{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Notebook 4: Linear Regression (Ising)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning Goal\n", "Let us now apply linear regression to an example that is familiar from Statistical Mechanics: the Ising model. The goal of this notebook is to revisit the concepts of in-sample and out-of-sample errors, as well as $L2$- and $L1$-regularization, in an example that is more intuitive to physicists. \n", "\n", "## Overview\n", "Consider the 1D Ising model with nearest-neighbor interactions \n", "\n", "$$H[\\boldsymbol{S}]=-J\\sum_{j=1}^L S_{j}S_{j+1}$$\n", "\n", "on a chain of length $L$ with periodic boundary conditions and $S_j=\\pm 1$ Ising spin variables. In one dimension, this paradigmatic model has no phase transition at finite temperature. \n", "\n", "\n", "### Exercises (optional): ### \n", "We invite the reader who is unfamiliar with the property of the Ising model to solve the following problems.\n", "
\n", "
• Compute the partition function of the Ising model in one dimension at inverse temperature $\\beta$ when $L\\rightarrow\\infty$ (thermodynamic limit):\n", " $$Z=\\sum_S \\exp(-\\beta H[S]).$$\n", "Here the sum is carried over all $2^L$ spin configurations.\n", "
• Compute the model's magnetization $M=\\langle\\sum_i S_i\\rangle$ in the same limit ($L\\rightarrow\\infty$). The expectation is taken with respect to the Boltzmann distribution:\n", " $$p(S)=\\frac{\\exp(-\\beta H[S])}{Z}$$\n", "
• How does $M$ behave as a function of the temperature $T=\\beta^{-1}$?\n", "
\n", "\n", "For a more detailed introduction we refer the reader to consult one of the many textbooks on the subject (see for instance Goldenfeld, Lubensky, Baxter , etc.).\n", "\n", "### Learning the Ising model ###\n", "\n", "Suppose your boss set $J=1$, drew a large number of spin configurations, and computed their Ising energies. Then, without telling you about the above Hamiltonian, he or she handed you a data set of $i=1\\ldots n$ points of the form $\\{(H[\\boldsymbol{S}^i],\\boldsymbol{S}^i)\\}$. Your task is to learn the Hamiltonian using Linear regression techniques. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.sparse as sp\n", "np.random.seed(12)\n", "\n", "\n", "import warnings\n", "# Comment this to turn on warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "### define Ising model aprams\n", "# system size\n", "L=40\n", "\n", "# create 10000 random Ising states\n", "states=np.random.choice([-1, 1], size=(10000,L))\n", "\n", "def ising_energies(states):\n", " \"\"\"\n", " This function calculates the energies of the states in the nn Ising Hamiltonian\n", " \"\"\"\n", " L = states.shape[1]\n", " J = np.zeros((L, L),)\n", " for i in range(L): \n", " J[i,(i+1)%L]=-1.0 # interaction between nearest-neighbors\n", " \n", " # compute energies\n", " E = np.einsum('...i,ij,...j->...',states,J,states)\n", "\n", " return E\n", "# calculate Ising energies\n", "energies=ising_energies(states)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Recasting the problem as a Linear Regression\n", "First of all, we have to decide on a model class (possible Hamiltonians) we use to fit the data. In the absence of any prior knowledge, one sensible choice is the all-to-all Ising model\n", "\n", "$$\n", "H_\\mathrm{model}[\\boldsymbol{S}^i] = - \\sum_{j=1}^L \\sum_{k=1}^L J_{j,k}S_{j}^iS_{k}^i.\n", "$$\n", "Notice that this model is uniquely defined by the non-local coupling strengths $J_{jk}$ which we want to learn. Importantly, this model is linear in ${\\mathbf J}$ which makes it possible to use linear regression.\n", "\n", "To apply linear regression, we would like to recast this model in the form\n", "$$\n", "H_\\mathrm{model}^i \\equiv \\mathbf{X}^i \\cdot \\mathbf{J},\n", "$$\n", "\n", "where the vectors $\\mathbf{X}^i$ represent all two-body interactions $\\{S_{j}^iS_{k}^i \\}_{j,k=1}^L$, and the index $i$ runs over the samples in the data set. To make the analogy complete, we can also represent the dot product by a single index $p = \\{j,k\\}$, i.e. $\\mathbf{X}^i \\cdot \\mathbf{J}=X^i_pJ_p$. Note that the regression model does not include the minus sign, so we expect to learn negative $J$'s." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# reshape Ising states into RL samples: S_iS_j --> X_p\n", "states=np.einsum('...i,...j->...ij', states, states)\n", "shape=states.shape\n", "states=states.reshape((shape[0],shape[1]*shape[2]))\n", "# build final data set\n", "Data=[states,energies]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical Experiments\n", "\n", "As we already mentioned a few times in the review, learning is not fitting: the subtle difference is that once we fit the data to obtain a candidate model, we expect it to generalize to unseen data not used for the fitting procedure. For this reason, we begin by specifying a training and test data sets" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# define number of samples\n", "n_samples=400\n", "# define train and test data sets\n", "X_train=Data[0][:n_samples]\n", "Y_train=Data[1][:n_samples] #+ np.random.normal(0,4.0,size=X_train.shape[0])\n", "X_test=Data[0][n_samples:3*n_samples//2]\n", "Y_test=Data[1][n_samples:3*n_samples//2] #+ np.random.normal(0,4.0,size=X_test.shape[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Evaluating the performance: coefficient of determination $R^2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In what follows the model performance (in-sample and out-of-sample) is evaluated using the so-called coefficient of determination, which is given by:\n", "\\begin{align}\n", "R^2 &= \\left(1-\\frac{u}{v}\\right),\\\\\n", "u&=(y_{pred}-y_{true})^2\\\\\n", "v&=(y_{true}-\\langle y_{true}\\rangle)^2\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The best possible score is 1.0 but it can also be negative. A constant model that always predicts the expected value of $y$, $\\langle y_{true}\\rangle$, disregarding the input features, would get a $R^2$ score of 0." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Applying OLS, Ridge regression and LASSO:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:492: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n", " ConvergenceWarning)\n" ] }, { "data": { "image/png": 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\n", 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