owlqn

Author: Elmar Langholz

owlqn or Orthant-Wise Limited-memory Quasi-Newton is a minimizer used for training machine learning models. It minimizes functions of the form f(w) = loss(w) + C |w|_1, where loss is an arbitrary differentiable convex loss function, and |w|_1 is the L1 norm of the weight (parameter) vector. It is based on the LBFGS Quasi-Newton algorithm, with modifications to deal with the fact that the L1 norm is not differentiable. It was developed and published by Galen Andrew and Jianfeng Gao on Scalable training of L1-regularized log-linear models.

Two examples of machine learning models used are the following:

• L1-regularized least squares models, where OWL-QN finds weights w that minimize: sum_i 0.5 |<w, x_i> - y_i|^2_2 + C |w|_1
• L1-regularized logistic regression models, where OWL-QN finds weights w that minimize: sum_i log_loss(w | x_i, y_i) + C |w|_1

Installation

npm install owlqn

Usage

// Include dependencies
var OWLQN = require('owlqn').OWLQN;
var LogisticRegression = require('owlqn').LogisticRegression;

// Declare logistic regression problem
var logisticRegressionOptions = {
    features: [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]],
    labels: [-1, -1, -1, -1, 1, -1, 1, -1, 1, 1],
    l2Weight: 0.0
};
var logisticRegression = new LogisticRegression(logisticRegressionOptions);

// Define owl-qn optimizer and minimize
var owlqn = new OWQLN();
var minimizeOptions = {
    differentiableFunction: logisticRegression,
    initializationVector: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
    l1Weight: 0.1,
    memoryParameter: 10,
    convergenceTolerance: 1e-4;
};
var result = owlqn.minimize(minimizeOptions);

Documentation

• OWLQN
• LeastSquares
• LogisticRegression

Examples

• LeastSquares
• LogisticRegression