{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"srand(1)\n",
"m = 25;\n",
"n = 10;\n",
"A = randn(m, n);\n",
"b = randn(m, 1);"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"using Convex, SCS\n",
"set_default_solver(SCSSolver(verbose=0));\n",
"gammas = logspace(-4, 2, 100);\n",
"x_values = zeros(n, length(gammas));\n",
"x = Variable(n);\n",
"for i=1:length(gammas)\n",
" cost = sum_squares(A*x - b) + gammas[i]*norm(x,1);\n",
" problem = minimize(cost, [norm(x, Inf) <= 1]);\n",
" solve!(problem);\n",
" x_values[:,i] = evaluate(x);\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot(...)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Plot the regularization path.\n",
"using Gadfly, DataFrames\n",
"df = DataFrame(λ=gammas, x=vec(x_values[1,:]), label=\"x1\")\n",
"for i=2:n\n",
" df = vcat(df, DataFrame(λ=gammas, x=vec(x_values[i,:]), label=string(\"x\", i)));\n",
"end\n",
"plot(df, x=\"λ\", y=\"x\", color=\"label\", Geom.line, Scale.x_log10, Guide.title(\"Entries of x vs λ\"))"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.3.9",
"language": "julia",
"name": "julia-0.3"
},
"language_info": {
"name": "julia",
"version": "0.3.9"
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"nbformat": 4,
"nbformat_minor": 0
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