{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regressione lineare su polinomio con determinazione della distribuzione predittiva" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import scipy.stats as st" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib.colors as mcolors\n", "from matplotlib import cm\n", "\n", "plt.style.use('fivethirtyeight')\n", "\n", "plt.rcParams['font.family'] = 'sans-serif'\n", "plt.rcParams['font.serif'] = 'Ubuntu'\n", "plt.rcParams['font.monospace'] = 'Ubuntu Mono'\n", "plt.rcParams['font.size'] = 10\n", "plt.rcParams['axes.labelsize'] = 10\n", "plt.rcParams['axes.labelweight'] = 'bold'\n", "plt.rcParams['axes.titlesize'] = 10\n", "plt.rcParams['xtick.labelsize'] = 8\n", "plt.rcParams['ytick.labelsize'] = 8\n", "plt.rcParams['legend.fontsize'] = 10\n", "plt.rcParams['figure.titlesize'] = 12\n", "plt.rcParams['image.cmap'] = 'jet'\n", "plt.rcParams['image.interpolation'] = 'none'\n", "plt.rcParams['figure.figsize'] = (12, 6)\n", "plt.rcParams['lines.linewidth'] = 2\n", "\n", "\n", "colors = ['xkcd:pale orange', 'xkcd:sea blue', 'xkcd:pale red', 'xkcd:sage green', 'xkcd:terra cotta', 'xkcd:dull purple', 'xkcd:teal', 'xkcd:goldenrod', 'xkcd:cadet blue', \n", " 'xkcd:scarlet']\n", "cmap_big = cm.get_cmap('Spectral', 512)\n", "cmap = mcolors.ListedColormap(cmap_big(np.linspace(0.7, 0.95, 256)))\n", "\n", "bbox_props = dict(boxstyle=\"round,pad=0.3\", fc=colors[0], alpha=.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$d$ funzioni base gaussiane, con medie intervallate in modo costante nel dominio considerato e varianza unitaria" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "def vphi(x, d, dom):\n", " l = np.linspace(domain[0], domain[1], d+1)\n", " mus = [(l[i]+l[i+1])/2.0 for i in range(len(l)-1)]\n", " return np.array([gaussian_basis(x, mus[i], 1) for i in range(d)]).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Funzione base gaussiana" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "def gaussian_basis(x, m, s):\n", " return np.exp(-((x-m)**2)/(2*s**2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Genera la matrice delle features e il vettore target" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "# dominio della feature\n", "domain=(0,2*np.pi)\n", "# numero di elementi da generare\n", "n=10\n", "# array delle feature generato uniformemente nel dominio\n", "X=np.random.uniform(domain[0], domain[1], n)\n", "\n", "# genera il vettore target mediante la funzione f e l'aggiunta di rumore gaussiano\n", "# funzione \n", "def f(x):\n", " return np.sin(x)\n", "# sd del rumore\n", "noise = .05\n", "\n", "#genera target\n", "t=np.array([(f(v)+np.random.normal(0,noise,1))[0] for v in X]).reshape(-1,1)\n", "\n", "# numero di funzioni base\n", "d=8\n", "# genera immagine di X per la regressione\n", "Phi = vphi(X,d, domain)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Iperparametri" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "# iperparametro per il prior\n", "alfa=.2\n", "# parametri del prior\n", "mu=np.zeros(d+1)\n", "sigma=np.eye(d+1)*alfa\n", "\n", "# parametro per la verosimiglianza\n", "beta=50" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Distribuzione predittiva dato un valore $v$" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "# media della distribuzione predittiva\n", "def m_pred(v):\n", " return m.T.dot(vphi(v,d,domain))\n", " \n", "# varianza della distribuzione predittiva \n", "def var_pred(v):\n", " v1=vphi(v,d,domain)\n", " return 1.0/beta+v1.dot(s.dot(v1.T))" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "# numero elementi considerati per il training\n", "l=10\n", "# estrazione del training set\n", "X_t, t_t = Phi[:l,:], t[:l]\n", "\n", "# derivazione di media e matrice di covarianza a posteriori\n", "s = np.linalg.inv(np.eye(d)+beta*np.dot(X_t.T,X_t))\n", "m=beta*s.dot(X_t.T.dot(t_t))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot della distribuzione predittiva" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# insieme dei valori considerati per il plot\n", "xx=np.linspace(min(X),max(X),500)\n", "# loro immagini per il calcolo della regressione\n", "phix=vphi(xx,d,domain)\n", "\n", "# calcolo di media e varianza della distribuzione predittiva per tutti i valori\n", "mx = np.vectorize(m_pred)(xx)\n", "sx= np.vectorize(var_pred)(xx)\n", "\n", "# visualizzazione\n", "fig = plt.figure(figsize=(16,8))\n", "ax = fig.gca()\n", "# plot della media\n", "ax.plot(xx,mx,'-', c=colors[9], alpha=1)\n", "# riempimento della regione a distanza minore di una sd dalla media\n", "ax.fill_between(xx, mx-np.sqrt(sx), mx+np.sqrt(sx), facecolor=colors[9], alpha=.15)\n", "# elementi dell'insieme\n", "ax.scatter(X[l:], t[l:], c=colors[1], marker='o', alpha=1)\n", "ax.scatter(X[:l], t[:l], c=colors[2], marker='o', alpha=1)\n", "# plot funzione originale\n", "ax.plot(xx,f(xx),'--',c=colors[1],alpha=1)\n", "plt.xlabel(u'$x$', fontsize=10)\n", "plt.ylabel(u'$y$', fontsize=10)\n", "plt.xticks(fontsize=10)\n", "plt.yticks(fontsize=10)\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "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": "3.8.0" } }, "nbformat": 4, "nbformat_minor": 2 }