ADVI-MNIST.jl

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ADVI on MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:36:45.637000+02:00",
     "start_time": "2019-09-03T17:36:45.612Z"
    }
   },
   "outputs": [],
   "source": [
    "using Revise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:36:46.803000+02:00",
     "start_time": "2019-09-03T17:36:45.615Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"/home/tor/.julia/dev/Bijectors/Project.toml\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Pkg\n",
    "Pkg.activate(\"/home/tor/.julia/dev/Bijectors\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:36:59.259000+02:00",
     "start_time": "2019-09-03T17:36:45.617Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Recompiling stale cache file /home/tor/.julia/compiled/v1.0/Bijectors/39uFz.ji for Bijectors [76274a88-744f-5084-9051-94815aaf08c4]\n",
      "└ @ Base loading.jl:1190\n"
     ]
    }
   ],
   "source": [
    "using Bijectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:31.469000+02:00",
     "start_time": "2019-09-03T17:36:45.618Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Recompiling stale cache file /home/tor/.julia/compiled/v1.0/Turing/gm4QC.ji for Turing [fce5fe82-541a-59a6-adf8-730c64b5f9a0]\n",
      "└ @ Base loading.jl:1190\n",
      "┌ Warning: Package Turing does not have StatsBase in its dependencies:\n",
      "│ - If you have Turing checked out for development and have\n",
      "│   added StatsBase as a dependency but haven't updated your primary\n",
      "│   environment's manifest file, try `Pkg.resolve()`.\n",
      "│ - Otherwise you may need to report an issue with Turing\n",
      "└ Loading StatsBase into Turing from project dependency, future warnings for Turing are suppressed.\n",
      "WARNING: Method definition vi(Turing.Model{pvars, dvars, F, TData, TDefaults} where TDefaults where TData where F where dvars where pvars, Turing.Variational.VariationalInference{AD} where AD) in module Variational at /home/tor/.julia/dev/Turing/src/variational/VariationalInference.jl:74 overwritten at /home/tor/.julia/dev/Turing/src/variational/VariationalInference.jl:229.\n",
      "┌ Info: Recompiling stale cache file /home/tor/.julia/compiled/v1.0/Plots/ld3vC.ji for Plots [91a5bcdd-55d7-5caf-9e0b-520d859cae80]\n",
      "└ @ Base loading.jl:1190\n",
      "┌ Info: [Turing]: global PROGRESS is set as true\n",
      "└ @ Turing /home/tor/.julia/dev/Turing/src/Turing.jl:24\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       ":reverse_diff"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import libraries.\n",
    "using Turing, Flux, Plots, Random\n",
    "\n",
    "# Hide sampling progress.\n",
    "Turing.turnprogress(true);\n",
    "\n",
    "# Use reverse_diff due to the number of parameters in neural networks.\n",
    "Turing.setadbackend(:reverse_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:41.265000+02:00",
     "start_time": "2019-09-03T17:36:45.620Z"
    }
   },
   "outputs": [],
   "source": [
    "using Turing: Variational\n",
    "using Turing.Variational: elbo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:41.321000+02:00",
     "start_time": "2019-09-03T17:36:45.622Z"
    }
   },
   "outputs": [],
   "source": [
    "using Turing.Variational: VariationalInference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:41.344000+02:00",
     "start_time": "2019-09-03T17:36:45.623Z"
    }
   },
   "outputs": [],
   "source": [
    "using StatsFuns: softplus, invsoftplus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:42.654000+02:00",
     "start_time": "2019-09-03T17:36:45.625Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MersenneTwister(UInt32[0x00000001], Random.DSFMT.DSFMT_state(Int32[1749029653, 1072851681, 1610647787, 1072862326, 1841712345, 1073426746, -198061126, 1073322060, -156153802, 1073567984  …  1977574422, 1073209915, 278919868, 1072835605, 1290372147, 18858467, 1815133874, -1716870370, 382, 0]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], UInt128[0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000  …  0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000], 1002, 0)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Random\n",
    "\n",
    "Random.seed!(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:42.677000+02:00",
     "start_time": "2019-09-03T17:36:45.627Z"
    }
   },
   "outputs": [],
   "source": [
    "using Flux.Data: MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:43.382000+02:00",
     "start_time": "2019-09-03T17:36:45.629Z"
    }
   },
   "outputs": [],
   "source": [
    "MNIST.load()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:43.882000+02:00",
     "start_time": "2019-09-03T17:36:45.631Z"
    }
   },
   "outputs": [],
   "source": [
    "imgs = MNIST.images();\n",
    "labels = MNIST.labels() .+ 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:44.544000+02:00",
     "start_time": "2019-09-03T17:36:45.633Z"
    }
   },
   "outputs": [],
   "source": [
    "data = float.(imgs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:45.003000+02:00",
     "start_time": "2019-09-03T17:36:45.635Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 28)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orig_size = size(data[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:45.092000+02:00",
     "start_time": "2019-09-03T17:36:45.637Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":reverse_diff"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This modification of the unpack function generates a series of vectors\n",
    "# given a network shape.\n",
    "function unpack(θ::AbstractVector, network_shape::AbstractVector)\n",
    "    index = 1\n",
    "    weights = []\n",
    "    biases = []\n",
    "    for layer in network_shape\n",
    "        rows, cols, _ = layer\n",
    "        size = rows * cols\n",
    "        last_index_w = size + index - 1\n",
    "        last_index_b = last_index_w + rows\n",
    "        push!(weights, reshape(θ[index:last_index_w], rows, cols))\n",
    "        push!(biases, reshape(θ[last_index_w+1:last_index_b], rows))\n",
    "        index = last_index_b + 1\n",
    "    end\n",
    "    return weights, biases\n",
    "end\n",
    "\n",
    "# Generate an abstract neural network given a shape, \n",
    "# and return a prediction.\n",
    "function nn_forward(x, θ::AbstractVector, network_shape::AbstractVector)\n",
    "    weights, biases = unpack(θ, network_shape)\n",
    "\n",
    "    layers = []\n",
    "    for i in eachindex(network_shape)\n",
    "        push!(layers, Dense(weights[i],\n",
    "            biases[i],\n",
    "            eval(network_shape[i][3])))\n",
    "    end\n",
    "    nn = Chain(layers...)\n",
    "    return nn(x)\n",
    "end\n",
    "\n",
    "# Set the backend.\n",
    "Turing.setadbackend(:reverse_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:48.156000+02:00",
     "start_time": "2019-09-03T17:36:45.639Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "categorical_nn (generic function with 5 methods)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@model categorical_nn(xs, ys, network_shape, num_params) = begin\n",
    "    θ ~ MvNormal(zeros(num_params), sig .* ones(num_params))\n",
    "    preds = softmax(nn_forward(xs, θ, network_shape))\n",
    "    \n",
    "    for i = 1:length(ys)\n",
    "        ys[i] ~ Categorical(preds[:, i])\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:48.586000+02:00",
     "start_time": "2019-09-03T17:36:45.641Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7850"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Specify the network architecture.\n",
    "network_shape = [\n",
    "    (10, 28 * 28, :identity),\n",
    "#     (10, 32, :identity)\n",
    "]\n",
    "\n",
    "# Regularization, parameter variance, and total number of\n",
    "# parameters.\n",
    "alpha = 0.09\n",
    "sig = sqrt(1.0 / alpha)\n",
    "num_params = sum([i * o + i for (i, o, _) in network_shape])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:49.124000+02:00",
     "start_time": "2019-09-03T17:36:45.643Z"
    }
   },
   "outputs": [],
   "source": [
    "xs = hcat(vec.(data)...)\n",
    "ys = labels;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:49.316000+02:00",
     "start_time": "2019-09-03T17:36:45.645Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gen_batch (generic function with 1 method)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gen_batch(data, batch_size) = begin\n",
    "    n = size(data.ys)[end]\n",
    "    indices = shuffle(1:n)\n",
    "    \n",
    "    return (\n",
    "        (\n",
    "            xs = view(data.xs, :, indices[i:i - 1 + batch_size]), \n",
    "            ys = view(data.ys, indices[i:i - 1 + batch_size])\n",
    "        )\n",
    "        for i = 1:batch_size:(n - batch_size + 1)\n",
    "    )\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:49.340000+02:00",
     "start_time": "2019-09-03T17:36:45.647Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "using Turing.Variational: SVI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:39:49.363000+02:00",
     "start_time": "2019-09-03T17:36:45.648Z"
    }
   },
   "outputs": [],
   "source": [
    "using Flux: Optimise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:51:26.397000+02:00",
     "start_time": "2019-09-03T17:51:26.367Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVI{Turing.Core.TrackerAD,ADVI{Turing.Core.TrackerAD},NamedTuple{(:xs, :ys),Tuple{Array{Float64,2},Array{Int64,1}}},typeof(gen_batch)}(ADVI{Turing.Core.TrackerAD}(1, 5), (xs = [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], ys = [6, 1, 5, 2, 10, 5, 2, 4, 2, 5  …  10, 3, 10, 6, 2, 9, 4, 6, 7, 9]), gen_batch, 60000)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BATCH_SIZE = 150\n",
    "\n",
    "full_data = (xs = xs, ys = ys)\n",
    "\n",
    "# model to be evaluated on batches\n",
    "example_batch = first(gen_batch(full_data, BATCH_SIZE))\n",
    "m = categorical_nn(example_batch..., network_shape, num_params)\n",
    "\n",
    "opt = Variational.DecayedADAGrad()\n",
    "\n",
    "# will be used as the \"inner\" variational inference algo\n",
    "advi = ADVI(1, 5)  # run optimization 25 times on ENTIRE dataset\n",
    "\n",
    "# wrap `ADVI`, providing the full data, the batch generator and total data-size\n",
    "svi = SVI(advi, full_data, gen_batch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:11.959000+02:00",
     "start_time": "2019-09-03T17:51:27.314Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: [SVI{ADVI}] Should only be seen once: optimizer created for θ\n",
      "│   objectid(θ) = 4040853847508768335\n",
      "└ @ Turing.Variational /home/tor/.julia/dev/Turing/src/variational/svi.jl:126\n",
      "\u001b[32m[SVI{ADVI}] Optimizing...100% Time: 0:06:44\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "TransformedDistribution{Turing.Core.TuringDiagNormal{Array{Float64,1},Array{Float64,1}},Stacked{Tuple{Inversed{Identity}},1},Multivariate}(\n",
       "dist: Turing.Core.TuringDiagNormal{Array{Float64,1},Array{Float64,1}}(\n",
       "m: [-0.0328898, 0.0123485, 0.00959929, -0.0181998, 0.0379754, -0.00653553, -0.0021004, 0.0224722, -0.0225695, 0.0311957  …  -0.32157, 0.922316, 0.920068, 0.193429, 0.492246, 2.88435, 0.225227, 1.67919, -1.74916, -0.0987295]\n",
       "σ: [0.0188955, 0.0219427, 0.0248201, 0.0218318, 0.018239, 0.018572, 0.0216814, 0.0238496, 0.0187545, 0.0197264  …  0.0180857, 0.00799453, 0.0618, 0.0444661, 0.0326439, 0.0562312, 0.0366669, 0.026788, 0.0128687, 0.0328581]\n",
       ")\n",
       "\n",
       "transform: Stacked{Tuple{Inversed{Identity}},1}((Inversed{Identity}(Identity()),), (1:7850,))\n",
       ")\n"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit\n",
    "q = vi(m, svi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:13.932000+02:00",
     "start_time": "2019-09-03T17:51:27.858Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-56643.83469464215"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_full = categorical_nn(full_data..., network_shape, num_params);\n",
    "elbo(svi.alg, q, m_full, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.237000+02:00",
     "start_time": "2019-09-03T17:51:28.130Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-5.045731649210917e6"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example_batch = first(gen_batch(full_data, 200))\n",
    "m = categorical_nn(example_batch..., network_shape, num_params);\n",
    "\n",
    "elbo(svi, q, m, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.261000+02:00",
     "start_time": "2019-09-03T17:51:28.402Z"
    }
   },
   "outputs": [],
   "source": [
    "using FixedPointNumbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.293000+02:00",
     "start_time": "2019-09-03T17:51:28.770Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "60000-element Array{Array{Float64,2},1}:\n",
       " [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       " [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       " [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       " [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       " [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
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      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.362000+02:00",
     "start_time": "2019-09-03T17:51:29.073Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "arr2img (generic function with 1 method)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2img(a) = (Gray ∘ FixedPointNumbers.Normed{UInt8,8}).(reshape(a, (28, 28)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.429000+02:00",
     "start_time": "2019-09-03T17:51:29.385Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "predict (generic function with 1 method)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(xs, θ, network_shape) = softmax(nn_forward(xs, θ, network_shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.482000+02:00",
     "start_time": "2019-09-03T17:51:29.719Z"
    }
   },
   "outputs": [
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       "28×28 Array{Gray{N0f8},2} with eltype Gray{Normed{UInt8,8}}:\n",
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     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "idx = 3\n",
    "\n",
    "arr2img(data[idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.661000+02:00",
     "start_time": "2019-09-03T17:51:30.017Z"
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   },
   "outputs": [],
   "source": [
    "res = []\n",
    "\n",
    "for i = 1:1000\n",
    "    θ_ = rand(q)\n",
    "    πs = predict(xs[:, idx], θ_, network_shape)\n",
    "    \n",
    "    push!(res, πs)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
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     "end_time": "2019-09-03T19:58:22.699000+02:00",
     "start_time": "2019-09-03T17:51:30.331Z"
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     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "histogram(argmax.(res) .- 1, bins=10, normed=true, bar_width=1.0)\n",
    "xticks!(0:9)\n",
    "xlims!(0.0, 10.0)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.747000+02:00",
     "start_time": "2019-09-03T17:51:30.633Z"
    }
   },
   "outputs": [],
   "source": [
    "imgs = MNIST.images(:test);\n",
    "labels = MNIST.labels(:test) .+ 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.801000+02:00",
     "start_time": "2019-09-03T17:51:30.945Z"
    }
   },
   "outputs": [],
   "source": [
    "data_test = float.(imgs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.932000+02:00",
     "start_time": "2019-09-03T17:51:31.170Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "data_test = hcat([reshape(d, :) for d in data_test]...);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:22.983000+02:00",
     "start_time": "2019-09-03T17:51:31.447Z"
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       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx = rand(1:size(data_test, 2))\n",
    "\n",
    "arr2img(data_test[:, idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:23.010000+02:00",
     "start_time": "2019-09-03T17:51:31.954Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "xs_test = data_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:23.488000+02:00",
     "start_time": "2019-09-03T17:51:32.274Z"
    }
   },
   "outputs": [],
   "source": [
    "res = []\n",
    "\n",
    "for i = 1:1000\n",
    "    θ_ = rand(q)\n",
    "    πs = predict(xs_test[:, idx], θ_, network_shape)\n",
    "    \n",
    "    push!(res, πs)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
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     "start_time": "2019-09-03T17:51:32.866Z"
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    "histogram(argmax.(res) .- 1, bins=10, normed=true, bar_width=1.0)\n",
    "xticks!(0:9)\n",
    "xlims!(0.0, 10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:35.989000+02:00",
     "start_time": "2019-09-03T17:51:33.249Z"
    }
   },
   "outputs": [],
   "source": [
    "labels_pred = []\n",
    "\n",
    "for idx = 1:size(xs_test, 2)\n",
    "    res = []\n",
    "\n",
    "    for i = 1:10\n",
    "        θ_ = rand(q)\n",
    "        πs = predict(xs_test[:, idx], θ_, network_shape)\n",
    "\n",
    "        push!(res, πs)\n",
    "    end\n",
    "    \n",
    "    y_pred = argmax(counts(argmax.(res), 1:10))\n",
    "    \n",
    "    if sum(iszero.(y_pred)) > 1\n",
    "        print(idx)\n",
    "    end\n",
    "    \n",
    "    push!(labels_pred, y_pred)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:36.015000+02:00",
     "start_time": "2019-09-03T17:51:33.691Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(labels_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-03T19:58:36.041000+02:00",
     "start_time": "2019-09-03T17:51:35.625Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9078"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(labels .== labels_pred) / length(labels)"
   ]
  }
 ],
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