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"#[#[#:line, :options=>{:x=>:m, :y=>:\"Test set\", :title=>\"Test set\", :color=>\"green\"}, :data=>\"109907ad-2330-4a2c-ab16-8723fdf8e7c8\"}, @xrange=[0, 8], @yrange=[-10.959248334611097, 6.22863542433814]>, #:line, :options=>{:x=>:m, :y=>:\"Training set\", :title=>\"Training set\", :color=>\"blue\"}, :data=>\"109907ad-2330-4a2c-ab16-8723fdf8e7c8\"}, @xrange=[0, 8], @yrange=[-10.724659158818707, 54.78957627143174]>], :options=>{:x_label=>\"Log likelihood for N=10\", :y_label=>\"\", :legend=>true, :zoom=>true, :width=>800, :xrange=>[0, 8], :yrange=>[-10.959248334611097, 54.78957627143174]}}>], :data=>{\"109907ad-2330-4a2c-ab16-8723fdf8e7c8\"=>#-10.959248334611097, :\"Training set\"=>-10.724659158818707, :m=>0}, {:\"Test set\"=>-8.394954941428635, :\"Training set\"=>-8.35172452595085, :m=>1}, {:\"Test set\"=>-8.405406955434055, :\"Training set\"=>-8.293834872758055, :m=>2}, {:\"Test set\"=>6.22863542433814, :\"Training set\"=>6.69355894304122, :m=>3}, {:\"Test set\"=>6.227504317715638, :\"Training set\"=>6.6936262828487525, :m=>4}, {:\"Test set\"=>3.442481754400797, :\"Training set\"=>9.935165809299908, :m=>5}, {:\"Test set\"=>2.6903231988997343, :\"Training set\"=>12.664068141026764, :m=>6}, {:\"Test set\"=>2.7092083106614098, :\"Training set\"=>12.894157291800312, :m=>7}, {:\"Test set\"=>3.327909256286116, :\"Training set\"=>54.78957627143174, :m=>8}]>}, :extension=>[]}>"
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"source": [
"require 'daru'\n",
"require 'nyaplot'\n",
"\n",
"N = 10\n",
"M = [0, 1, 3, 9]\n",
"\n",
"def normal_rand(mu = 0, sigma = 1.0)\n",
" random = Random.new\n",
" (Math.sqrt(-2 * Math.log(random.rand)) * Math.sin(2 * Math::PI * random.rand) * sigma) + mu\n",
"end\n",
"\n",
"\n",
"def create_dataset(num)\n",
" dataset = Daru::DataFrame.new({'x': [], 'y': []}) \n",
"\n",
" num.times do |i|\n",
" x = i.to_f / (num - 1).to_f\n",
" y = Math.sin(2 * Math::PI * x) + normal_rand(0, 0.3)\n",
" dataset.add_row(Daru::Vector.new([x, y], index: [:x, :y]))\n",
" end\n",
" \n",
" return dataset\n",
"end\n",
"\n",
"def log_likelihood(dataset, f)\n",
" dev = 0.0\n",
" n = dataset.size.to_f\n",
" dataset.each_row do |line|\n",
" x = line.x\n",
" y = line.y\n",
" dev += (y - f.call(x))**2\n",
" end\n",
" err = dev * 0.5\n",
" beta = n / dev\n",
" -beta * err + 0.5 * n * Math.log(0.5 * beta / Math::PI)\n",
"end\n",
"\n",
"def resolve(dataset, m)\n",
" t = dataset.y\n",
"\n",
" columns = {}\n",
" (m+1).times do |i|\n",
" columns[\"x**#{i}\"] = dataset.x ** i\n",
" end\n",
" phi = Daru::DataFrame.new(columns)\n",
"\n",
" tmp = (phi.transpose.to_matrix * phi.to_matrix).inv\n",
" ws = (tmp * phi.transpose.to_matrix) * Vector.elements(t.to_a)\n",
"\n",
" f = lambda {|x|\n",
" y = 0\n",
" ws.each_with_index do |w, i|\n",
" y += w * (x ** i)\n",
" end\n",
"\n",
" y\n",
" }\n",
"\n",
" sigma2 = 0.0\n",
" dataset.each_row do |line|\n",
" sigma2 += (f.call(line.x) - line.y)**2\n",
" end\n",
" sigma2 /= dataset.size\n",
"\n",
" return f, ws, Math.sqrt(sigma2)\n",
"end\n",
"\n",
"train_set = create_dataset(N)\n",
"test_set = create_dataset(N)\n",
"df_ws = {}\n",
"\n",
"fig = Nyaplot::Frame.new\n",
"\n",
"M.each_with_index do |m, c|\n",
" f, ws, sigma = resolve(train_set, m)\n",
" df_ws[\"M=#{m}\"] = Daru::Vector.new(ws, name: \"M=#{m}\")\n",
" \n",
" plot = Nyaplot::Plot.new\n",
" sc = plot.add_with_df(train_set.to_nyaplotdf, :scatter, :x, :y)\n",
" sc.title(\"train_set\")\n",
" sc.color('blue')\n",
" \n",
" linex = (0..1).step(1.0 / (101 - 1)).to_a\n",
" liney = linex.map do |x|\n",
" Math.sin(2 * Math::PI * x)\n",
" end\n",
" line_answer = plot.add(:line, linex, liney)\n",
" line_answer.title('answer')\n",
" line_answer.color('green')\n",
" \n",
" liney = linex.map do |x|\n",
" f.call(x)\n",
" end\n",
" line_middle = plot.add(:line, linex, liney)\n",
" line_middle.title(\"Sigma=#{sprintf(\"%.2f\", sigma)}\")\n",
" line_middle.color('red')\n",
" line_upper = plot.add(:line, linex, liney.map {|y| y + sigma })\n",
" line_upper.color('red')\n",
" line_lower = plot.add(:line, linex, liney.map {|y| y - sigma } )\n",
" line_lower.color('red')\n",
"\n",
" plot.configure do\n",
" x_label(\"M=#{m}\")\n",
" y_label('')\n",
" xrange([-0.05, 1.05])\n",
" yrange([-1.5, 1.5])\n",
" legend(true)\n",
" height(300)\n",
" width(490)\n",
" end\n",
" \n",
" fig.add(plot)\n",
"end\n",
"\n",
"fig.show\n",
"\n",
"df = Daru::DataFrame.new({m: [], 'Test set': [], 'Training set': []}) \n",
"9.times do |m|\n",
" f, ws, sigma = resolve(train_set, m)\n",
" train_mlh = log_likelihood(train_set, f)\n",
" test_mlh = log_likelihood(test_set, f)\n",
" df.add_row(Daru::Vector.new([m, test_mlh, train_mlh], index: [:m, 'Test set'.to_sym, 'Training set'.to_sym]))\n",
"end\n",
"\n",
"df.plot(type: [:line, :line], x: [:m, :m], y: ['Test set'.to_sym, 'Training set'.to_sym]) do |plot, diagrams|\n",
" test_set_diagram = diagrams[0]\n",
" train_set_diagram = diagrams[1]\n",
" \n",
" train_set_diagram.title('Training set')\n",
" train_set_diagram.color('blue')\n",
" test_set_diagram.title('Test set')\n",
" test_set_diagram.color('green')\n",
" \n",
" plot.x_label(\"Log likelihood for N=#{N}\")\n",
" plot.y_label('')\n",
" plot.legend(true)\n",
"end\n"
]
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