{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# GOWL Example" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The autoreload extension is already loaded. To reload it, use:\n", " %reload_ext autoreload\n" ] } ], "source": [ "import numpy as np\n", "from src.models.gowl import GOWLModel\n", "\n", "from src.data.make_synthetic_data import generate_theta_star_gowl, standardize\n", "from src.visualization.visualize import plot_multiple_theta_matrices_2d\n", "from sklearn.covariance import GraphicalLasso\n", "\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the Graphical Order Weighted $\\ell_1$ (GOWL) estimator to be the solution to the following constrained optimization problem:\n", "\n", "$$\\min_{\\Theta \\succ 0} - \\log \\text{det } \\Theta + \\text{tr}(S \\Theta) + \\Omega_{\\text{OWL}} (\\Theta)$$\n", "\n", "where \n", "\n", "$$\\Omega_{\\text{OWL}} (\\Theta) = \\lambda^T |\\text{vechs}(\\Theta)|_{\\downarrow} = \\sum_{i=1}^K \\lambda_i |\\text{vechs}(\\Theta)|_{[i]}$$\n", "\n", "Here $\\Theta \\in \\mathbb{R}^{p \\times p}$, $\\text{vechs}(\\Theta)_{[i]}$ is the $i^{th}$ largest off-diagonal component in magnitude of $\\Theta$, $K = (p^2 - p)/2$, and $\\lambda_1 \\ge \\lambda_2 \\ge \\cdots \\ge \\lambda_p \\ge 0$. The goal of this estimator is to identify correlated groups within the precision matrix estimator $\\hat{\\Theta}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Synthetic Data Example\n", "\n", "We design our first example for a very low $p$ and specify one group of size two. As is custom in the literature we also standardize our design matrix $X$." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "p = 10\n", "n = 100\n", "n_blocks = 1\n", "theta_star_eps, blocks, theta_star = generate_theta_star_gowl(p=p,\n", " alpha=0.5,\n", " noise=0.1,\n", " n_blocks=n_blocks,\n", " block_min_size=2,\n", " block_max_size=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hyperparameters should be chosen by cross-validation, but for this example we will choose $\\lambda_1 = 0.001$ and $\\lambda_2 = 0.01$. Now that we have generated $\\theta^*$ and $\\theta^* + \\varepsilon$ we can generate a dataset by drawing i.i.d. from $N(0, (\\theta^* + \\varepsilon)^{-1}$ distribution." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "theta_star_eps = theta_star_eps[0] # by default we generate 1 trial, but for simulations we generate many trials\n", "sigma = np.linalg.inv(theta_star_eps)\n", "n = 100\n", "X = np.random.multivariate_normal(np.zeros(p), sigma, n)\n", "X = standardize(X) # Standardize data to have mean zero and unit variance.\n", "S = np.cov(X.T)\n", "\n", "lam1 = 0.001 # controls sparsity\n", "lam2 = 0.01 # encourages equality of coefficients" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have generated the dataset, we can apply the GOWL model using G-ISTA with backtracking line search enabled and duality gap stopping criteria." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iterations: 17\n", "Duality Gap: -0.05034415853389618 < 1e-05. Exiting.\n" ] } ], "source": [ "model = GOWLModel(X, S, lam1, lam2, 'backtracking', max_iters=100000)\n", "model.fit()\n", "theta_gowl = model.theta_hat" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's compare the GOWL theta estimate to the Graphical LASSO model." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "gl = GraphicalLasso()\n", "gl.fit(S)\n", "theta_glasso = gl.get_precision()" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_multiple_theta_matrices_2d([\n", " theta_star, theta_star_eps, theta_glasso, theta_gowl\n", "], [\n", " f\"1 Block of Size 2\", 'True Theta + $\\epsilon$', 'GLASSO', 'GOWL'\n", "])" ] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }