Learning distributions on compact support with Normalizing Flows

normalizing_flow_compact_support.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning distributions on compact support using Normalizing Flows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalizing Flows [1] are powerful density estimators that have shown to be able to learn complex distributions, e.g., of natural images [2]. \n",
    "\n",
    "Recently, I was interested in learning a distribution on line segments which only has compact support, i.e., the support is not $\\mathbb{R}$ but only defined on a compact interval $[a, b]$ along the line segment. \n",
    "\n",
    "The vanilla formulation of Normalizing Flows [1] only considers distributions with support in $\\mathbb{R}$, and a quick literature research did not yield any solutions to the problem. By dwelling on this problem for a bit, I came up with a solution by carefully applying invertible transformations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The idea\n",
    "\n",
    "Consider a vanilla normalizing flow stacking a set of invertible and differentiable transformations $\\{f_1, \\dots, f_n \\}$. After applying common transformations (e.g. radial [1] or affine coupling [3] transform) the support of the function is still $\\mathbb{R}$. This is visualized in Fig. 1.\n",
    "\n",
    "Now, in order to obtain a distribution with compact support we require a function that is invertible, differentiable (in order to satisfy the constrains within normalizing flows), and additionaly we want the function to have a compact co-domain. One such choice, is the logistic function \n",
    "\n",
    "$$\n",
    "f_{n+1}: \\mathbb{R} \\mapsto [0, 1], f_{n+1}(x) = \\frac{1}{1 + e^{-x}}\n",
    "$$\n",
    "\n",
    "which is visualized as transformation in the first part of Fig. 2.\n",
    "\n",
    "After applying the logistic function, we can use a simple affine transformation $f_{n+2}$ in order to move and scale the support $[0, 1]$ to our desired interval as shown in the second part of Fig. 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['figure.dpi'] = 300\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "from torch import nn\n",
    "import numpy as np\n",
    "from tqdm import trange\n",
    "import torch.distributions as tdist\n",
    "import seaborn as sns\n",
    "from pyro.distributions.transforms import SigmoidTransform, AffineTransform\n",
    "from pyro.distributions.transforms import Radial\n",
    "\n",
    "sns.set(context=\"notebook\", style=\"whitegrid\")\n",
    "\n",
    "params = {\n",
    "    'text.usetex' : True,\n",
    "    'font.size' : 11,\n",
    "    \"font.serif\": [],\n",
    "    \"font.sans-serif\": [],\n",
    "    \"font.monospace\": [],\n",
    "    \"pgf.rcfonts\": False,   # don't setup fonts from rc parameters\n",
    "    \"font.family\": \"serif\",\n",
    "    \"text.latex.preamble\": [\n",
    "        r\"\\usepackage{lmodern}\",\n",
    "        r\"\\usepackage{amsmath}\",\n",
    "    ],\n",
    "    \"pgf.preamble\": [\n",
    "        r\"\\usepackage{lmodern}\",\n",
    "        r\"\\usepackage{amsmath}\",\n",
    "    ],\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Action!\n",
    "\n",
    "Next, we are going to use the [Pyro](https://pyro.ai/) library which itself is based on PyTorch to implement our idea and test the implemenation by learning a simple 1D distribution with compact support.\n",
    "\n",
    "In order to be able to learn the parameters of the normalizing flow efficently using maximum likelihood, we **need to be able to evaluate the likelihood of individual samples of our dataset**. Therefore, we are going to use the _inverse_ parameterization which allows us to transform our training sample backwards through the transformation shown in Fig. 1 and 2 in order to evalute the density of the sample in latent distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class InvSigmoidTransform(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.transform = SigmoidTransform().inv\n",
    "        \n",
    "    def forward(self, x):\n",
    "        return self.transform(x)\n",
    "    \n",
    "    def log_abs_det_jacobian(self, z, z_next):\n",
    "        return self.transform.log_abs_det_jacobian(z, z_next).sum(1)\n",
    "\n",
    "\n",
    "class InvAffineTransformModule(nn.Module):\n",
    "    def __init__(self, loc, scale):\n",
    "        super().__init__()\n",
    "        self.loc = loc\n",
    "        self.scale = scale\n",
    "        self.transform = AffineTransform(loc, scale).inv\n",
    "        \n",
    "    def forward(self, x):\n",
    "        return self.transform(x)\n",
    "    \n",
    "    def log_abs_det_jacobian(self, z, z_next):\n",
    "        return self.transform.log_abs_det_jacobian(z, z_next).sum(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us define the model in code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class NormalizingFlowDensity(nn.Module):\n",
    "    def __init__(self, dim, flow_length, flow_type=\"radial_flow\", loc=0, scale=1, **kwargs):\n",
    "        super(NormalizingFlowDensity, self).__init__()\n",
    "        self.dim = dim\n",
    "        self.flow_length = flow_length\n",
    "        self.flow_type = flow_type\n",
    "\n",
    "        self.mean = nn.Parameter(torch.zeros(self.dim), requires_grad=False)\n",
    "        self.cov = nn.Parameter(torch.eye(self.dim), requires_grad=False)\n",
    "        \n",
    "        modules = [\n",
    "            # Affine transformation of the [0, 1] interval \n",
    "            InvAffineTransformModule(loc=loc, scale=scale),\n",
    "            # Squeeze R into [0, 1] interval\n",
    "            InvSigmoidTransform()\n",
    "        ]\n",
    "        if self.flow_type == \"radial_flow\":\n",
    "            self.transforms = modules.extend([Radial(dim) for _ in range(flow_length)])\n",
    "        else:\n",
    "            raise NotImplementedError\n",
    "        \n",
    "        self.transforms = nn.ModuleList(modules)\n",
    "        \n",
    "    def forward(self, z):\n",
    "        sum_log_jacobians = 0\n",
    "        for transform in self.transforms:\n",
    "            z_next = transform(z)\n",
    "            sum_log_jacobians = sum_log_jacobians + transform.log_abs_det_jacobian(\n",
    "                z, z_next\n",
    "            )\n",
    "            z = z_next\n",
    "\n",
    "        return z, sum_log_jacobians\n",
    "\n",
    "    def log_prob(self, x):\n",
    "        z, sum_log_jacobians = self.forward(x)\n",
    "        log_prob_z = tdist.MultivariateNormal(self.mean, self.cov).log_prob(z)\n",
    "        log_prob_x = log_prob_z + sum_log_jacobians\n",
    "        return log_prob_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that since we want to use _inverse_ parameterization, we add the inverse of the transforms in reverse order into the list. Further, we can set the support of the distribution using the parameters `loc` and `scale`.\n",
    "\n",
    "We can use the `log_prob` function, which takes a datapoint $x$, computes the inverse transformation and returns the log likelihood for that datapoint $\\log p(x)$ for training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def piecewise_uniform_dist(loc=1, scale=1):\n",
    "    samples1 = tdist.uniform.Uniform(0, 0.5).sample((200,))\n",
    "    samples2 = tdist.uniform.Uniform(0.5, 1.0).sample((300,))\n",
    "    samples3 = tdist.uniform.Uniform(1.0, 1.5).sample((500,))\n",
    "    \n",
    "    return torch.cat([samples1, samples2, samples3]).unsqueeze(1) * scale + loc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we consider the following 1D example distribution which is a piecewise uniform with support $[1.0, 2.5]$ shown in Fig. 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$p(x)$')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.hlines([0.4, 0.6, 1.0], [1.0, 1.5, 2.0], [1.5, 2.0, 2.5], lw=3)\n",
    "ax.vlines([1.0, 1.5, 2.0, 2.5], [0., 0.4, 0.6, 0.], [0.4, 0.6, 1.0, 1.0], ls=\"--\")\n",
    "ax.set_xlim(0.5, 3.)\n",
    "ax.set_ylim(0.0, 1.1)\n",
    "ax.set_xlabel(r\"$x$\")\n",
    "ax.set_ylabel(r\"$p(x)$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to learn the parameters $\\theta$ of the normalizing flow, we can simply maximize the likelihood \n",
    "\n",
    "$$\n",
    "\\arg\\max_{\\theta} p_{\\theta}(x)\n",
    "$$\n",
    "\n",
    "which corresponds the following training code where we appropriately for the target distribution set the `loc` parameter to $1$ and the `scale` parameter to $1.5$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = torch.utils.data.TensorDataset(piecewise_uniform_dist())\n",
    "dataloader = torch.utils.data.DataLoader(dataset, batch_size=512)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loss: 0.367: 100%|███████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:15<00:00,  6.43it/s]\n"
     ]
    }
   ],
   "source": [
    "net = NormalizingFlowDensity(dim=1, flow_length=100, flow_type=\"radial_flow\", loc=1, scale=1.5)\n",
    "optimizer = torch.optim.Adam(net.parameters(), lr=5e-2)\n",
    "\n",
    "epochs = 100\n",
    "device = \"cpu\"\n",
    "net.to(device)\n",
    "\n",
    "epoch_iter = trange(epochs)\n",
    "for epoch in epoch_iter:\n",
    "    losses = []\n",
    "    for batch in dataloader:\n",
    "        data = batch[0].to(device)\n",
    "        log_prob = net.log_prob(data)\n",
    "\n",
    "        loss = -log_prob.mean()\n",
    "        losses.append(loss.item())\n",
    "\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        optimizer.zero_grad()\n",
    "    \n",
    "    epoch_iter.set_description(f\"Loss: {np.mean(losses):.03f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can plot the learned density in Fig. 4. Note that the density is only defined in the interval $[1.0, 2.5]$, however points outside the interval evaluate to $0$ due to clamping by Pyro."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5, 3.0)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(1.0, 2.5, 1000)\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, [net.log_prob(torch.Tensor([[x_val]])).exp().detach().cpu().numpy() for x_val in x])\n",
    "ax.set_ylabel(r\"$p_{\\theta}(x)$\")\n",
    "ax.set_xlabel(r\"x\")\n",
    "ax.set_xlim(0.5, 3.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the result is not perfect this gives a powerful framework for learning distributions on compact support. One can probably improve the result quite a bit by using more powerful transformations in the \"base\" flow (in fact one can use any existing invertible and differentiable transformation!) and by increasing the depth of the flow.\n",
    "\n",
    "## Conclusion\n",
    "Overall, we have seen how one can learn a distribution with compact support using normalizing flows by leveraging some simple transformations in the final layers and demonstrated some proof-of-concept results on a 1D toy example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "b986840316e161d79aa58f1ef92a75b218d1af4cb104d4f608bfeb53d183ad32"
  },
  "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": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}