Metropolis-Hastings sampler in PyTorch. Made to explore possibility of bayesian computation in PyTorch.

mhsampler-in-pytorch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from torch.autograd import Variable\n",
    "from scipy import stats\n",
    "import numpy as np\n",
    "import tqdm\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# from pymc3 examples\n",
    "# https://pymc-devs.github.io/pymc3/notebooks/getting_started.html\n",
    "\n",
    "np.random.seed(123)\n",
    "\n",
    "# True parameter values\n",
    "alpha, sigma = 1, 1\n",
    "beta = [1, 2.5]\n",
    "\n",
    "# Size of dataset\n",
    "size = 100\n",
    "\n",
    "# Predictor variable\n",
    "X1 = np.random.randn(size).astype(np.float32)\n",
    "X2 = (np.random.randn(size) * 0.2).astype(np.float32)\n",
    "\n",
    "# Simulate outcome variable\n",
    "Y = (alpha + beta[0]*X1 + beta[1]*X2 + np.random.randn(size)*sigma).astype(np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Distribution(nn.Parameter):\n",
    "    def __new__(cls, *args, **kwargs):\n",
    "        return super(Distribution, cls).__new__(cls, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Normal(Distribution):\n",
    "    def __init__(self, mu=0, sd=1, observed=False):\n",
    "        self(mu, sd, 1)\n",
    "        self.mu = mu\n",
    "        self.sd = sd\n",
    "        self.observed = observed\n",
    "        \n",
    "    @property\n",
    "    def sd(self):\n",
    "        return self._sd\n",
    "    \n",
    "    @sd.setter\n",
    "    def sd(self, value):\n",
    "        if isinstance(value, Variable):\n",
    "            self._sd = value\n",
    "            \n",
    "        else:\n",
    "            self._sd = Variable(torch.Tensor([value]))\n",
    "            \n",
    "    @property\n",
    "    def mu(self):\n",
    "        return self._mu\n",
    "    \n",
    "    @mu.setter\n",
    "    def mu(self, value):\n",
    "        if isinstance(value, Variable):\n",
    "            self._mu = value\n",
    "            \n",
    "        else:\n",
    "            self._mu = Variable(torch.Tensor([value]))\n",
    "    \n",
    "    def __call__(self, mu, sd, size=None):\n",
    "        self.mu = mu\n",
    "        self.sd = sd\n",
    "        \n",
    "        mu = self.mu.data.numpy()\n",
    "        sd = self.sd.data.numpy()\n",
    "\n",
    "        if size is not None:\n",
    "            data = stats.norm.rvs(mu, sd, size).astype(np.float32)\n",
    "        \n",
    "        else:\n",
    "            data = stats.norm.rvs(mu, sd).astype(np.float32)\n",
    "            \n",
    "        self.data = torch.from_numpy(data)\n",
    "            \n",
    "        return self\n",
    "    \n",
    "    def logp(self, x, mu=None, sd=None):\n",
    "        if mu is None:\n",
    "            mu = self.mu\n",
    "        \n",
    "        if sd is None:\n",
    "            sd = self.sd\n",
    "\n",
    "        if torch.min(sd.data < 0) > 0:\n",
    "            return -np.inf\n",
    "\n",
    "        return 0.5 * (torch.log(1 / (2 * np.pi * sd.expand_as(x) ** 2)) \\\n",
    "                      - (x - mu.expand_as(x)) ** 2 * (1 / sd.expand_as(x) ** 2))\n",
    "    \n",
    "class HalfNormal(Distribution):\n",
    "    def __init__(self, sd=1, observed=False):\n",
    "        self(sd, size=1)\n",
    "        self.observed = observed\n",
    "        \n",
    "    @property\n",
    "    def sd(self):\n",
    "        return self._sd\n",
    "    \n",
    "    @sd.setter\n",
    "    def sd(self, value):\n",
    "        if isinstance(value, Variable):\n",
    "            self._sd = value\n",
    "            \n",
    "        else:\n",
    "            self._sd = Variable(torch.Tensor([value]))\n",
    "    \n",
    "    def __call__(self, sd, size=None):\n",
    "        self.sd = sd\n",
    "        \n",
    "        sd = self.sd.data.numpy()\n",
    "            \n",
    "        if size is not None:\n",
    "            data = stats.halfnorm.rvs(scale=sd, size=size).astype(np.float32)\n",
    "        \n",
    "        else:\n",
    "            data = stats.halfnorm.rvs(scale=sd).astype(np.float32)\n",
    "\n",
    "        self.data = torch.from_numpy(data)\n",
    "            \n",
    "        return self\n",
    "    \n",
    "    def logp(self, x, sd=None):\n",
    "        if sd is None:\n",
    "            sd = self.sd\n",
    "        \n",
    "        if torch.min(sd.data < 0) > 0:\n",
    "            return -np.inf\n",
    "        \n",
    "        return 0.5 * torch.log(2 / (np.pi * sd ** 2)) - x ** 2 / (2 * sd ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Model(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        \n",
    "        self.alpha = Normal(0, 10)\n",
    "        self.beta1 = Normal(0, 10)\n",
    "        self.beta2 = Normal(0, 10)\n",
    "        self.sigma = HalfNormal(1)\n",
    "        self.Y = Normal(0, 1, observed=True)\n",
    "        \n",
    "    def forward(self, X1, X2):\n",
    "        line = self.alpha.expand_as(X1) + self.beta1.expand_as(X1) * X1 + self.beta2.expand_as(X2) * X2\n",
    "        \n",
    "        return self.Y(line, self.sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_params(model):\n",
    "    params = model.parameters()\n",
    "    latents = []\n",
    "    observed = []\n",
    "\n",
    "    for param in params:\n",
    "        if param.observed:\n",
    "            observed.append(param)\n",
    "\n",
    "        else:\n",
    "            latents.append(param)\n",
    "            \n",
    "    return latents, observed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logp(latents, observed, latent_val, observed_val, X):\n",
    "    log_latent = 0\n",
    "    log_likelihood = 0\n",
    "    \n",
    "    for id, latent in enumerate(latents):\n",
    "        latent.data = latent_val[id].data\n",
    "        \n",
    "    model(*X)\n",
    "    \n",
    "    for id, latent in enumerate(latents):\n",
    "        log_latent += latent.logp(latent_val[id])\n",
    "\n",
    "    for id, observe in enumerate(observed):\n",
    "        ll = observe.logp(observed_val[id]).sum()\n",
    "        log_likelihood += ll\n",
    "        \n",
    "    return log_latent + log_likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Model()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable containing:\n",
       "-149.7702\n",
       "[torch.FloatTensor of size 1]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init_a = Variable(torch.Tensor([1]))\n",
    "init_b1 = Variable(torch.Tensor([1]))\n",
    "init_b2 = Variable(torch.Tensor([2.5]))\n",
    "init_s = Variable(torch.Tensor([1]))\n",
    "\n",
    "o_v = [Variable(torch.from_numpy(Y))]\n",
    "x_v = [Variable(torch.from_numpy(X1)), Variable(torch.from_numpy(X2))]\n",
    "\n",
    "latent, observe = get_params(model)\n",
    "\n",
    "logp(latent, observe, [init_a, init_b1, init_b2, init_s], o_v, x_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sample(model, init, n_iter, X, Y):\n",
    "    latent, observe = get_params(model)\n",
    "    \n",
    "    lp_old = logp(latent, observe, init, Y, X).data.numpy()\n",
    "    sample_N = len(latent)\n",
    "    \n",
    "    chain = []\n",
    "    probs = []\n",
    "\n",
    "    accept = 0\n",
    "\n",
    "    current_sample = []\n",
    "    for i in init:\n",
    "        current_sample.append(i.clone())\n",
    "        \n",
    "    new_sample = []\n",
    "\n",
    "    for i in tqdm.trange(n_iter):\n",
    "        propose = torch.from_numpy((np.random.randn(sample_N) / 10).astype(np.float32))\n",
    "        \n",
    "        for no, i in enumerate(current_sample):\n",
    "            new_sample.append(Variable(i.data + propose[no]))\n",
    "\n",
    "        lp_new = logp(latent, observe, new_sample, Y, X).data.numpy()\n",
    "        accept_p = np.log(np.random.rand())\n",
    "        ratio = lp_new - lp_old\n",
    "\n",
    "        if np.isfinite(ratio) and lp_new - lp_old > accept_p:\n",
    "            lp_old = lp_new\n",
    "            \n",
    "            for no, i in enumerate(new_sample):\n",
    "                current_sample[no] = i\n",
    "\n",
    "            accept += 1\n",
    "            \n",
    "        new_sample = []\n",
    "\n",
    "        chain.append(torch.cat([sample.data for sample in current_sample]).numpy())\n",
    "        probs.append(lp_old)\n",
    "        \n",
    "    return chain, probs, accept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [00:19<00:00, 517.14it/s]\n"
     ]
    }
   ],
   "source": [
    "init_a = Variable(torch.Tensor([0.5]))\n",
    "init_b1 = Variable(torch.Tensor([0.5]))\n",
    "init_b2 = Variable(torch.Tensor([0.5]))\n",
    "init_s = Variable(torch.Tensor([0.5]))\n",
    "\n",
    "chain, probs, accept = sample(model, [init_a, init_b1, init_b2, init_s], 10000, x_v, o_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3754"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c_a = [c[0] for c in chain]\n",
    "c_b0 = [c[1] for c in chain]\n",
    "c_b1 = [c[2] for c in chain]\n",
    "c_s = [c[3] for c in chain]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZmUJqpRNR+m6ro5KB4GwZBRYmHgd1lg2nrNhrLRBGBJM2W5mIaB5enYHEw02P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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f57a963ee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axarr = plt.subplots(2, 2, figsize=(12, 6))\n",
    "\n",
    "axarr[0, 0].plot(c_a)\n",
    "axarr[0, 0].set_title('a')\n",
    "axarr[0, 1].plot(c_s)\n",
    "axarr[0, 1].set_title('s')\n",
    "axarr[1, 0].plot(c_b0)\n",
    "axarr[1, 0].set_title('b0')\n",
    "axarr[1, 1].plot(c_b1)\n",
    "axarr[1, 1].set_title('b1')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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N73QZ8xPg76vqm21Y35/RPZUD6KbTbkNSfgC8ji65/rm2+U/opmE/EHgw8Fbg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\nYEItSZIkDeD/AGUPZs8bDpZyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f57a9185da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axarr = plt.subplots(2, 2, figsize=(12, 6))\n",
    "\n",
    "axarr[0, 0].hist(c_a, bins=20)\n",
    "axarr[0, 0].set_title('a ' + str(np.mean(c_a)))\n",
    "axarr[0, 1].hist(c_s, bins=20)\n",
    "axarr[0, 1].set_title('s ' + str(np.mean(c_s)))\n",
    "axarr[1, 0].hist(c_b0, bins=20)\n",
    "axarr[1, 0].set_title('b0 ' + str(np.mean(c_b0)))\n",
    "axarr[1, 1].hist(c_b1, bins=20)\n",
    "axarr[1, 1].set_title('b1 ' + str(np.mean(c_b1)))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}