[Interactive] Bernoulli mass function (pmf) vs. RelaxedBernoulli density function (pdf).ipynb

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   "cell_type": "code",
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   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
      "  return f(*args, **kwds)\n",
      "/usr/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
      "  return f(*args, **kwds)\n",
      "/usr/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
      "  return f(*args, **kwds)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_n = 9\n",
    "probs = 0.8\n",
    "temperature = 0.5\n",
    "\n",
    "num_samples = 5000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('seaborn-colorblind')\n",
    "\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif', serif=['Lato'], size=16)\n",
    "plt.rc('animation', convert_path='/usr/bin/convert')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'TensorFlow version: 1.10.0'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'TensorFlow version: ' + tf.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.enable_eager_execution()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "golden_size = lambda width: (width, 2. * width / (1 + np.sqrt(5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = tf.linspace(0., 1., 1 << log_n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bernoulli"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description='probs', max=0.99, min=0.05, step=0.05), Output()), _…"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(probs=(0.05, 0.99, 0.05))\n",
    "def plot_bernoulli(probs):\n",
    "    \n",
    "    d = tfp.distributions.Bernoulli(probs=probs)\n",
    "    \n",
    "    fig, ax = plt.subplots(figsize=golden_size(8))\n",
    "\n",
    "    ax.set_title(r'$p(x) = \\mathrm{{Bernoulli}}(\\rho={:0.2f})$'.format(probs))\n",
    "\n",
    "    ax.plot(x.numpy(), d.prob(x).numpy(), linestyle='--')\n",
    "    ax.axvline(x=0., ymin=0., ymax=d.prob(0.).numpy(), marker='o', color='k')\n",
    "    ax.axvline(x=1., ymin=0., ymax=d.prob(1.).numpy(), marker='o', color='k')\n",
    "\n",
    "    ax.set_xlabel(r'$x$')\n",
    "\n",
    "    ax.set_ylabel(r'$p(x)$')\n",
    "    ax.set_ylim(0., 1.1)\n",
    "\n",
    "    plt.show()    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "model_id": "c6ef5ec09ff140fb98aa198aa30754d6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description='probs', max=0.99, min=0.05, step=0.05), Output()), _…"
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     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "@interact(probs=(0.05, 0.99, 0.05))\n",
    "def plot_bernoulli_samples(probs):\n",
    "\n",
    "    d = tfp.distributions.Bernoulli(probs=probs)\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=golden_size(8))\n",
    "\n",
    "    ax.set_title(r'$p(x) = \\mathrm{{Bernoulli}}(\\rho={:0.2f})$'.format(probs))\n",
    "    \n",
    "    sns.distplot(d.sample(num_samples), kde=False, hist=True, ax=ax)\n",
    "\n",
    "    ax.set_ylim(0, num_samples)\n",
    "    ax.set_ylabel('nbr. of samples')\n",
    "    ax.set_xlabel(r'$x$')\n",
    "\n",
    "    plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Relaxed Bernoulli (Binary Concrete)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description='probs', max=0.99, min=0.05, step=0.05), FloatSlider(…"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(probs=(0.05, 0.99, 0.05), temperature=(0.01, 3.0, 0.1))\n",
    "def plot_relaxed_bernoulli(probs, temperature):\n",
    "\n",
    "    d = tfp.distributions.RelaxedBernoulli(probs=probs, temperature=temperature)\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=golden_size(8))\n",
    "\n",
    "    ax.set_title(r'$p(x) = \\mathrm{{BinConcrete}}(\\rho={:0.2f}, \\tau={:0.2f})$'.format(probs, temperature))\n",
    "\n",
    "    ax.plot(x.numpy(), d.prob(x).numpy())\n",
    "\n",
    "    ax.set_xlabel(r'$x$')\n",
    "\n",
    "    ax.set_ylabel(r'$p(x)$')\n",
    "    ax.set_ylim(0., 5.)\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description='probs', max=0.99, min=0.05, step=0.05), FloatSlider(…"
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     },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(probs=(0.05, 0.99, 0.05), temperature=(0.01, 3.0, 0.1))\n",
    "def plot_relaxed_bernoulli_samples(probs, temperature):\n",
    "\n",
    "    d = tfp.distributions.RelaxedBernoulli(probs=probs, temperature=temperature)\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=golden_size(8))\n",
    "\n",
    "    ax.set_title(r'$p(x) = \\mathrm{{BinConcrete}}(\\rho={:0.2f}, \\tau={:0.2f})$'.format(probs, temperature))\n",
    "\n",
    "    sns.distplot(d.sample(num_samples), kde=False, hist=True, ax=ax)\n",
    "    \n",
    "    ax.set_ylim(0, num_samples)\n",
    "    ax.set_ylabel('nbr. of samples')\n",
    "    ax.set_xlabel(r'$x$')\n",
    "\n",
    "    plt.show()"
   ]
  }
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