nonlinear_prob_model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f934baee",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "from torch.autograd import Variable  # CHECK: do I need this?\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.style.use('ggplot')\n",
    "from scipy.stats import norm\n",
    "\n",
    "import time\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ea7738a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c6f5a0bd",
   "metadata": {},
   "source": [
    "### Simulate data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "020f031f",
   "metadata": {},
   "outputs": [],
   "source": [
    "input_size = 2   # input is theta and z_i\n",
    "output_size = 2  # output is mu_i and log(sigma_i) \n",
    "\n",
    "class likelihood_NN(nn.Module):\n",
    "    \"\"\"\n",
    "    Defines a method to evaluate a likelihood.\n",
    "\n",
    "    NOTE: This doesn't need to be an nn.module. A regular function would suffice.\n",
    "    However, if we want to experiment with likelihood based on a neural network,\n",
    "    this class can be adapted.\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self):\n",
    "        super(likelihood_NN, self).__init__()\n",
    "        \n",
    "    def forward_mean(self, theta, z):\n",
    "        m = theta[:, None] + torch.sin(z) * z + z\n",
    "        return m\n",
    "    \n",
    "    def forward_sd(self, theta, z):\n",
    "        s = torch.cos(z)\n",
    "        return s\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6df28831",
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.manual_seed(1789)  # use a fixed seed for simulation data\n",
    "likelihood_nn = likelihood_NN().to(device)\n",
    "\n",
    "theta = torch.randn(1)\n",
    "\n",
    "n = 10000\n",
    "theta_rep = theta.repeat(n)\n",
    "z = 5 * torch.randn(n)\n",
    "x = torch.randn(n, 1)\n",
    "\n",
    "f_mean = likelihood_nn.forward_mean(theta, z)\n",
    "f_sd = likelihood_nn.forward_sd(theta, z)\n",
    "\n",
    "x = f_mean.reshape(n, 1) + x * torch.exp(f_sd).reshape(n, 1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "19374e53",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's examine the data, in particular, plot x as a function of z.\n",
    "plt.scatter(z.detach().numpy(), x.detach().numpy())\n",
    "plt.xlabel(\"z\")\n",
    "plt.ylabel(\"x\")\n",
    "plt.savefig(\"to_discuss/z_deep.pdf\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4e89763f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_78810/3367864121.py:7: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  fig.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot x\n",
    "nbins = 100\n",
    "fig, axs = plt.subplots(1, 1)\n",
    "axs.hist(x.numpy(), bins = nbins, density = True)\n",
    "axs.set_title(\"p(x)\")\n",
    "fig.savefig(\"to_discuss/p_deep.pdf\")\n",
    "fig.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "472bf409",
   "metadata": {},
   "source": [
    "### Distributions for ELBO\n",
    "Can use the same distributions for factorized and amortized VI. For amorizted VI, the arguments `nu_mean_z` and `nu_sd_z` will be the output of the inference network. Note that the joint $p(x, \\theta, z)$ uses the known likelihood network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6d588f90",
   "metadata": {},
   "outputs": [],
   "source": [
    "# vanilla implementation (not vectorized)\n",
    "def log_joint(x, theta, z):\n",
    "    \"\"\"\n",
    "    Returns the log joint over x, theta, and z.    \n",
    "    x: observed variable\n",
    "    theta: global latent variable\n",
    "    z: local latent variable.\n",
    "    \"\"\"\n",
    "    f_mean = likelihood_nn.forward_mean(theta, z).reshape(n, 1)\n",
    "    f_sd = likelihood_nn.forward_sd(theta, z).reshape(n, 1)\n",
    "        \n",
    "    return -0.5 * torch.sum(z**2) - torch.sum(torch.div((x - f_mean)**2,\n",
    "                                              2 * torch.exp(f_sd)**2))\n",
    "\n",
    "def log_q(theta, z, nu_mean_theta, nu_sd_theta, nu_mean_z, nu_sd_z):\n",
    "    \"\"\"\n",
    "    Returns the log density of the approximation q.\n",
    "    theta: global latent variable\n",
    "    z: local latent variable.\n",
    "    nu_mean_theta: variational mean for theta.\n",
    "    nu_sd_theta: variational standard deviation for theta.\n",
    "    nu_mean_z: variational mean for z.\n",
    "    nu_sd_z: variational standard deviation for z.\n",
    "    \"\"\"\n",
    "    log_q_theta = - torch.log(nu_sd_theta) - 1 / (2 * nu_sd_theta**2)\\\n",
    "                    * (theta - nu_mean_theta)**2\n",
    "    log_q_z = torch.sum(- torch.log(nu_sd_z) - 1 / (2 * nu_sd_z**2)\\\n",
    "                          * (z - nu_mean_z)**2)\n",
    "    return log_q_theta + log_q_z\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3200b719",
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_joint_v(x, theta, z):\n",
    "    \"\"\"\n",
    "    Returns the log joint over x, theta, and z. This version is vectorized if we want\n",
    "    to compute Monte Carlo estimates of the ELBO in parallel.\n",
    "    x: observed variable\n",
    "    theta: global latent variable\n",
    "    z: local latent variable.\n",
    "    \"\"\"\n",
    "    f_mean = likelihood_nn.forward_mean(theta, z)\n",
    "    f_sd = likelihood_nn.forward_sd(theta, z)\n",
    "\n",
    "    return -0.5 * torch.sum(z**2, dim = 1)\\\n",
    "        - torch.sum(torch.div((x - f_mean)**2, 2 * torch.exp(f_sd)**2), dim = 1)\n",
    "\n",
    "\n",
    "def log_q_v(theta, z, nu_mean_theta, nu_sd_theta, nu_mean_z, nu_sd_z):\n",
    "    \"\"\"\n",
    "    Returns the log density of the approximation q. This version is vectorized if\n",
    "    we want to compute Monte Carlo estimates of the ELBO in parallel.\n",
    "    theta: global latent variable\n",
    "    z: local latent variable.\n",
    "    nu_mean_theta: variational mean for theta.\n",
    "    nu_sd_theta: variational standard deviation for theta.\n",
    "    nu_mean_z: variational mean for z.\n",
    "    nu_sd_z: variational standard deviation for z.\n",
    "    \"\"\"\n",
    "    log_q_theta = - torch.log(nu_sd_theta) - 1 / (2 * nu_sd_theta**2)\\\n",
    "                    * (theta - nu_mean_theta)**2\n",
    "    log_q_z = torch.sum(- torch.log(nu_sd_z) - 1 / (2 * nu_sd_z**2)\\\n",
    "                          * (z - nu_mean_z)**2, dim = 1)\n",
    "    return log_q_theta + log_q_z\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1cc084ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TEST: check that the vectorized and non-vectorized log densities return the same output.\n",
    "if(False):\n",
    "    theta = theta.to(device)\n",
    "    z = z.to(device)\n",
    "    nu_mean_theta = torch.randn(1).to(device)\n",
    "    nu_sd_theta = torch.exp(torch.randn(1, 1)).to(device)\n",
    "    nu_mean_z = torch.randn((n, 1)).to(device)\n",
    "    nu_sd_z = torch.exp(torch.randn((n, 1))).to(device)\n",
    "\n",
    "    print(log_joint(x, theta, z))\n",
    "    print(log_joint_v(x.reshape(n, 1), theta.reshape((1, 1)), z.reshape(1, n, 1)))\n",
    "\n",
    "\n",
    "    log_q_evaluated = log_q(theta, z.reshape(n, 1), nu_mean_theta, nu_sd_theta, nu_mean_z, nu_sd_z)\n",
    "\n",
    "    log_q_v_evaluated = log_q_v(theta, z.reshape(1, n, 1), nu_mean_theta,\n",
    "                                nu_sd_theta, nu_mean_z, nu_sd_z)\n",
    "\n",
    "    print(log_q_evaluated)\n",
    "    print(log_q_v_evaluated)\n",
    "\n",
    "    print(log_q_evaluated.shape)\n",
    "    print(log_q_v_evaluated.shape)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "5eb87eb3",
   "metadata": {},
   "source": [
    "### Model class for amortized VI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c4c9733b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Architecture for the inference network (for now stick to three layers.)\n",
    "inf_input_size = 1  # inference network only takes in x_i\n",
    "\n",
    "class MCElbo_AVI(torch.nn.Module):\n",
    "    \"\"\"\n",
    "    A neural network class for amortized VI. This class is designed to compute the ELBO\n",
    "    and store variational parameters.\n",
    "    \"\"\"\n",
    "    def __init__(self, inf_nn_width):\n",
    "        \"\"\"\n",
    "        Initiliaze the AVI class. The inference neural network takes in an input of size\n",
    "        inf_input_size, has two hidden layers, and produces an output of size 1. The linear\n",
    "        layers store both weights and biases (intercepts). The inference network outputs\n",
    "        the variational mean and standard deviation of q(z).\n",
    "        The variational mean and standard deviation, nu_mean_theta and nu_sd_theta, are \n",
    "        estimated seperately.\n",
    "        inf_nn_width: width of the inference neural network.\n",
    "        \"\"\"\n",
    "        super(MCElbo_AVI, self).__init__()\n",
    "\n",
    "        # variational parameters for q(theta) # ToDO: set initial value\n",
    "        self.nu_mean_theta = torch.nn.Parameter(torch.randn(1, 1), requires_grad = True)\n",
    "        self.nu_sd_theta_log = torch.nn.Parameter(torch.randn(1, 1), requires_grad = True)\n",
    "        \n",
    "        # define inference neural network for the mean\n",
    "        self.m1 = nn.Linear(inf_input_size, inf_nn_width)\n",
    "        self.m2 = nn.Linear(inf_nn_width, inf_nn_width)\n",
    "        self.m3 = nn.Linear(inf_nn_width, 1)\n",
    "        \n",
    "        # define inference neural network for the log sd\n",
    "        self.s1 = nn.Linear(inf_input_size, inf_nn_width)\n",
    "        self.s2 = nn.Linear(inf_nn_width, inf_nn_width)\n",
    "        self.s3 = nn.Linear(inf_nn_width, 1)\n",
    "\n",
    "        self.mc_samples = 100\n",
    "        \n",
    "    def forward_mean(self, x):\n",
    "        \"\"\"\n",
    "        Feeds observation x into the infernece network and returns the variational mean\n",
    "        of q(z).\n",
    "        \"\"\"\n",
    "        y = F.relu(self.m1(x))\n",
    "        y = F.relu(self.m2(y))\n",
    "        y = self.m3(y)\n",
    "        return y\n",
    "    \n",
    "    def forward_log_sd(self, x):\n",
    "        \"\"\"\n",
    "        Feeds observation z into the inference network and returns the variational log\n",
    "        stabdard deviation of q(z).\n",
    "        NOTE: no reason to do this operation and the above operation seperately.\n",
    "        Something to fix.\n",
    "        \"\"\"\n",
    "        y = F.relu(self.s1(x))\n",
    "        y = F.relu(self.s2(y))\n",
    "        y = self.s3(y)\n",
    "        return y\n",
    "    \n",
    "    def generate_rand(self, m):\n",
    "        \"\"\"\n",
    "        Uses reparam trick to draw sampls from q. Generates auxiliary variables from\n",
    "        a standard normal.\n",
    "        m: number of samples for Monte Carlo estimate of ELBO.\n",
    "        \"\"\"\n",
    "        eps_theta = torch.randn((m, 1)).to(device)\n",
    "        eps_z = torch.randn(m, n, 1).to(device)\n",
    "        return eps_theta, eps_z\n",
    "    \n",
    "    def reparam(self, eps_theta, eps_z, nu_mean_z, nu_sd_z):\n",
    "        \"\"\"\n",
    "        Transforms standard normal samples into draws from q(theta, z).\n",
    "        eps_theta: standard normal sample with same shape as theta.\n",
    "        eps_z: standard normal sample with same shape as z.\n",
    "        nu_mean_z: variational mean for q(z).\n",
    "        nu_sd_z: variational standard deviation for q(z).\n",
    "\n",
    "        NOTE: no need to pass variational parameters of q(theta) since these\n",
    "        are already stored in class.  \n",
    "        \"\"\"\n",
    "        return eps_theta.mul(torch.exp(self.nu_sd_theta_log)).add(self.nu_mean_theta),\\\n",
    "               eps_z.mul(nu_sd_z).add(nu_mean_z)\n",
    "    \n",
    "    def compute_elbo(self, x):\n",
    "        \"\"\"\n",
    "        Evaluate Monte Carlo estimator of ELBO (all calculations are parallelized).\n",
    "        x: observatiosn.\n",
    "        \"\"\"\n",
    "        nu_mean_z = self.forward_mean(x)\n",
    "        nu_sd_z = torch.exp(self.forward_log_sd(x))\n",
    "        eps_theta, eps_z = self.generate_rand(self.mc_samples)\n",
    "        theta, z = self.reparam(eps_theta, eps_z, nu_mean_z, nu_sd_z)\n",
    "\n",
    "        Elbo = log_joint_v(x, theta, z)\\\n",
    "            - log_q_v(theta, z, self.nu_mean_theta, torch.exp(self.nu_sd_theta_log),\n",
    "                      nu_mean_z, nu_sd_z)\n",
    "        return torch.mean(Elbo)\n",
    "    \n",
    "    # Additional function to create a common initialization with FVI\n",
    "    def FVI_param(self, x):\n",
    "        \"\"\"\n",
    "        Return variational parameters. For q(z), these are obtained using the\n",
    "        inference network.\n",
    "        \"\"\"\n",
    "        nu_mean_z = self.forward_mean(x)\n",
    "        nu_sd_z = self.forward_log_sd(x)\n",
    "        \n",
    "        return self.nu_mean_theta, self.nu_sd_theta_log, nu_mean_z, nu_sd_z\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "25a7af5d",
   "metadata": {},
   "source": [
    "### Factorized VI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8f68028e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_weights(m):\n",
    "    \"\"\"\n",
    "    Initialize the weights and biases to 0.\n",
    "    This amounts to starting with all q(z_i)'s a standard Gaussian.\n",
    "    \"\"\"\n",
    "    if isinstance(m, nn.Linear):\n",
    "        m.weight.data.fill_(0.01)\n",
    "        m.bias.data.fill_(0.01)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f855685c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialisation for FVI\n",
    "# Generate initial values for variational parameters and use them to initialize FVI.\n",
    "torch.manual_seed(1954)\n",
    "init_nn_width = 2\n",
    "model_av = MCElbo_AVI(init_nn_width).to(device)\n",
    "x = x.to(device)\n",
    "\n",
    "# NOTE: by default, parameters of the inference NN are initialized at the same value,\n",
    "# which means the elements of nu_mean_z and nu_sd_z_log have the same starting value.\n",
    "nu_mean_theta_init, nu_sd_theta_log_init,\\\n",
    "    nu_mean_z_init, nu_sd_z_log_init = model_av.FVI_param(x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a2cab152",
   "metadata": {},
   "outputs": [],
   "source": [
    "class MCElbo_FVI(nn.Module):\n",
    "    \"\"\"\n",
    "    A neural network class for facrtorized VI. This class is designed to compute the ELBO\n",
    "    and store variational parameters.\n",
    "    NOTE: Description of functions are the same as for MCElbo_AVI. These two should really\n",
    "    be a single class.\n",
    "    \"\"\"    \n",
    "    def __init__(self, nu_mean_theta_init, nu_sd_theta_log_init,\n",
    "                 nu_mean_z_init, nu_sd_z_log_init, const_z = False):\n",
    "        super(MCElbo_FVI, self).__init__()\n",
    "\n",
    "        self.const_z = const_z\n",
    "\n",
    "        # Use common initialization\n",
    "        self.nu_mean_theta = torch.nn.Parameter(nu_mean_theta_init, requires_grad = True)\n",
    "        self.nu_sd_theta_log = torch.nn.Parameter(nu_sd_theta_log_init, requires_grad = True)\n",
    "\n",
    "        if (const_z):\n",
    "            self.nu_mean_z = torch.nn.Parameter(nu_mean_z_init[0])\n",
    "            self.nu_sd_z_log = torch.nn.Parameter(nu_sd_z_log_init[0])\n",
    "        else:\n",
    "            self.nu_mean_z = torch.nn.Parameter(nu_mean_z_init, requires_grad = True)\n",
    "            self.nu_sd_z_log = torch.nn.Parameter(nu_sd_z_log_init, requires_grad = True)\n",
    "\n",
    "        self.mc_samples = 100\n",
    "    \n",
    "    def generate_rand(self, m):\n",
    "        eps_theta = torch.randn((m, 1)).to(device)\n",
    "        eps_z = torch.randn((m, n, 1)).to(device)\n",
    "        return eps_theta, eps_z\n",
    "\n",
    "    def reparam(self, eps_theta, eps_z, nu_sd_z_log, nu_mean_z):\n",
    "        return eps_theta.mul(torch.exp(self.nu_sd_theta_log)).add(self.nu_mean_theta),\\\n",
    "               eps_z.mul(torch.exp(nu_sd_z_log)).add(nu_mean_z)\n",
    "\n",
    "    def compute_elbo(self, x):\n",
    "        if self.const_z:\n",
    "            nu_mean_z = self.nu_mean_z.repeat((x.shape[0], 1))\n",
    "            nu_sd_z_log = self.nu_sd_z_log.repeat((x.shape[0], 1))\n",
    "        else:\n",
    "            nu_mean_z = self.nu_mean_z\n",
    "            nu_sd_z_log = self.nu_sd_z_log\n",
    "\n",
    "        eps_theta, eps_z = self.generate_rand(self.mc_samples)\n",
    "        theta, z = self.reparam(eps_theta, eps_z, nu_sd_z_log, nu_mean_z)\n",
    "\n",
    "        Elbo = log_joint_v(x, theta, z)\\\n",
    "          - log_q_v(theta, z, \n",
    "                    self.nu_mean_theta, torch.exp(self.nu_sd_theta_log),\n",
    "                    self.nu_mean_z, torch.exp(self.nu_sd_z_log))\n",
    "        return torch.mean(Elbo)       \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "cb00c3fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss (FVI):  tensor(-448985.6562, device='cuda:0', grad_fn=<MeanBackward0>)\n",
      "-----\n",
      "loss (AVI):  tensor(-599177.1250, device='cuda:0', grad_fn=<MeanBackward0>)\n"
     ]
    }
   ],
   "source": [
    "# Sanity check: make sure both models return the same ELBO (within Monte Carlo error)\n",
    "x = x.to(device)\n",
    "model = MCElbo_FVI(nu_mean_theta_init, nu_sd_theta_log_init,\n",
    "                   nu_mean_z_init, nu_sd_z_log_init).to(device)\n",
    "print(\"loss (FVI): \", model.compute_elbo(x))\n",
    "print(\"-----\")\n",
    "print(\"loss (AVI): \", model_av.compute_elbo(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "1bb46b46",
   "metadata": {},
   "outputs": [],
   "source": [
    "def vi_init(seed, init_manifold = True, init_nn_width = 2):\n",
    "    torch.manual_seed(seed)\n",
    "    if (init_manifold):\n",
    "        model_av = MCElbo_AVI(init_nn_width).to(device)\n",
    "        nu_mean_theta, nu_sd_theta_log,\\\n",
    "            nu_mean_z, nu_sd_z_log = model_av.FVI_param(x)\n",
    "    else:\n",
    "        nu_mean_theta = torch.randn((1, 1))\n",
    "        nu_sd_theta_log = torch.randn((1, 1))\n",
    "        nu_mean_z = torch.rand((n, 1))\n",
    "        nu_sd_z_log = torch.rand((n, 1))\n",
    "    \n",
    "    return nu_mean_theta, nu_sd_theta_log, nu_mean_z, nu_sd_z_log\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c58a3546",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss tensor(444824.3125)\n"
     ]
    }
   ],
   "source": [
    "seed = 1954\n",
    "torch.manual_seed(seed)\n",
    "init_manifold = False\n",
    "nu_mean_theta_init, nu_sd_theta_log_init, nu_mean_z_init, nu_sd_z_log_init\\\n",
    "        = vi_init(seed, init_manifold)\n",
    "\n",
    "model = MCElbo_FVI(nu_mean_theta_init, nu_sd_theta_log_init,\n",
    "                   nu_mean_z_init, nu_sd_z_log_init).to(device)\n",
    "\n",
    "n_iter_optimizer = 10\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr = 1e-2)\n",
    "loss_saved = torch.empty(n_iter_optimizer)\n",
    "\n",
    "print_output = True\n",
    "\n",
    "start_time = time.time()\n",
    "for i in range(n_iter_optimizer):\n",
    "        loss = - model.compute_elbo(x)\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        loss_saved[i] = loss.data\n",
    "        if (i % 5000 == 0 and print_output):\n",
    "            print(\"loss\", loss_saved[i])\n",
    "end_time = time.time()\n",
    "run_time = end_time - start_time\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "9d4935c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_fvi(seed, n_iter_optimizer, init_manifold = False, print_output = False, const_z = False):\n",
    "    torch.manual_seed(seed)\n",
    "    nu_mean_theta_init, nu_sd_theta_log_init, nu_mean_z_init, nu_sd_z_log_init\\\n",
    "        = vi_init(seed, init_manifold)\n",
    "\n",
    "    model = MCElbo_FVI(nu_mean_theta_init, nu_sd_theta_log_init,\n",
    "                       nu_mean_z_init, nu_sd_z_log_init, const_z).to(device)\n",
    "\n",
    "    optimizer = torch.optim.Adam(model.parameters(), lr = 1e-2)\n",
    "    loss_saved = torch.empty(n_iter_optimizer)\n",
    "\n",
    "    start_time = time.time()\n",
    "    for i in range(n_iter_optimizer):\n",
    "        loss = - model.compute_elbo(x)\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        loss_saved[i] = loss.data\n",
    "        if (i % 5000 == 0 and print_output):\n",
    "            print(\"loss\", loss_saved[i])\n",
    "    end_time = time.time()\n",
    "    run_time = end_time - start_time\n",
    "    return loss_saved, run_time\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "48a72353",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss tensor(32402.4824)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Do a single run and examine the result\n",
    "if (True):\n",
    "    seed = 1954\n",
    "    n_iter_optimizer = int(20e3)\n",
    "    loss_saved, time_fvi = run_fvi(seed, n_iter_optimizer)\n",
    "    print(\"loss\", loss_saved[n_iter_optimizer - 1].data)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "4576b6ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if True:\n",
    "    plt.plot(loss_saved, label = \"F-VI\")\n",
    "    plt.plot(loss_constant_saved, label = \"Const\")\n",
    "    plt.yscale(\"log\")\n",
    "    plt.xscale(\"log\")\n",
    "    plt.legend(loc = \"best\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "97aa18b4",
   "metadata": {},
   "source": [
    "### Amortized VI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "c04761d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_avi(seed, inf_nn_width, n_iter_optimizer, print_output = False):\n",
    "    torch.manual_seed(seed)\n",
    "    model_av = MCElbo_AVI(inf_nn_width).to(device)\n",
    "    \n",
    "    optimizer = torch.optim.Adam(model_av.parameters(), lr = 1e-2)\n",
    "    \n",
    "    loss_av_saved = torch.empty((n_iter_optimizer,)) # np.empty(n_iter_optimizer)\n",
    "\n",
    "    start_time = time.time()\n",
    "    for i in range(n_iter_optimizer):\n",
    "        loss_av = - model_av.compute_elbo(x)\n",
    "        optimizer.zero_grad()\n",
    "        loss_av.backward()\n",
    "        optimizer.step()\n",
    "        loss_av_saved[i] = loss_av.data\n",
    "        if i % 5000 == 0 and print_output:\n",
    "            print(\"loss\", loss_av_saved[i])\n",
    "    end_time = time.time()\n",
    "    run_time = end_time - start_time\n",
    "    return loss_av_saved, run_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "ccebf396",
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to run the experiments over multiple seeds\n",
    "def run_experiment(seed, n_iter_optimizer, nn_widths, init_manifold = False, include_fvi = True):\n",
    "    loss_all = torch.empty((n_iter_optimizer, 2 + nn_widths.size))\n",
    "    saved_times = np.empty(2 + nn_widths.size)\n",
    "\n",
    "    for i in range(nn_widths.size):\n",
    "        loss_avi, time_avi = run_avi(seed, nn_widths[i], n_iter_optimizer)\n",
    "        loss_all[:, i + 2] = loss_avi\n",
    "        saved_times[i + 2] = time_avi\n",
    "    \n",
    "    if include_fvi:\n",
    "        loss_fvi, time_fvi = run_fvi(seed, n_iter_optimizer, init_manifold)\n",
    "        loss_all[:, 0] = loss_fvi\n",
    "        saved_times[0] = time_fvi\n",
    "\n",
    "        loss_const, time_const = run_fvi(seed, n_iter_optimizer, init_manifold, const_z=True)\n",
    "        loss_all[:, 1] = loss_const\n",
    "        saved_times[1] = time_const\n",
    "\n",
    "\n",
    "    np.save(\"deliv/nonlin_loss_\" + str(seed) + \"_lock\" + str(init_manifold), loss_all.detach().numpy())\n",
    "    np.save(\"deliv/nonlin_time_\" + str(seed) + \"_lock\" + str(init_manifold), saved_times)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ca11ceb6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed:  1789\n",
      "seed:  1790\n",
      "seed:  1791\n",
      "seed:  1792\n",
      "seed:  1793\n",
      "seed:  1794\n",
      "seed:  1795\n",
      "seed:  1796\n",
      "seed:  1797\n",
      "seed:  1798\n"
     ]
    }
   ],
   "source": [
    "n_iter_optimizer = int(20e3)\n",
    "nn_widths = np.array([1, 2, 4, 8, 16, 24, 32])\n",
    "\n",
    "init_seed = 1789\n",
    "for i in range(10):\n",
    "    seed = init_seed + i\n",
    "    print(\"seed: \", seed)\n",
    "    run_experiment(seed, n_iter_optimizer, nn_widths = nn_widths, init_manifold = False)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "fe6802fc",
   "metadata": {},
   "source": [
    "## Analyze results\n",
    "Let's start by analyzing one realization of the experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5493f977",
   "metadata": {},
   "outputs": [],
   "source": [
    "# read saved input\n",
    "seed = 1797\n",
    "init_manifold = False\n",
    "loss_all = np.load(\"deliv/nonlin_loss_\" + str(seed) + \"_lock\" + str(init_manifold) + \".npy\")\n",
    "\n",
    "loss_saved = loss_all[:, 0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9d2ca796",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_773497/3623882381.py:1: MatplotlibDeprecationWarning: The seaborn styles shipped by Matplotlib are deprecated since 3.6, as they no longer correspond to the styles shipped by seaborn. However, they will remain available as 'seaborn-v0_8-<style>'. Alternatively, directly use the seaborn API instead.\n",
      "  plt.style.use('seaborn-white')  # seaborn-v0_8-white\n"
     ]
    }
   ],
   "source": [
    "plt.style.use('seaborn-white')  # seaborn-v0_8-white\n",
    "\n",
    "params = {'axes.labelsize': 18,'axes.titlesize':25, 'legend.fontsize': 20, 'xtick.labelsize': 15,\n",
    "          'ytick.labelsize': 15}\n",
    "plt.rcParams.update(params)\n",
    "\n",
    "linewidth = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6fce72e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig, ax =  plt.subplots()\n",
    "plotted_widths = np.array([1, 4, 16])\n",
    "\n",
    "\n",
    "ax.plot(loss_all[:, 1], label = 'Const', linewidth = linewidth, color = 'red')\n",
    "ax.plot(loss_all[:, 0], label = 'F-VI', linewidth = linewidth, color = 'black')\n",
    "nn_widths = np.array([1, 2, 4, 8, 16, 24, 32])\n",
    "for i in range(nn_widths.size):\n",
    "    if (nn_widths[i] in plotted_widths):\n",
    "        ax.plot(loss_all[:, i + 2], label = \"k = \" + str(nn_widths[i]), alpha = 0.5,\n",
    "                 linewidth = linewidth)\n",
    "plt.yscale(\"log\")\n",
    "plt.xscale(\"log\")\n",
    "plt.legend(loc = \"best\")\n",
    "plt.gca().invert_yaxis()\n",
    "plt.grid(which = 'minor', visible = 'true', c = 'grey', alpha = 0.25)\n",
    "plt.title(\"Nonlinear probabilistic model\")\n",
    "\n",
    "plt.savefig(\"to_discuss/elbo_nonlin_normal_\" + str(seed) + \".pdf\", bbox_inches='tight')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "049062f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_window(loss, index_center, window):\n",
    "    return np.mean(loss[(index_center - window):(index_center + window)])\n",
    "\n",
    "def sd_window(loss, index_center, window):\n",
    "    return np.std(loss[(index_center - window):(index_center + window)]) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "82d24d5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_iter_optimizer = int(20000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "357ba7b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FVI:  32399.064  +/-  4.291028\n",
      "Const:  36700.816  +/-  13.823418\n",
      "k = 1:  35638.93  +/-  4.291028\n",
      "k = 2:  32593.287  +/-  13.823418\n",
      "k = 4:  32511.203  +/-  16.640911\n",
      "k = 8:  32392.904  +/-  4.6295853\n",
      "k = 16:  32386.713  +/-  4.288995\n",
      "k = 24:  32385.643  +/-  4.221525\n",
      "k = 32:  nan  +/-  8.967478\n"
     ]
    }
   ],
   "source": [
    "# Get asymptotic ELBO\n",
    "window = 500\n",
    "index_center = n_iter_optimizer - window\n",
    "print(\"FVI: \", mean_window(loss_all[:, 0], index_center, window), \" +/- \",\n",
    "      sd_window(loss_all[:, 0], index_center, window))\n",
    "\n",
    "print(\"Const: \", mean_window(loss_all[:, 1], index_center, window), \" +/- \",\n",
    "      sd_window(loss_all[:, 1], index_center, window))\n",
    "\n",
    "for i in range(nn_widths.size):\n",
    "  print(\"k = \" + str(nn_widths[i]) + \": \", mean_window(loss_all[:, i + 2],\n",
    "        index_center, window), \" +/- \",\n",
    "        sd_window(loss_all[:, i], index_center, window))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ecf901e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Estimate of the convergence\n",
    "# If oracle = False, compare subsequent windows.\n",
    "def iter_convergence(loss, rel_tol = 0.01, init_iteration = 10, window = 10,\n",
    "                     grid = 10, max_iteration = 20000, oracle = True, set_target = 0):\n",
    "    iteration = init_iteration\n",
    "    tol = 0\n",
    "    diff = tol + 1\n",
    "    while(diff > tol and iteration < max_iteration):\n",
    "        iteration += grid\n",
    "        if (oracle):\n",
    "            target = set_target\n",
    "        else:\n",
    "            target = mean_window(loss, iteration - grid, window)\n",
    "\n",
    "        tol = rel_tol * abs(target)\n",
    "        diff = abs(mean_window(loss, iteration, window) - target)\n",
    "        # print(\"diff:\", diff)\n",
    "        # print(\"tol:\", tol)\n",
    "    return iteration\n",
    "\n",
    "# Q: should we report convergence to F-VI's solution or for each individual solution?\n",
    "def iter_conv_wrapper(loss, loss_benchmark, rel_tol = 0.01, window = 10):\n",
    "    return iter_convergence(loss, oracle = True, rel_tol = rel_tol,\n",
    "                            set_target = mean_window(loss_benchmark, 19500, window))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4f1afda4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FVI: 1440\n",
      "k = 1:  20000\n",
      "k = 2:  2140\n",
      "k = 4:  570\n",
      "k = 8:  910\n",
      "k = 16:  640\n",
      "k = 24:  330\n",
      "k = 32:  15910\n"
     ]
    }
   ],
   "source": [
    "print(\"FVI:\", iter_conv_wrapper(loss_all[:, 0], loss_all[:, 0]))\n",
    "for i in range(nn_widths.size):\n",
    "  print(\"k = \" + str(nn_widths[i]) + \": \",\n",
    "        iter_conv_wrapper(loss_all[:, i + 2], loss_all[:, 0]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "732f5429",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get results across multiple seeds\n",
    "init_seed = 1789\n",
    "num_seed = 10\n",
    "init_manifold = False\n",
    "n_algorithms = 9\n",
    "num_tol = 3\n",
    "rel_tol = np.array([0.5, 0.1, 0.01])\n",
    "\n",
    "iter_to_conv = np.empty((num_seed, n_algorithms, num_tol))\n",
    "Elbo_final = np.empty((num_seed, n_algorithms)) \n",
    "\n",
    "for i in range(num_seed):\n",
    "    loss_all = np.load(\"deliv/nonlin_loss_\" + str(init_seed + i) + \"_lock\" + str(init_manifold) + \".npy\")\n",
    "\n",
    "    for j in range(n_algorithms):\n",
    "        Elbo_final[i, j] = mean_window(loss_all[:, j], n_iter_optimizer - window, window)\n",
    "        for k in range(num_tol):\n",
    "            # Use F-VI as the benchmark for the asymptotic ELBO\n",
    "            iter_to_conv[i, j, k] = iter_conv_wrapper(loss_all[:, j], loss_all[:, 0], rel_tol[k])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3fb83d9b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "median iter:\n",
      " [[  180.   440.  1280.]\n",
      " [  165. 20000. 20000.]\n",
      " [   65. 20000. 20000.]\n",
      " [   60.   540. 20000.]\n",
      " [   40.   160.  1045.]\n",
      " [   20.    65.  1060.]\n",
      " [   20.    60.   555.]\n",
      " [   20.    65.   520.]\n",
      " [   25.    45.   250.]]\n",
      "min iter:\n",
      " [[  170.   410.  1200.]\n",
      " [   90. 20000. 20000.]\n",
      " [   20.  2330. 20000.]\n",
      " [   20.    50.  2140.]\n",
      " [   20.    20.   230.]\n",
      " [   20.    20.   110.]\n",
      " [   20.    40.   170.]\n",
      " [   20.    30.   160.]\n",
      " [   20.    20.    20.]]\n",
      "max iter:\n",
      " [[  250.   780.  2680.]\n",
      " [  310. 20000. 20000.]\n",
      " [20000. 20000. 20000.]\n",
      " [20000. 20000. 20000.]\n",
      " [20000. 20000. 20000.]\n",
      " [ 9020.  9080. 20000.]\n",
      " [20000. 20000. 20000.]\n",
      " [17930. 17930. 17930.]\n",
      " [15910. 20000. 20000.]]\n",
      "[3.23990402e+04 3.67008309e+04 3.96557605e+04 3.74381424e+04\n",
      " 3.93635100e+04 3.25944828e+04 8.15405111e+13            nan\n",
      "            nan]\n"
     ]
    }
   ],
   "source": [
    "print(\"median iter:\\n\", np.median(iter_to_conv, axis = 0))\n",
    "print(\"min iter:\\n\", np.min(iter_to_conv, axis = 0))\n",
    "print(\"max iter:\\n\", np.max(iter_to_conv, axis = 0))\n",
    "print(np.mean(Elbo_final, axis = 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9778c40a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([32398.86132812, 36700.09765625, 35638.7265625 , 32593.28710938,\n",
       "       32391.85546875, 32386.98632812, 32385.97851562, 32385.56835938,\n",
       "       32385.38476562])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get final Elbo\n",
    "np.nanmin(Elbo_final, axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "25e433a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "iter_to_conv_flat = np.transpose(iter_to_conv[:,:,2]).reshape(num_seed * n_algorithms)\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b7ec8044",
   "metadata": {},
   "outputs": [],
   "source": [
    "algo_names = np.array(\"F-VI\")\n",
    "algo_names = np.append(algo_names, \"const\")\n",
    "for i in range(n_algorithms - 2):\n",
    "    algo_names = np.append(algo_names, \"k=\" + str(nn_widths[i]))\n",
    "\n",
    "#algo_names = np.repeat(algo_names, num_seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "75057ef2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.scatter(x = algo_names, y = iter_to_conv_flat, color = \"black\", alpha = 0.25)\n",
    "\n",
    "plt.boxplot(iter_to_conv[:,:,2], labels=algo_names, patch_artist=True,\n",
    "             boxprops = dict(facecolor = \"lightblue\"), vert=False\n",
    "             )\n",
    "plt.xscale(\"log\")\n",
    "plt.grid(which='minor', visible='true', c='grey', alpha = 0.25)\n",
    "# plt.xticks(rotation=45)\n",
    "plt.gca().invert_yaxis()\n",
    "\n",
    "plt.title(\"Nonlinear probabilistic model\")\n",
    "plt.ylabel(\" \")\n",
    "plt.xlabel(\"Number of iterations to convergence\")\n",
    "\n",
    "plt.savefig(\"to_discuss/conv_nonlin_boxplot.pdf\", bbox_inches='tight')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "6bd455fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_data = [np.random.normal(0, std, size=100) for std in range(1, 4)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "29452c3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9, 10)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(np.transpose(iter_to_conv[:,:,2]))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.15"
  },
  "vscode": {
   "interpreter": {
    "hash": "5b7e68a6523d9654d119e3ab45bb2c5c51f02effa6643d52b99addcee48c066f"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}