{ "cells": [ { "cell_type": "markdown", "id": "5aee0df6", "metadata": {}, "source": [ "## Conformal Prediction\n", "\n", "Conformal prediction computes confidence \"intervals\" associated to any black box prediction method, without assuming any prior model on the sample in the dataset. It computes the interval as quantile of runs of the method over the points in the dataset.\n", "\n", "The main reference is\n", "\n", "> Glenn Shafer, Vladimir Vovk, [A Tutorial on Conformal Prediction](https://jmlr.csail.mit.edu/papers/volume9/shafer08a/shafer08a.pdf)" ] }, { "cell_type": "code", "execution_count": 1, "id": "483e206b", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "82842a06", "metadata": {}, "source": [ "Generate input data." ] }, { "cell_type": "code", "execution_count": 2, "id": "6a7eb67e", "metadata": {}, "outputs": [], "source": [ "def phi0(x): return np.concatenate( (x*0+1, x, x**2, x**3), axis=1 )\n", "n = 200 # number of points \n", "X0 = 8*( np.random.rand(n,1)-.5 )+.5\n", "w0 = np.array([0,-5,0,1]) # coefficients\n", "Y0 = phi0(X0) @ w0 + np.random.randn(n) * 7" ] }, { "cell_type": "markdown", "id": "8c40e858", "metadata": {}, "source": [ "Display data." ] }, { "cell_type": "code", "execution_count": 3, "id": "0254b2b5", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(X0,Y0, '.');" ] }, { "cell_type": "markdown", "id": "be55d035", "metadata": {}, "source": [ "We consider a simple least square method as estimator, but the method works for any black box function of some data $X = (x_i)_{i}$, $Y=(y_i)_i$\n", "\n", "$$\n", " \\hat y(x|X,Y) \\triangleq \\langle \\varphi(x), \\hat w(x|Z) \\rangle\n", " \\quad\\text{where}\\quad\n", " \\hat w(x|X,Y) \\triangleq\n", " \\text{arg}\\min_{w \\in \\mathbb{R}^d} \\sum_i | \\langle \\varphi(z_i), w \\rangle - y_i |^2\n", "$$\n", "where $\\phi(x) \\in \\mathbb{R}^d$ is some feature vector.\n", "We consider here polynomial features $\\varphi(z) = (1,x,\\ldots,x^{d-1})$." ] }, { "cell_type": "code", "execution_count": 4, "id": "edf2465d", "metadata": {}, "outputs": [], "source": [ "def phi(x): return np.concatenate( (x*0+1, x, x**2, x**3), axis=1 )" ] }, { "cell_type": "markdown", "id": "37266336", "metadata": {}, "source": [ "Implements $\\hat w(x|X,Y)$ and $\\hat y(x|X,Y)$." ] }, { "cell_type": "code", "execution_count": 5, "id": "af4c9f8e", "metadata": {}, "outputs": [], "source": [ "def hat_w(X,Y): return np.linalg.pinv(phi(X))@Y\n", "def hat_y(x,w): return phi(x) @ w" ] }, { "cell_type": "markdown", "id": "55101fe4", "metadata": {}, "source": [ "Display the prediction at the sample of the dataset." ] }, { "cell_type": "code", "execution_count": 6, "id": "d6f2ff47", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(X0,Y0, '.')\n", "plt.plot(X0, hat_y(X0,hat_w(X0,Y0)), 'r.');" ] }, { "cell_type": "markdown", "id": "a0b0421b", "metadata": {}, "source": [ "The conformance function $S(x,y|X,Y)$ checkes the accuacy of the prediction\n", "$$\n", " S(x,y|X,Y) \\triangleq |y-\\hat y(x|X,Y)|.\n", "$$\n", "To ease implementation, we implement it as a function of the parameter $w=\\hat w(x|X,Y)$ of the model." ] }, { "cell_type": "code", "execution_count": 7, "id": "9fcefb0e", "metadata": {}, "outputs": [], "source": [ "def S(x,y, w): return np.abs(y-hat_y(x,w))" ] }, { "cell_type": "code", "execution_count": 8, "id": "9c8a9a84", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(X0,Y0,c=S(X0,Y0,hat_w(X0,Y0)), s=15, vmax=10)\n", "plt.plot(X0, hat_y(X0,hat_w(X0,Y0)), 'r.');" ] }, { "cell_type": "markdown", "id": "ec2ea6e8", "metadata": {}, "source": [ "The conformal prediction compute a score $C(x,y|X,Y)$ which is obtained by computing the rank of conformance at the point of interest\n", "$$\n", " V \\triangleq S(x,y| X \\cup x, Y \\cup y).\n", "$$\n", "among all possible scores at the samples \n", "$$\n", " V_i \\triangleq S(X_i,Y_i| X \\cup x, Y \\cup y)\n", "$$\n", "This score is thus defined as\n", "$$\n", " C(x,y|X,Y) \\triangleq \\frac{1}{n+1} \\sum_{i} 1_{V_i \\leq V}\n", "$$" ] }, { "cell_type": "code", "execution_count": 9, "id": "84c27717", "metadata": {}, "outputs": [], "source": [ "def conformal(x,y):\n", " V = np.zeros(n)\n", " w = hat_w(np.append(X0,x).reshape(n+1,1),np.append(Y0,y))\n", " for i in range(n):\n", " V[i] = S(X0[i,:].reshape(1,1),Y0[i], w)\n", " return (1 + np.sum( V<=S(np.array(x).reshape(1,1),y, w) ) ) / (n+1)" ] }, { "cell_type": "markdown", "id": "6a8fbb11", "metadata": {}, "source": [ "For some confidence level $\\alpha \\in [0,1]$, this scores defines a confidence \"interval\" (it does not need to be connected, but in most cases it is)\n", "$$\n", " I_\\alpha(x|X,Y) \\triangleq \\{ y : C(x,y|X,Y) \\leq 1-\\alpha \\}. \n", "$$\n", "The fundamental theorem of conformal prediction is that this interval has a covering property, in the sense that \n", "$$\n", " \\mathbb{P}(y \\in I_\\alpha(x|X,Y)) \\geq 1-\\alpha\n", "$$\n", "where the probability is taken with respect to random $(x,y,X_1,\\ldots,X_n,Y_1,\\ldots,Y_n)$, all assumed to be independant and identically distributed. " ] }, { "cell_type": "markdown", "id": "59a98d73", "metadata": {}, "source": [ "We compute the value of $C(x,y|X,Y)$ on a grid of $x$ and $y$." ] }, { "cell_type": "code", "execution_count": 10, "id": "e839d6b9", "metadata": {}, "outputs": [], "source": [ "nx = 80\n", "ny = 70\n", "xlist = np.linspace(min(X0),max(X0),nx)\n", "ylist = np.linspace(min(Y0),max(Y0),ny)\n", "R = np.zeros((nx,ny))\n", "for ix in range(nx):\n", " for iy in range(ny):\n", " R[ix,iy] = conformal(xlist[ix],ylist[iy])" ] }, { "cell_type": "markdown", "id": "3524f18b", "metadata": {}, "source": [ "Display the confidence intervals as level sets of the function $C(\\cdot,\\cdot,X,Y)$." ] }, { "cell_type": "code", "execution_count": 11, "id": "89b65abd", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "CS = plt.contour(xlist.flatten(),ylist.flatten(), R.T, levels=np.linspace(0,1,11))\n", "plt.plot(xlist.flatten(), hat_y(xlist,hat_w(X0,Y0)), 'k-')\n", "plt.plot(X0,Y0, 'k.', 'MarkerSize', 15)\n", "plt.axis([min(X0),max(X0),min(Y0),max(Y0)]);" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.1" } }, "nbformat": 4, "nbformat_minor": 5 }