Gaussian_example_jax.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Gaussian_example_jax.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "TPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/vicgalle/sgmcmc-force/blob/master/Gaussian_example_jax.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5CTEVmyKmkfp",
        "colab_type": "code",
        "outputId": "acd11e7e-c8f1-4b6a-f940-9f9951b94c0d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "# Grab newest JAX version.\n",
        "!pip install --upgrade -q jax==0.1.54 jaxlib==0.1.37\n",
        "\n",
        "use_tpu = True\n",
        "if use_tpu:\n",
        "# Make sure the Colab Runtime is set to Accelerator: TPU.\n",
        "  import requests\n",
        "  import os\n",
        "  if 'TPU_DRIVER_MODE' not in globals():\n",
        "    url = 'http://' + os.environ['COLAB_TPU_ADDR'].split(':')[0] + ':8475/requestversion/tpu_driver_nightly'\n",
        "    resp = requests.post(url)\n",
        "    TPU_DRIVER_MODE = 1\n",
        "\n",
        "  # The following is required to use TPU Driver as JAX's backend.\n",
        "  from jax.config import config\n",
        "  config.FLAGS.jax_xla_backend = \"tpu_driver\"\n",
        "  config.FLAGS.jax_backend_target = \"grpc://\" + os.environ['COLAB_TPU_ADDR']\n",
        "  print(config.FLAGS.jax_backend_target)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[K     |████████████████████████████████| 256kB 3.4MB/s \n",
            "\u001b[K     |████████████████████████████████| 25.4MB 1.2MB/s \n",
            "\u001b[?25h  Building wheel for jax (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "grpc://10.5.67.234:8470\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "27TqNtiQF97X",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import jax\n",
        "import jax.numpy as np\n",
        "from jax import random\n",
        "\n",
        "key = random.PRNGKey(0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cRWoxSCNGU4o",
        "colab_type": "code",
        "outputId": "3c6c6ad5-6c83-43aa-ba40-0bd01acc0517",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "source": [
        "d = 2\n",
        "N = 6\n",
        "\n",
        "key, subkey = random.split(key)\n",
        "x0 = 3. + 0.25*random.normal(key, (N, d))\n",
        "print(x0)"
      ],
      "execution_count": 134,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[3.2593813 3.1996868]\n",
            " [2.9687963 3.0197053]\n",
            " [3.0067084 3.0664346]\n",
            " [2.8299875 3.3063397]\n",
            " [2.9118252 2.6788821]\n",
            " [3.0338914 3.0519772]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GlH-PZjUFjTl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "eta = 0.01\n",
        "s = 1.\n",
        "h = 2*s**2\n",
        "\n",
        "def K(x):\n",
        "    xmx = np.expand_dims(x, 0) - np.expand_dims(x, 1)\n",
        "    norm = np.einsum('ijk,ijk->ij', xmx, xmx)\n",
        "    return np.exp(-(norm)/h)\n",
        "\n",
        "def g_K(x):\n",
        "    # we avoid calling autograd since the function is non-scalar, for better efficiency\n",
        "    xmx = np.expand_dims(x, 0) - np.expand_dims(x, 1)\n",
        "    return np.expand_dims(K(x), -1) * (2.*xmx/h)\n",
        "\n",
        "def logp(x):\n",
        "    # in this simple case we can sum everything...\n",
        "    return -np.sum(x**2)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vcfwWB9IFjkP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from jax import grad, jit\n",
        "\n",
        "def svgd(x0, logp, T = 100):\n",
        "    \n",
        "    x = x0\n",
        "    g_logp = grad(logp)\n",
        "    xs = [x0]\n",
        "\n",
        "    update_svgd = jit( lambda x : K(x) @ g_logp(x) + g_K(x).sum(0) ) \n",
        "\n",
        "    for i in range(T):\n",
        "        x = x + eta * update_svgd(x)   \n",
        "        xs.append(x)\n",
        "    return x, np.asarray(xs)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PPORLz1tFjsP",
        "colab_type": "code",
        "outputId": "8c520a14-c27d-4fdf-aa0a-1917bf3347b9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "source": [
        "x, xs = svgd(x0, logp, T=200)\n",
        "x"
      ],
      "execution_count": 137,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DeviceArray([[ 1.001397  ,  0.44423074],\n",
              "             [-0.9243896 , -0.38732374],\n",
              "             [-0.30366102, -0.00298705],\n",
              "             [-0.31783342,  1.0628091 ],\n",
              "             [ 0.48936245, -0.9865278 ],\n",
              "             [ 0.19265223, -0.05246079]], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 137
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NlEk7asBFj9K",
        "colab_type": "code",
        "outputId": "c03c765d-d10e-43bb-8d4e-747a40725b15",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "xs.mean(), xs[:, :, 0].std(), xs[:, :, 1].std()"
      ],
      "execution_count": 138,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(DeviceArray(0.18421564, dtype=float32),\n",
              " DeviceArray(0.6957327, dtype=float32),\n",
              " DeviceArray(0.73811656, dtype=float32))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 138
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tst2wYgVFklc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sgldr(x0, logp, T = 100, key = key):\n",
        "    \n",
        "    x = x0\n",
        "    g_logp = grad(logp)\n",
        "    xs = [x0]\n",
        "\n",
        "    update_sgldr = jit( lambda x, key : ( eta * ( K(x) @ g_logp(x) + g_K(x).sum(0)) + np.linalg.cholesky(2 * eta * K(x)) @ random.normal(key, (N, d)), random.split(key)[0] ) )\n",
        "\n",
        "    for i in range(T):\n",
        "        x_upd, key = update_sgldr(x, key)\n",
        "        x = x + x_upd\n",
        "        xs.append(x)\n",
        "    return x, np.asarray(xs)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F-f3gpFcFk59",
        "colab_type": "code",
        "outputId": "3a8e00cc-a126-4e79-9bda-6af126aacd5d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "source": [
        "x, xs_sgldr = sgldr(x0, logp, 200, key)\n",
        "x"
      ],
      "execution_count": 140,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DeviceArray([[ 0.7705375 ,  0.04373644],\n",
              "             [-1.867171  ,  0.7200786 ],\n",
              "             [ 0.5204219 , -0.44146377],\n",
              "             [ 0.3483814 ,  0.9848946 ],\n",
              "             [-0.61981845, -0.9191437 ],\n",
              "             [ 1.2486017 , -0.43471223]], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 140
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z2Kd4AFwFkw9",
        "colab_type": "code",
        "outputId": "6b27f753-38d5-4028-949b-9c88945b3dae",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "plt.plot(xs[:, :,0], xs[:, :,1], 'k-')\n",
        "plt.plot(xs_sgldr[:, :,0], xs_sgldr[:, :,1], 'c', alpha=0.4)\n",
        "\n",
        "from matplotlib.lines import Line2D\n",
        "colors = ['black', 'cyan']\n",
        "lines = [Line2D([0], [0], color=c, linewidth=2, linestyle='-') for c in colors]\n",
        "labels = ['SVGD', 'SGLD+R']\n",
        "plt.legend(lines, labels)\n",
        "\n",
        "plt.axis('equal');\n",
        "\n",
        "\n",
        "plt.savefig('svgd_vs_sgldr.png', dpi=300)\n",
        "\n",
        "from google.colab import files\n",
        "files.download('svgd_vs_sgldr.png')"
      ],
      "execution_count": 144,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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59913A+e8/PHHzPnrL/RK8s9Vua2EXAhRpLClfyu3wi2m8O/A5vNx0G7njMtFY7OZ1StX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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6ngqM6H5FkPb",
        "colab_type": "code",
        "outputId": "07dc0d33-d9ea-483f-ef5c-fda0ea775960",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "xs_sgldr.mean(), xs_sgldr[:, :, 0].std(), xs_sgldr[:, :, 1].std()"
      ],
      "execution_count": 142,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(DeviceArray(0.0837023, dtype=float32),\n",
              " DeviceArray(0.8976763, dtype=float32),\n",
              " DeviceArray(0.86983895, dtype=float32))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 142
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pPB49uYEj3ZF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}