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Chapter 5 + 6

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{
"cells": [
{
"cell_type": "code",
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"metadata": {},
"outputs": [],
"source": [
"using CSV\n",
"using DataFrames\n",
"using Plots\n",
"using StatsPlots\n",
"using GLM\n",
"using Statistics\n",
"using Distributions\n",
"using Random\n",
"using MultivariateStats"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"autoData = CSV.File(\"dataset/Auto.csv\"; missingstring=\"?\") |> DataFrame;"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"getMSEOfValidation (generic function with 1 method)"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function getMSEOfValidation(train, validation)\n",
" ols_1 = lm(@formula(mpg ~ horsepower), train);\n",
" ols_2 = lm(@formula(mpg ~ horsepower + horsepower^2), train);\n",
" ols_3 = lm(@formula(mpg ~ horsepower + horsepower^2 + horsepower^3), train);\n",
" ols_4 = lm(@formula(mpg ~ horsepower + horsepower^2 + horsepower^3 + horsepower^4), train);\n",
" ols_5 = lm(@formula(mpg ~ horsepower + horsepower^2 + horsepower^3 + horsepower^4 + horsepower^5), train);\n",
" ols_6 = lm(@formula(mpg ~ horsepower + horsepower^2 + horsepower^3 + horsepower^4 + horsepower^5 + horsepower^6), train);\n",
" ols_7 = lm(@formula(mpg ~ horsepower + horsepower^2 + horsepower^3 + horsepower^4 + horsepower^5 + horsepower^6 + horsepower^7), train);\n",
" ols_8 = lm(@formula(mpg ~ horsepower + horsepower^2 + horsepower^3 + horsepower^4 + horsepower^5 + horsepower^6 + horsepower^7 + horsepower^8), train);\n",
" ols_9 = lm(@formula(mpg ~ horsepower + horsepower^2 + horsepower^3 + horsepower^4 + horsepower^5 + horsepower^6 + horsepower^7 + horsepower^8 + horsepower^9), train);\n",
" ols_10 = lm(@formula(mpg ~ horsepower + horsepower^2 + horsepower^3 + horsepower^4 + horsepower^5 + horsepower^6 + horsepower^7 + horsepower^8 + horsepower^9 + horsepower^10), train);\n",
"\n",
" all_models = [ols_1, ols_2, ols_3, ols_4, ols_5, ols_6, ols_7, ols_8, ols_9, ols_10];\n",
" result = []\n",
" for model in all_models\n",
" p = predict(model, validation)\n",
" mse = sum((validation[:mpg] - p).^2) / length(p)\n",
" push!(result, mse)\n",
" end\n",
" return result\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
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"metadata": {},
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}
],
"source": [
"# Figure 5.2\n",
"clean_autoData = dropmissing(autoData, :horsepower)\n",
"\n",
"indices = collect(1: nrow(clean_autoData))\n",
"shuffle!(indices)\n",
"\n",
"train = clean_autoData[indices[1:196], :]\n",
"validation = clean_autoData[indices[197:end], :]\n",
"\n",
"mse = getMSEOfValidation(train, validation)\n",
"p1 = plot(mse, xlabel=\"Degree of Polynomial\", ylabel=\"Mean Squared Error\", legend=false, markershape = :hexagon, lc=\"red\", markercolor = :red)\n",
"\n",
"p2 = plot(mse)\n",
"for i=1:10\n",
" shuffle!(indices)\n",
" train = clean_autoData[indices[1:196], :]\n",
" validation = clean_autoData[indices[197:end], :]\n",
" mse = getMSEOfValidation(train, validation)\n",
"\n",
" p2 = plot!(mse, xlabel=\"Degree of Polynomial\", ylabel=\"Mean Squared Error\", legend=false)\n",
"end\n",
"\n",
"plot(p1, p2)"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
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},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Figure 5.4\n",
"mse = zeros(10)\n",
"for i in 1:nrow(clean_autoData)\n",
" indices = collect(1:nrow(clean_autoData))\n",
" popat!(indices, i)\n",
" train = clean_autoData[indices, :]\n",
" validation = clean_autoData[[i], :]\n",
" mse = mse + getMSEOfValidation(train, validation)\n",
"end\n",
"\n",
"mse = mse / nrow(clean_autoData)\n",
"p1 = plot(mse, xlabel=\"Degree of Polynomial\", ylabel=\"Mean Squared Error\", legend=false, markershape = :hexagon, lc=\"blue\", markercolor = :blue, title=\"LOOCV\")\n",
"\n",
"############################\n",
"indices = collect(1:nrow(clean_autoData))\n",
"batch = nrow(clean_autoData) ÷ 10\n",
"n = nrow(clean_autoData)\n",
"\n",
"mse_k = zeros(10, 9)\n",
"for i in 1:9\n",
" shuffle!(indices)\n",
" for k in 1:10\n",
" sInd = (k - 1) * batch + 1\n",
" eInd = k * batch\n",
" if k == 10\n",
" eInd = n\n",
" end\n",
" validation = clean_autoData[indices[sInd:eInd], :]\n",
" rest = collect(1:n)\n",
" splice!(rest, collect(sInd:eInd))\n",
" train = clean_autoData[indices[rest], :]\n",
" mse_k[:, i] += getMSEOfValidation(train, validation)\n",
" end\n",
"end\n",
"mse_k = mse_k ./ 10\n",
"p2 = plot(mse_k, xlabel=\"Degree of Polynomial\", ylabel=\"Mean Squared Error\", legend=false, title=\"10-fold CV\")\n",
"\n",
"plot(p1, p2)"
]
},
{
"cell_type": "code",
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"metadata": {},
"outputs": [],
"source": []
}
],
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Chapter_06.ipynb
+359
View File
@@ -0,0 +1,359 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using CSV\n",
"using DataFrames\n",
"using Plots\n",
"using StatsPlots\n",
"using GLM\n",
"using Statistics\n",
"using Distributions\n",
"using Random\n",
"using MultivariateStats"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"FullNormal(\n",
"dim: 2\n",
"μ: [0.0, 0.0]\n",
"Σ: [1.0 1.0; 1.0 2.0]\n",
")\n"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"μ = [0, 0]\n",
"σ = [1.0 1.0; 1.0 2.0]\n",
"dist = Distributions.MvNormal(μ, σ)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2×100 Array{Float64,2}:\n",
" 1.90728 0.417492 0.514817 0.453653 … 0.991181 1.40246 0.892847\n",
" 0.710246 0.31368 -0.209396 -0.669405 1.54026 1.47478 1.03204"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sample = rand(dist, 100) # the random samples are close to Figure 6.14"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"PCA(indim = 2, outdim = 2, principalratio = 1.0)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = fit(PCA, sample)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
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},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"proj = projection(p) # get principle component\n",
"x = sample[1, :]\n",
"y = sample[2, :]\n",
"\n",
"scatter(x, y)\n",
"first_pca = proj[:, 2] # principle components are sorted in descending order\n",
"second_pca = proj[:, 1]\n",
"plot!([-2, 2], [(2 * first_pca[1] / first_pca[2]), (-2 * first_pca[1] / first_pca[2])])\n",
"plot!([-2, 2], [(2 * second_pca[1] / second_pca[2]), (-2 * second_pca[1] / second_pca[2])])\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
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