Pinkoi sharing material: Google Optimize and Bayesian estimation

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README.md

Pinkoi Sharing Material: Google Optimize and Bayesian Estimation

bayesian_update_demo.ipynb

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   "source": [
    "## Imports"
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   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interactive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper Functions"
   ]
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   "source": [
    "def normal_kernel(x, mean, sigma=1):\n",
    "    return np.exp(-(x-mean)**2/2*sigma**2)"
   ]
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   "cell_type": "code",
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   "source": [
    "# the prior\n",
    "def prior(mu, mu_mean, mu_sigma):\n",
    "    return normal_kernel(mu, mu_mean, mu_sigma)"
   ]
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   "cell_type": "code",
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   "source": [
    "# the likelihood\n",
    "def lh(x, mu):\n",
    "    return np.exp(-np.sum((x - mu)**2)/(2*10))"
   ]
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   "cell_type": "code",
   "execution_count": 7,
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   "source": [
    "# the data source\n",
    "def gen_data(num=10, mu=np.pi, sigma=1.0):\n",
    "    return sigma*np.random.randn(num) + mu"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## Basic Case"
   ]
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   "source": [
    "# Bayesian Updating\n",
    "num_iter = 150\n",
    "mus = np.linspace(-5, 5, 1000)\n",
    "init_mean = -3\n",
    "init_std = 1\n",
    "num_data = 5"
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    "post_dists = [prior(mus, init_mean, init_std)]\n",
    "for i in range(num_iter):\n",
    "    x = gen_data(num_data)\n",
    "    prior_d = post_dists[-1]\n",
    "    # compute posterior\n",
    "    post_d = np.array([pri*lh(x, mu) for pri, mu in zip(prior_d, mus)])\n",
    "    post_dists.append(post_d/post_d.sum()) # normalize posterior to make it a distribution"
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    "def plot(frame):\n",
    "    post_d = post_dists[frame]\n",
    "    plt.figure('dist')\n",
    "    plt.plot(mus, post_d)\n",
    "    plt.xlabel('$\\mu$')\n",
    "    plt.title('Posterio Distribution of $\\mu$')\n",
    "    plt.show()"
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    "interactive_plot = interactive(plot, frame=(0, len(post_dists)-1))\n",
    "interactive_plot.children[0].value=0"
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    "mus[post_dists[-1].argmax()]"
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   "cell_type": "markdown",
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   "source": [
    "## Source Data Distribution Shift"
   ]
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    "shift_at = 50\n",
    "num_iter = 400\n",
    "mus = np.linspace(-7, 7, 1000)\n",
    "init_mean = -5\n",
    "init_std = 1\n",
    "num_data = 5"
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    "post_dists = [prior(mus, init_mean, init_std)]\n",
    "for i in range(num_iter):\n",
    "    if i < shift_at:\n",
    "        x = gen_data(num_data, 1)\n",
    "    else:\n",
    "        x = gen_data(num_data, -1)\n",
    "    prior_d = post_dists[-1]\n",
    "    # compute posterior\n",
    "    post_d = np.array([pri*lh(x, mu) for pri, mu in zip(prior_d, mus)])\n",
    "    post_dists.append(post_d/post_d.sum()) # normalize posterior to make it a distribution"
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    "interactive_plot # Bayesian estimation is adaptive"
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