dp.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Stochaskell, version 0.1.0\n",
       "Copyright (C) 2015-2020 David A Roberts\n",
       "This program comes with ABSOLUTELY NO WARRANTY.\n",
       "This is free software, and you are welcome to redistribute it\n",
       "under certain conditions; see the LICENSE for details.\n",
       "\n",
       "Using installation directory at \n",
       "  /home/jovyan/stochaskell"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "{-# LANGUAGE FlexibleContexts, MonadComprehensions, NoImplicitPrelude, RebindableSyntax #-}\n",
    "import Language.Stochaskell\n",
    "stochaskell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "pickStick :: RVec -> P Z\n",
    "pickStick sticks = do\n",
    "  stick <- pmf (pickStickPMF sticks)\n",
    "  return stick\n",
    "\n",
    "pickStickPMF :: RVec -> RVec\n",
    "pickStickPMF sticks =\n",
    "  let sticks' = vector [ 1 - (sticks!i) | i <- 1...infinity ]\n",
    "      rems = scanlE (*) 1 sticks'\n",
    "      probs = vector [ (sticks!i) * (rems!i) | i <- 1...infinity ]\n",
    "  in probs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "dp :: R -> P R -> P (P R)\n",
    "dp alpha proc = do\n",
    "  sticks <- joint vector [ beta 1 alpha | i <- 1...infinity ] :: P RVec\n",
    "  atoms  <- joint vector [ proc         | i <- 1...infinity ]\n",
    "  let randomDistribution = do\n",
    "        stick <- pickStick sticks\n",
    "        return (atoms!stick)\n",
    "  return randomDistribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "dpmm :: Z -> P RVec\n",
    "dpmm n = do\n",
    "  let base = uniform 0 100\n",
    "  paramDist <- dp 5 base\n",
    "  params <- joint vector [ paramDist | j <- 1...n ]\n",
    "  values <- joint vector [ normal (params!j) 1 | j <- 1...n ]\n",
    "  return values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "--- Generating Church code ---\n",
       "(define (pmf probs)\n",
       "  (letrec ((go (lambda (j u)\n",
       "                 (if (<= u (probs j)) j\n",
       "                     (go (+ j 1) (- u (probs j)))))))\n",
       "    (go 1 (uniform 0 1))))\n",
       "(define (bernoulli p) (if (flip p) 1 0))\n",
       "\n",
       "(define (model) (letrec (\n",
       "  \n",
       "  \n",
       "  (v_0_2 (mem (lambda (i_1_1) (letrec (\n",
       "    (v_1_0 (- 1 (x_church_0_0 i_1_1))))\n",
       "    v_1_0))))\n",
       "  (v_0_3 (mem (lambda (i_1_0) (if (= 1 i_1_0) 1 (letrec (\n",
       "    (i_1_11 (v_0_2 (- i_1_0 1)))\n",
       "    (i_1_12 (v_0_3 (- i_1_0 1)))\n",
       "    (v_1_0 (* i_1_12 i_1_11)))\n",
       "    v_1_0)))))\n",
       "  (v_0_4 (mem (lambda (i_1_1) (letrec (\n",
       "    (v_1_0 (* (x_church_0_0 i_1_1) (v_0_3 i_1_1))))\n",
       "    v_1_0))))\n",
       "  \n",
       "  (v_0_6 (mem (lambda (i_1_1) (letrec (\n",
       "    )\n",
       "    (x_church_0_1 (x_church_0_2 i_1_1))))))\n",
       "  \n",
       "  (x_church_0_0 (mem (lambda (i_1_1) (letrec (\n",
       "    )\n",
       "    (beta 1 5)))))\n",
       "  (x_church_0_1 (mem (lambda (i_1_1) (letrec (\n",
       "    )\n",
       "    (uniform 0 100)))))\n",
       "  (x_church_0_2 (mem (lambda (i_1_1) (letrec (\n",
       "    )\n",
       "    (pmf v_0_4)))))\n",
       "  (x_church_0_3 (mem (lambda (i_1_1) (letrec (\n",
       "    )\n",
       "    (gaussian (v_0_6 i_1_1) 1))))))\n",
       "  x_church_0_3))\n",
       "(map (model) (iota 10000 1))\n",
       "Now using node v0.10.26 (npm v1.4.3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import Language.Church\n",
    "values <- simChurchVec (dpmm 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    ":opt svg\n",
    "import Language.Stochaskell.Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "toRenderable . plot . return . histToPlot $ defaultPlotHist\n",
    "  { _plot_hist_values = values, _plot_hist_bins = 100, _plot_hist_range = Just (0,100) }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import IHaskell.Display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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