09_教師なし学習_生成モデル入門.nextjournal.ipynb

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\u69d8\u3005\u306a\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u624b\u6cd5\u306e\u7d39\u4ecb\n\n\u3044\u3064\u3082\u306e\u3088\u3046\u306b\u53f3\u4e0a\u306e\u300cRemix\u300d\u30dc\u30bf\u30f3\u3092\u62bc\u3057\u3066\u81ea\u5206\u7528\u306e\u8907\u88fd\u3092\u4f5c\u6210\u3059\u308c\u3070\u3001\u5404\u30bb\u30eb\u3092\u300cShift+Enter\u300d\u3067\u5b9f\u884c\u3057\u306a\u304c\u3089\u8aad\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\n\n\u7de8\u96c6\u3092\u884c\u306a\u3063\u305f\u5f8c\u306f\u3001Windows\u3067\u306f\u300cCtrl+s\u300d\u3001Mac\u3067\u306f\u300cCmd+s\u300d\u3067\u4fdd\u5b58\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\n\n\u307e\u305a\u3001\u5fc5\u8981\u306a\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u8aad\u307f\u8fbc\u307f\u307e\u3059"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"9d3d7b08-8ab1-4568-ac55-57344cd1b2cf","kind":"code","language":"julia"}},"source":["using Plots, CSV, Statistics, LinearAlgebra"],"outputs":[],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["# \u30c7\u30fc\u30bf\u306e\u4f5c\u6210"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"589236ab-064d-4e59-bf7f-cf8c0222b655","kind":"code","language":"julia"}},"source":["# 3\u3064\u306e\u6b63\u898f\u5206\u5e03\u304b\u3089\u6210\u308b\u30c7\u30fc\u30bf\u3092\u4f5c\u308b\nN = 60\n\nx_class1 = randn(Float64, 20, 2) .- 3.0\nx_class2 = randn(Float64, 20, 2) .+ 0.0\nx_class3 = randn(Float64, 20, 2) .+ 3.0\n\nX = [x_class1; x_class2; x_class3]\n\nscatter(X[1:20, 1], X[1:20, 2], xlims=(-5,6), ylims=(-5,6), markersize=8, label=\"class 1\")\n\nscatter!(X[21:40, 1], X[21:40, 2], xlims=(-5,6), ylims=(-5,6), markersize=8, label=\"class 2\")\n\nscatter!(X[41:60, 1], X[41:60, 2], xlims=(-8,8), ylims=(-8,8), markersize=8, label=\"class 3\", xlabel=\"x1\", ylabel=\"x2\", legend=:topleft)"],"outputs":[{"output_type":"execute_result","data":{"image\/svg+xml":"<?xml version=\"1.0\" 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inv_cov = 1.0 .\/ sqrt.(gmm_covariances)\n    precisions = inv_cov.^2\n    log_det = sum(log.(inv_cov), dims=2)\n    log_prob .= sum(gmm_mu.^2 .* precisions, dims=2)' .- 2.0 .* (X * (gmm_mu .* precisions)') .+ (X.^2 * precisions')\n    weighted_log_prob .=  -0.5 .* (d .* log.(2.0 .* pi) .+ log_prob) .+ log_det' .+ log.(gmm_pi)'\n    log_prob_norm = logsumexp(weighted_log_prob, dims=2)\n    log_resp = weighted_log_prob .- log_prob_norm\n\n    # M-step\n    resp = exp.(log_resp)\n    nk = sum(resp, dims=1)\n    gmm_mu .= (resp' * X) .\/ nk'\n    X2 = (resp' * (X .* X)) .\/ nk'\n    gmm_covariances .= X2 .- gmm_mu.^2\n    gmm_pi .= (nk .\/ N)[:]\n  end\n\n  for n = 1:N\n    class[n] = argmax(weighted_log_prob[n, :])\n  end\n\n  return class, gmm_pi, gmm_mu, gmm_covariances\nend"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"train_gmm"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"code","metadata":{"nextjournal":{"id":"9ae05ef9-5fed-4a2d-898a-d3d14ef36033","kind":"code","language":"julia"}},"source":["# K=3\u3068\u3057\u3066\u3001GMM\u3092\u884c\u3046\nclass, gmm_pi, gmm_mu, gmm_covariances = train_gmm(X, 3)"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"([3, 3, 3, 3, 3, 3, 3, 3, 3, 3  \u2026  2, 2, 2, 2, 1, 2, 2, 2, 2, 2], [0.336331, 0.316698, 0.34697], [-0.105808 0.414232; 2.81128 3.19656; -3.11407 -2.54243], [0.390987 0.369001; 0.80482 0.530497; 0.531999 0.645906])"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"code","metadata":{"nextjournal":{"id":"4bca6051-3627-4613-a1e7-db2b7f196832","kind":"code","language":"julia"}},"source":["gmm_pi"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"3-element Array{Float64,1}:\n 0.336331\n 0.316698\n 0.34697"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"code","metadata":{"nextjournal":{"id":"005114a5-6678-46d7-8734-606d472cdad4","kind":"code","language":"julia"}},"source":["gmm_mu"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"3\u00d72 Array{Float64,2}:\n -0.105808   0.414232\n  2.81128    3.19656\n -3.11407   -2.54243"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"code","metadata":{"nextjournal":{"id":"2ee2d00d-b8cf-4a32-afa4-63a5cea1f50c","kind":"code","language":"julia"}},"source":["gmm_covariances"],"outputs":[{"output_type":"execute_result","data":{"text\/plain":"3\u00d72 Array{Float64,2}:\n 0.390987  0.369001\n 0.80482   0.530497\n 0.531999  0.645906"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"code","metadata":{"nextjournal":{"id":"c3609c23-5efb-4e79-ae2c-3a47e3ee611e","kind":"code","language":"julia"}},"source":["# 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2232.76,907.204 2256.76,907.204 2232.76,907.204 2232.76,735.212 2256.76,735.212 2232.76,735.212 2232.76,563.22 2256.76,563.22 2232.76,563.22 2232.76,391.228 \n  2256.76,391.228 2232.76,391.228 2232.76,219.236 2256.76,219.236 2232.76,219.236 2232.76,47.2441 2256.76,47.2441 2232.76,47.2441 \n  \"\/>\n<\/svg>\n"},"execution_count":1,"metadata":{}}],"execution_count":1},{"cell_type":"markdown","metadata":{},"source":["# \u968e\u5c64\u7684\u306a\u30c7\u30fc\u30bf"]},{"cell_type":"code","metadata":{"nextjournal":{"id":"916f015d-e328-4456-8700-ac1bcb0acb57","kind":"code","language":"julia"}},"source":["# 3\u3064\u306e\u30b5\u30a4\u30ba\u304c\u7570\u306a\u308b(\u6b63\u898f\u5206\u5e03\u306e\u5206\u6563\u304c\u7570\u306a\u308b)\u30c7\u30fc\u30bf\u3092\u4f5c\u308b\nN = 300\n\nx_class1 = randn(Float64, 100, 2)\nx_class1[:, 1] .= x_class1[:, 1] .- 8.0\nx_class1[:, 2] .= x_class1[:, 2] .+ 8.0\n\nx_class2 = 5.0 .* randn(Float64, 100, 2)\n\nx_class3 = randn(Float64, 100, 2)\nx_class3[:, 1] .= x_class3[:, 1] .+ 8.0\nx_class3[:, 2] .= x_class3[:, 2] .+ 8.0\n\nx = [x_class1; x_class2; x_class3]\n\nscatter(x[1:100, 1], x[1:100, 2], xlims=(-15,15), ylims=(-15,15), markersize=8, label=\"class 1\")\n\nscatter!(x[101:200, 1], x[101:200, 2], xlims=(-15,15), ylims=(-15,15), markersize=8, label=\"class 2\")\n\nscatter!(x[201:300, 1], x[201:300, 2], xlims=(-15,15), ylims=(-15,15), markersize=8, label=\"class 3\", xlabel=\"x1\", ylabel=\"x2\", legend=:bottomright)"],"outputs":[{"output_type":"execute_result","data":{"image\/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\"?>\n<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"600\" height=\"400\" viewBox=\"0 0 2400 1600\">\n<defs>\n  <clipPath id=\"clip000\">\n    <rect x=\"0\" y=\"0\" width=\"2400\" height=\"1600\"\/>\n  <\/clipPath>\n<\/defs>\n<path clip-path=\"url(#clip000)\" d=\"\nM0 1600 L2400 1600 L2400 0 L0 0  Z\n  \" fill=\"#ffffff\" fill-rule=\"evenodd\" 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