupling layer with masking and conditioner.\"\"\"\n",
    "        self.mask = mask\n",
    "        self.conditioner = conditioner\n",
    "        self.bijector = bijector\n",
    "\n",
    "    def forward_and_log_det(self, x):\n",
    "        \"\"\"Transforms masked indices of `x` conditioned on unmasked indices using bijector.\"\"\"\n",
    "        x_cond = np.where(self.mask, 0.0, x)\n",
    "        bijector_params = self.conditioner(x_cond)\n",
    "        y, log_det = self.bijector(bijector_params).forward_and_log_det(x)\n",
    "        log_det = np.where(self.mask, log_det, 0.0)\n",
    "        y = np.where(self.mask, y, x)\n",
    "        return y, np.sum(log_det, axis=-1)\n",
    "\n",
    "    def inverse_and_log_det(self, y):\n",
    "        \"\"\"Transforms masked indices of `y` conditioned on unmasked indices using bijector.\"\"\"\n",
    "        y_cond = np.where(self.mask, 0.0, y)\n",
    "        bijector_params = self.conditioner(y_cond)\n",
    "        x, log_det = self.bijector(bijector_params).inverse_and_log_det(y)\n",
    "        log_det = np.where(self.mask, log_det, 0.0)\n",
    "        x = np.where(self.mask, x, y)\n",
    "        return x, np.sum(log_det, axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RealNVP(nn.Module):\n",
    "    n_transforms: int = 4\n",
    "    d_params: int = 2\n",
    "    d_hidden: int = 128\n",
    "    n_layers: int = 4\n",
    "\n",
    "    def setup(self):\n",
    "        self.mask_list = [np.arange(self.d_params) % 2 == i % 2 for i in range(self.n_transforms)]\n",
    "        self.conditioner_list = [MLP(self.d_hidden, 2 * self.d_params, self.n_layers) for _ in range(self.n_transforms)]\n",
    "        self.base_dist = tfp.distributions.Normal(loc=np.zeros(self.d_params), scale=np.ones(self.d_params))\n",
    "    \n",
    "    def log_prob(self, x):\n",
    "        log_prob = np.zeros(x.shape[:-1])\n",
    "        for mask, conditioner in zip(self.mask_list[::-1], self.conditioner_list[::-1]):\n",
    "            x, ldj = MaskedCoupling(mask, conditioner, AffineBijector).inverse_and_log_det(x)\n",
    "            log_prob += ldj\n",
    "        return log_prob + self.base_dist.log_prob(x).sum(-1)\n",
    "\n",
    "    def sample(self, sample_shape, key, n_transforms=None):\n",
    "        x = self.base_dist.sample(key, sample_shape)\n",
    "        for mask, conditioner in zip(self.mask_list[:n_transforms], self.conditioner_list[:n_transforms]):\n",
    "            x, _ = MaskedCoupling(mask, conditioner, AffineBijector).forward_and_log_det(x)\n",
    "        return x\n",
    "\n",
    "    def __call__(self, x):\n",
    "        return self.log_prob(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([-3.35979128, -2.8513697 , -2.8622152 , -3.03087519], dtype=float64)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = RealNVP()\n",
    "\n",
    "key = jax.random.PRNGKey(0)\n",
    "params = model.init(key, x[:2])\n",
    "\n",
    "# Test log_prob\n",
    "model.apply(params, x[:4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = optax.adam(learning_rate=1e-3)\n",
    "opt_state = opt.init(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def train_step(params, opt_state, x):\n",
    "    def loss_fn(params):\n",
    "        return -model.apply(params, x).mean()\n",
    "    loss, grad = jax.value_and_grad(loss_fn)(params)\n",
    "    updates, opt_state = opt.update(grad, opt_state)\n",
    "    params = optax.apply_updates(params, updates)\n",
    "    return loss, params, opt_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [01:31<00:00, 108.79it/s, val=1.407515638835097]\n"
     ]
    }
   ],
   "source": [
    "n_steps = 10_000\n",
    "n_batch = 128\n",
    "\n",
    "with trange(n_steps) as steps:\n",
    "    for step in steps:\n",
    "\n",
    "        # Draw a random batches from x\n",
    "        key, subkey = jax.random.split(key)\n",
    "        idx = jax.random.choice(key, x.shape[0], shape=(n_batch,))\n",
    "        \n",
    "        x_batch = x[idx]\n",
    "\n",
    "        loss, params, opt_state = train_step(params, opt_state, x_batch)\n",
    "\n",
    "        steps.set_postfix(val=loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate some samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples = 100_000\n",
    "x_sample = model.apply(params, key, (n_samples,), method=model.sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.0, 2.0)"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.hist2d(x_sample[:, 0], x_sample[:, 1], bins=100)\n",
    "plt.xlim(-2 ,2)\n",
    "plt.ylim(-2, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "torch-mps",
   "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": 2
}