SCGExperiment.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils.func_utils import accept, jacobian, autocovariance, get_log_likelihood, \\\n",
    "    get_data, binarize, normal_kl, acl_spectrum, ESS\n",
    "from utils.distributions import Gaussian, GMM, GaussianFunnel, gen_ring\n",
    "from utils.layers import Linear, Sequential, Zip, Parallel, ScaleTanh\n",
    "from utils.dynamics import Dynamics\n",
    "from utils.sampler import propose\n",
    "from utils.notebook_utils import get_hmc_samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Network architecture\n",
    "\n",
    "We define the network architecture for our L2HMC network. We first embed the first two variables ($\\{x, \\partial_x U\\}$ or $\\{v, x_m\\}$) as well as the time, formatted as $\\tau(t) = \\left(\\cos(\\frac{2\\pi t}{M}), \\sin(\\frac{2\\pi t}{M})\\right)$. They are forwarded through an MLP and then produce $S, T$ and $Q$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def network(x_dim, scope, factor):\n",
    "    with tf.variable_scope(scope):\n",
    "        net = Sequential([\n",
    "            Zip([\n",
    "                Linear(x_dim, 10, scope='embed_1', factor=1.0 / 3),\n",
    "                Linear(x_dim, 10, scope='embed_2', factor=factor * 1.0 / 3),\n",
    "                Linear(2, 10, scope='embed_3', factor=1.0 / 3),\n",
    "                lambda _: 0.,\n",
    "            ]),\n",
    "            sum,\n",
    "            tf.nn.relu,\n",
    "            Linear(10, 10, scope='linear_1'),\n",
    "            tf.nn.relu,\n",
    "            Parallel([\n",
    "                Sequential([\n",
    "                    Linear(10, x_dim, scope='linear_s', factor=0.001), \n",
    "                    ScaleTanh(x_dim, scope='scale_s')\n",
    "                ]),\n",
    "                Linear(10, x_dim, scope='linear_t', factor=0.001),\n",
    "                Sequential([\n",
    "                    Linear(10, x_dim, scope='linear_f', factor=0.001),\n",
    "                    ScaleTanh(x_dim, scope='scale_f'),\n",
    "                ])\n",
    "            ])  \n",
    "        ])\n",
    "        \n",
    "    return net"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribution\n",
    "\n",
    "We define our energy function. It is a Gaussian distribution with zero mean. The covariance is a $\\pi/4$ rotation of the eigenvalues $[100, 10^{-1}]$. We set up our dynamics which take as input our energy function, the number of time step of our operator, the (learnable) step-size and our architecture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0 float64\n"
     ]
    }
   ],
   "source": [
    "x_dim = 2\n",
    "mu = np.zeros(2,)\n",
    "cov = np.array([[50.05, -49.95], [-49.95, 50.05]])\n",
    "\n",
    "distribution = Gaussian(mu, cov)\n",
    "dynamics = Dynamics(x_dim, distribution.get_energy_function(), T=10, eps=0.1, net_factory=network)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can directly sample from this distribution and plot it for sanity-check."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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mhXK3zIJN7+vNXTGrv6+X++ef3IISmVm3cg2/YJ5mwczahWv4Batn8ZQSL6JiZs3kgD8B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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f760b575b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "S = distribution.get_samples(200)\n",
    "plt.title('Strongly Correlated Gaussian (SCG)')\n",
    "plt.scatter(S[:, 0], S[:, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We set up the loss on both $p(\\xi)$ (here `x`) and $q(\\xi)$ (here `z`). We then train with Adam with a learning rate of $10^{-3}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = tf.placeholder(tf.float32, shape=(None, x_dim))\n",
    "z = tf.random_normal(tf.shape(x))\n",
    "\n",
    "Lx, _, px, output = propose(x, dynamics, do_mh_step=True)\n",
    "Lz, _, pz, _ = propose(z, dynamics, do_mh_step=False)\n",
    "\n",
    "loss = 0.\n",
    "\n",
    "v1 = (tf.reduce_sum(tf.square(x - Lx), axis=1) * px) + 1e-4\n",
    "v2 = (tf.reduce_sum(tf.square(z - Lz), axis=1) * pz) + 1e-4\n",
    "scale = 0.1\n",
    "\n",
    "loss += scale * (tf.reduce_mean(1.0 / v1) + tf.reduce_mean(1.0 / v2))\n",
    "loss += (- tf.reduce_mean(v1) - tf.reduce_mean(v2)) / scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "global_step = tf.Variable(0., name='global_step', trainable=False)\n",
    "learning_rate = tf.train.exponential_decay(1e-3, global_step, 1000, 0.96, staircase=True)\n",
    "optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)\n",
    "train_op = optimizer.minimize(loss, global_step=global_step)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training loop described in Algorithm $1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step: 0 / 5000, Loss: -8.53e+01, Acceptance sample: 0.90, LR: 0.00100\n",
      "Step: 100 / 5000, Loss: -1.81e+02, Acceptance sample: 0.71, LR: 0.00100\n",
      "Step: 200 / 5000, Loss: -3.95e+02, Acceptance sample: 0.52, LR: 0.00100\n",
      "Step: 300 / 5000, Loss: -3.81e+03, Acceptance sample: 0.29, LR: 0.00100\n",
      "Step: 400 / 5000, Loss: -5.68e+03, Acceptance sample: 0.40, LR: 0.00100\n",
      "Step: 500 / 5000, Loss: -5.11e+03, Acceptance sample: 0.36, LR: 0.00100\n",
      "Step: 600 / 5000, Loss: -7.86e+03, Acceptance sample: 0.36, LR: 0.00100\n",
      "Step: 700 / 5000, Loss: -6.44e+03, Acceptance sample: 0.43, LR: 0.00100\n",
      "Step: 800 / 5000, Loss: -6.91e+03, Acceptance sample: 0.38, LR: 0.00100\n",
      "Step: 900 / 5000, Loss: -7.25e+03, Acceptance sample: 0.38, LR: 0.00100\n",
      "Step: 1000 / 5000, Loss: -8.84e+03, Acceptance sample: 0.42, LR: 0.00096\n",
      "Step: 1100 / 5000, Loss: -8.59e+03, Acceptance sample: 0.38, LR: 0.00096\n",
      "Step: 1200 / 5000, Loss: -6.43e+03, Acceptance sample: 0.42, LR: 0.00096\n",
      "Step: 1300 / 5000, Loss: -8.85e+03, Acceptance sample: 0.41, LR: 0.00096\n",
      "Step: 1400 / 5000, Loss: -7.26e+03, Acceptance sample: 0.41, LR: 0.00096\n",
      "Step: 1500 / 5000, Loss: -8.91e+03, Acceptance sample: 0.41, LR: 0.00096\n",
      "Step: 1600 / 5000, Loss: -8.43e+03, Acceptance sample: 0.43, LR: 0.00096\n",
      "Step: 1700 / 5000, Loss: -8.09e+03, Acceptance sample: 0.41, LR: 0.00096\n",
      "Step: 1800 / 5000, Loss: -9.05e+03, Acceptance sample: 0.46, LR: 0.00096\n",
      "Step: 1900 / 5000, Loss: -8.33e+03, Acceptance sample: 0.47, LR: 0.00096\n",
      "Step: 2000 / 5000, Loss: -8.38e+03, Acceptance sample: 0.45, LR: 0.00092\n",
      "Step: 2100 / 5000, Loss: -7.62e+03, Acceptance sample: 0.45, LR: 0.00092\n",
      "Step: 2200 / 5000, Loss: -9.87e+03, Acceptance sample: 0.44, LR: 0.00092\n",
      "Step: 2300 / 5000, Loss: -7.12e+03, Acceptance sample: 0.45, LR: 0.00092\n",
      "Step: 2400 / 5000, Loss: -1.06e+04, Acceptance sample: 0.42, LR: 0.00092\n",
      "Step: 2500 / 5000, Loss: -8.92e+03, Acceptance sample: 0.45, LR: 0.00092\n",
      "Step: 2600 / 5000, Loss: -9.62e+03, Acceptance sample: 0.40, LR: 0.00092\n",
      "Step: 2700 / 5000, Loss: -8.36e+03, Acceptance sample: 0.46, LR: 0.00092\n",
      "Step: 2800 / 5000, Loss: -1.03e+04, Acceptance sample: 0.47, LR: 0.00092\n",
      "Step: 2900 / 5000, Loss: -1.11e+04, Acceptance sample: 0.47, LR: 0.00092\n",
      "Step: 3000 / 5000, Loss: -7.69e+03, Acceptance sample: 0.46, LR: 0.00088\n",
      "Step: 3100 / 5000, Loss: -1.04e+04, Acceptance sample: 0.43, LR: 0.00088\n",
      "Step: 3200 / 5000, Loss: -9.23e+03, Acceptance sample: 0.45, LR: 0.00088\n",
      "Step: 3300 / 5000, Loss: -1.05e+04, Acceptance sample: 0.49, LR: 0.00088\n",
      "Step: 3400 / 5000, Loss: -1.03e+04, Acceptance sample: 0.46, LR: 0.00088\n",
      "Step: 3500 / 5000, Loss: -7.31e+03, Acceptance sample: 0.43, LR: 0.00088\n",
      "Step: 3600 / 5000, Loss: -9.99e+03, Acceptance sample: 0.44, LR: 0.00088\n",
      "Step: 3700 / 5000, Loss: -1.03e+04, Acceptance sample: 0.40, LR: 0.00088\n",
      "Step: 3800 / 5000, Loss: -8.73e+03, Acceptance sample: 0.48, LR: 0.00088\n",
      "Step: 3900 / 5000, Loss: -9.78e+03, Acceptance sample: 0.45, LR: 0.00088\n",
      "Step: 4000 / 5000, Loss: -1.02e+04, Acceptance sample: 0.43, LR: 0.00085\n",
      "Step: 4100 / 5000, Loss: -8.87e+03, Acceptance sample: 0.44, LR: 0.00085\n",
      "Step: 4200 / 5000, Loss: -9.07e+03, Acceptance sample: 0.44, LR: 0.00085\n",
      "Step: 4300 / 5000, Loss: -8.29e+03, Acceptance sample: 0.46, LR: 0.00085\n",
      "Step: 4400 / 5000, Loss: -1.10e+04, Acceptance sample: 0.44, LR: 0.00085\n",
      "Step: 4500 / 5000, Loss: -9.78e+03, Acceptance sample: 0.49, LR: 0.00085\n",
      "Step: 4600 / 5000, Loss: -9.69e+03, Acceptance sample: 0.47, LR: 0.00085\n",
      "Step: 4700 / 5000, Loss: -7.73e+03, Acceptance sample: 0.48, LR: 0.00085\n",
      "Step: 4800 / 5000, Loss: -1.06e+04, Acceptance sample: 0.44, LR: 0.00085\n",
      "Step: 4900 / 5000, Loss: -1.01e+04, Acceptance sample: 0.49, LR: 0.00085\n"
     ]
    }
   ],
   "source": [
    "n_steps = 5000\n",
    "n_samples = 200\n",
    "\n",
    "samples = np.random.randn(n_samples, x_dim)\n",
    "\n",
    "sess = tf.Session()\n",
    "sess.run(tf.global_variables_initializer())\n",
    "\n",
    "for t in range(n_steps):\n",
    "    _, loss_, samples, px_, lr_ = sess.run([\n",
    "        train_op,\n",
    "        loss,\n",
    "        output[0],\n",
    "        px,\n",
    "        learning_rate,\n",
    "    ], {x: samples})\n",
    "\n",
    "    if t % 100 == 0:\n",
    "        print 'Step: %d / %d, Loss: %.2e, Acceptance sample: %.2f, LR: %.5f' % (t, n_steps, loss_, np.mean(px_), lr_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After training, we generate $200$ chains for $2000$ steps for evaluation purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = distribution.get_samples(n=n_samples)\n",
    "final_samples = []\n",
    "\n",
    "for t in range(2000):\n",
    "    final_samples.append(np.copy(samples))\n",
    "\n",
    "    feed_dict = {\n",
    "        x: samples,\n",
    "    }\n",
    "\n",
    "    samples = sess.run(output[0], feed_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We compute the HMC chains with **auto-correlation spectrums** as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "L2HMC_samples = np.array(final_samples)\n",
    "HMC_samples_1 = get_hmc_samples(2, 0.1, distribution.get_energy_function(), sess, steps=2000, samples=samples)\n",
    "HMC_samples_2 = get_hmc_samples(2, 0.15, distribution.get_energy_function(), sess, steps=2000, samples=samples)\n",
    "HMC_samples_3 = get_hmc_samples(2, 0.2, distribution.get_energy_function(), sess, steps=2000, samples=samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "scale = np.sqrt(np.trace(cov))\n",
    "L2HMC = acl_spectrum(L2HMC_samples, scale=scale)\n",
    "HMC1 = acl_spectrum(HMC_samples_1, scale=scale)\n",
    "HMC2 = acl_spectrum(HMC_samples_2, scale=scale)\n",
    "HMC3 = acl_spectrum(HMC_samples_3, scale=scale)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot auto-correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GqV/WnyxzkZ6VZylsqlYlasuWZyYFgNdqvMbGkI18evhTlrVZltbEBwBbFxi2E/bNgx3T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\nqmhR0Gg0Gk0VLQoajUajqfL/AfGnMqa76vP6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7494076e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xaxis = 10 * np.arange(300)\n",
    "plt.plot(xaxis, L2HMC[:300], label='L2HMC')\n",
    "plt.plot(xaxis, HMC1[:300], label='HMC $\\epsilon=0.1$')\n",
    "plt.plot(xaxis, HMC2[:300], label='HMC $\\epsilon=0.15$')\n",
    "plt.plot(xaxis, HMC3[:300], label='HMC $\\epsilon=0.2$')\n",
    "plt.ylabel('Auto-correlation')\n",
    "plt.xlabel('Gradient Computations')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now compute the **Effective Sample Size** (ESS)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ESS L2HMC: 2.61e-01 -- ESS HMC: 5.63e-03 -- Ratio: 46\n"
     ]
    }
   ],
   "source": [
    "print 'ESS L2HMC: %.2e -- ESS HMC: %.2e -- Ratio: %d' % (ESS(L2HMC), ESS(HMC2), ESS(L2HMC) / ESS(HMC2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize a single chain of L2HMC for $50$ time steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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la2V84pWZTej09Fzg1XS9lojsN3fW1B4jeXxew+cxLt/0TS7fNLfHOeW+FnBQ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\nEP8fYAhuDNW7UV8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f744c0e4a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(S[:, 0], S[:, 1])\n",
    "plt.plot(L2HMC_samples[:50, 1, 0], L2HMC_samples[:50, 1, 1], color='orange', marker='o', alpha=0.8)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}