{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Kernel Ridge Regression\n",
    "\n",
    "*You are seeing the\n",
    "notebook output generated by\n",
    "[Literate.jl](https://github.com/fredrikekre/Literate.jl) from the\n",
    "[Julia source file](https://github.com/JuliaGaussianProcesses/KernelFunctions.jl/blob/master/examples/kernel-ridge-regression/script.jl).\n",
    "The rendered HTML can be viewed [in the docs](https://juliagaussianprocesses.github.io/KernelFunctions.jl/dev/examples/kernel-ridge-regression/).*"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Building on linear regression, we can fit non-linear data sets by introducing a feature space. In a higher-dimensional feature space, we can overfit the data; ridge regression introduces regularization to avoid this. In this notebook we show how we can use KernelFunctions.jl for *kernel* ridge regression."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "# Loading and setup of required packages\n",
    "using KernelFunctions\n",
    "using LinearAlgebra\n",
    "using Distributions\n",
    "\n",
    "# Plotting\n",
    "using Plots;\n",
    "default(; lw=2.0, legendfontsize=11.0, ylims=(-150, 500));\n",
    "\n",
    "using Random: seed!\n",
    "seed!(42);"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Toy data\n",
    "Here we use a one-dimensional toy problem. We generate data using the fourth-order polynomial $f(x) = (x+4)(x+1)(x-1)(x-3)$:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=2}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "cell_type": "code",
   "source": [
    "f_truth(x) = (x + 4) * (x + 1) * (x - 1) * (x - 3)\n",
    "\n",
    "x_train = -5:0.5:5\n",
    "x_test = -7:0.1:7\n",
    "\n",
    "noise = rand(Uniform(-20, 20), length(x_train))\n",
    "y_train = f_truth.(x_train) + noise\n",
    "y_test = f_truth.(x_test)\n",
    "\n",
    "plot(x_test, y_test; label=raw\"$f(x)$\")\n",
    "scatter!(x_train, y_train; seriescolor=1, label=\"observations\")"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Linear regression\n",
    "For training inputs $\\mathrm{X}=(\\mathbf{x}_n)_{n=1}^N$ and observations $\\mathbf{y}=(y_n)_{n=1}^N$, the linear regression weights $\\mathbf{w}$ using the least-squares estimator are given by\n",
    "$$\n",
    "\\mathbf{w} = (\\mathrm{X}^\\top \\mathrm{X})^{-1} \\mathrm{X}^\\top \\mathbf{y}\n",
    "$$\n",
    "We predict at test inputs $\\mathbf{x}_*$ using\n",
    "$$\n",
    "\\hat{y}_* = \\mathbf{x}_*^\\top \\mathbf{w}\n",
    "$$\n",
    "This is implemented by `linear_regression`:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function linear_regression(X, y, Xstar)\n",
    "    weights = (X' * X) \\ (X' * y)\n",
    "    return Xstar * weights\n",
    "end;"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "A linear regression fit to the above data set:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=2}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "cell_type": "code",
   "source": [
    "y_pred = linear_regression(x_train, y_train, x_test)\n",
    "scatter(x_train, y_train; label=\"observations\")\n",
    "plot!(x_test, y_pred; label=\"linear fit\")"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Featurization\n",
    "We can improve the fit by including additional features, i.e. generalizing to $\\tilde{\\mathrm{X}} = (\\phi(x_n))_{n=1}^N$, where $\\phi(x)$ constructs a feature vector for each input $x$. Here we include powers of the input, $\\phi(x) = (1, x, x^2, \\dots, x^d)$:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=8}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "cell_type": "code",
   "source": [
    "function featurize_poly(x; degree=1)\n",
    "    return repeat(x, 1, degree + 1) .^ (0:degree)'\n",
    "end\n",
    "\n",
    "function featurized_fit_and_plot(degree)\n",
    "    X = featurize_poly(x_train; degree=degree)\n",
    "    Xstar = featurize_poly(x_test; degree=degree)\n",
    "    y_pred = linear_regression(X, y_train, Xstar)\n",
    "    scatter(x_train, y_train; legend=false, title=\"fit of order $degree\")\n",
    "    return plot!(x_test, y_pred)\n",
    "end\n",
    "\n",
    "plot((featurized_fit_and_plot(degree) for degree in 1:4)...)"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "Note that the fit becomes perfect when we include exactly as many orders in the features as we have in the underlying polynomial (4).\n",
    "\n",
    "However, when increasing the number of features, we can quickly overfit to noise in the data set:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=2}",
      "image/png": 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     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "cell_type": "code",
   "source": [
    "featurized_fit_and_plot(20)"
   ],
   "metadata": {},
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Ridge regression\n",
    "To counteract this unwanted behaviour, we can introduce regularization. This leads to *ridge regression* with $L_2$ regularization of the weights ([Tikhonov regularization](https://en.wikipedia.org/wiki/Tikhonov_regularization)).\n",
    "Instead of the weights in linear regression,\n",
    "$$\n",
    "\\mathbf{w} = (\\mathrm{X}^\\top \\mathrm{X})^{-1} \\mathrm{X}^\\top \\mathbf{y}\n",
    "$$\n",
    "we introduce the ridge parameter $\\lambda$:\n",
    "$$\n",
    "\\mathbf{w} = (\\mathrm{X}^\\top \\mathrm{X} + \\lambda \\mathbb{1})^{-1} \\mathrm{X}^\\top \\mathbf{y}\n",
    "$$\n",
    "As before, we predict at test inputs $\\mathbf{x}_*$ using\n",
    "$$\n",
    "\\hat{y}_* = \\mathbf{x}_*^\\top \\mathbf{w}\n",
    "$$\n",
    "This is implemented by `ridge_regression`:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=8}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "cell_type": "code",
   "source": [
    "function ridge_regression(X, y, Xstar, lambda)\n",
    "    weights = (X' * X + lambda * I) \\ (X' * y)\n",
    "    return Xstar * weights\n",
    "end\n",
    "\n",
    "function regularized_fit_and_plot(degree, lambda)\n",
    "    X = featurize_poly(x_train; degree=degree)\n",
    "    Xstar = featurize_poly(x_test; degree=degree)\n",
    "    y_pred = ridge_regression(X, y_train, Xstar, lambda)\n",
    "    scatter(x_train, y_train; legend=false, title=\"\\$\\\\lambda=$lambda\\$\")\n",
    "    return plot!(x_test, y_pred)\n",
    "end\n",
    "\n",
    "plot((regularized_fit_and_plot(20, lambda) for lambda in (1e-3, 1e-2, 1e-1, 1))...)"
   ],
   "metadata": {},
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Kernel ridge regression\n",
    "Instead of constructing the feature matrix explicitly, we can use *kernels* to replace inner products of feature vectors with a kernel evaluation: $\\langle \\phi(x), \\phi(x') \\rangle = k(x, x')$ or $\\tilde{\\mathrm{X}} \\tilde{\\mathrm{X}}^\\top = \\mathrm{K}$, where $\\mathrm{K}_{ij} = k(x_i, x_j)$.\n",
    "\n",
    "To apply this \"kernel trick\" to ridge regression, we can rewrite the ridge estimate for the weights\n",
    "$$\n",
    "\\mathbf{w} = (\\mathrm{X}^\\top \\mathrm{X} + \\lambda \\mathbb{1})^{-1} \\mathrm{X}^\\top \\mathbf{y}\n",
    "$$\n",
    "using the [matrix inversion lemma](https://tlienart.github.io/pub/csml/mtheory/matinvlem.html#basic_lemmas)\n",
    "as\n",
    "$$\n",
    "\\mathbf{w} = \\mathrm{X}^\\top (\\mathrm{X} \\mathrm{X}^\\top + \\lambda \\mathbb{1})^{-1} \\mathbf{y}\n",
    "$$\n",
    "where we can now replace the inner product with the kernel matrix,\n",
    "$$\n",
    "\\mathbf{w} = \\mathrm{X}^\\top (\\mathrm{K} + \\lambda \\mathbb{1})^{-1} \\mathbf{y}\n",
    "$$\n",
    "And the prediction yields another inner product,\n",
    "$$\n",
    "\\hat{y}_* = \\mathbf{x}_*^\\top \\mathbf{w} = \\langle \\mathbf{x}_*, \\mathbf{w} \\rangle = \\mathbf{k}_* (\\mathrm{K} + \\lambda \\mathbb{1})^{-1} \\mathbf{y}\n",
    "$$\n",
    "where $(\\mathbf{k}_*)_n = k(x_*, x_n)$.\n",
    "\n",
    "This is implemented by `kernel_ridge_regression`:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function kernel_ridge_regression(k, X, y, Xstar, lambda)\n",
    "    K = kernelmatrix(k, X)\n",
    "    kstar = kernelmatrix(k, Xstar, X)\n",
    "    return kstar * ((K + lambda * I) \\ y)\n",
    "end;"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now, instead of explicitly constructing features, we can simply pass in a `PolynomialKernel` object:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=8}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "cell_type": "code",
   "source": [
    "function kernelized_fit_and_plot(kernel, lambda=1e-4)\n",
    "    y_pred = kernel_ridge_regression(kernel, x_train, y_train, x_test, lambda)\n",
    "    if kernel isa PolynomialKernel\n",
    "        title = string(\"order \", kernel.degree)\n",
    "    else\n",
    "        title = string(nameof(typeof(kernel)))\n",
    "    end\n",
    "    scatter(x_train, y_train; label=nothing)\n",
    "    return plot!(x_test, y_pred; label=nothing, title=title)\n",
    "end\n",
    "\n",
    "plot((kernelized_fit_and_plot(PolynomialKernel(; degree=degree, c=1)) for degree in 1:4)...)"
   ],
   "metadata": {},
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "source": [
    "However, we can now also use kernels that would have an infinite-dimensional feature expansion, such as the squared exponential kernel:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=2}",
      "image/png": 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    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
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