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/*
* File: PrimalEstimatedSubGradient.java
* Authors: Justin Basilico
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright January 18, 2010, Sandia Corporation.
* Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
* license for use of this work by or on behalf of the U.S. Government. Export
* of this program may require a license from the United States Government.
* See CopyrightHistory.txt for complete details.
*
*/
package gov.sandia.cognition.learning.algorithm.svm;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.collection.CollectionUtil;
import gov.sandia.cognition.learning.algorithm.AbstractAnytimeSupervisedBatchLearner;
import gov.sandia.cognition.learning.data.DatasetUtil;
import gov.sandia.cognition.learning.data.InputOutputPair;
import gov.sandia.cognition.learning.function.categorization.LinearBinaryCategorizer;
import gov.sandia.cognition.statistics.DiscreteSamplingUtil;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.math.matrix.Vectorizable;
import gov.sandia.cognition.util.ArgumentChecker;
import gov.sandia.cognition.util.Randomized;
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
/**
* An implementation of the Primal Estimated Sub-Gradient Solver (PEGASOS)
* algorithm for learning a linear support vector machine (SVM).
*
* @author Justin Basilico
* @since 3.1
*/
@PublicationReference(
author={"Shai Shalev-Shwartz", "Yoram Singer", "Nathan Srebro"},
title="Pegasos: Primal Estimated sub-GrAdient SOlver for SVM",
year=2007,
type=PublicationType.Conference,
publication="Proceedings of the 24th International Conference on Machine Learning",
url="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.74.8513"
)
public class PrimalEstimatedSubGradient
extends AbstractAnytimeSupervisedBatchLearner
implements Randomized
{
/** The default sample size is {@value}. */
public static final int DEFAULT_SAMPLE_SIZE = 100;
/** The default regularization weight is {@value}. */
public static final double DEFAULT_REGULARIZATION_WEIGHT = 0.0001;
/** The default maximum number of iterations is {@value}. */
public static final int DEFAULT_MAX_ITERATIONS = 10000;
/** The sample size requested by the user. The actual sample size may be
* less than this in the case that the sample size is larger than the
* amount of data given in the training set. */
protected int sampleSize;
/** The weight assigned to the regularization term in the algorithm, which
* is often represented as lambda. */
protected double regularizationWeight;
/** The random number generator to use. */
protected Random random;
/** The size of the data in the training set. */
protected transient int dataSize;
/** The data represented as a list. */
protected transient ArrayList> dataList;
/** The dimensionality of the dataset. */
protected transient int dimensionality;
/** The minimum of the sample size and the data size. */
protected transient int dataSampleSize;
/** A vector used to compute the update for the weight vector. It acts as a
* workspace so that multiple vectors do not need to be created in the
* algorithm, thus reducing the overall number of objects created. */
protected transient Vector update;
/** The categorizer learned as a result of the algorithm. */
protected transient LinearBinaryCategorizer result;
/**
* Creates a new {@code PrimalEstimatedSubGradient} with default parameters.
*/
public PrimalEstimatedSubGradient()
{
this(DEFAULT_SAMPLE_SIZE, DEFAULT_REGULARIZATION_WEIGHT,
DEFAULT_MAX_ITERATIONS, new Random());
}
/**
* Creates a new {@code PrimalEstimatedSubGradient} with the given
* parameters.
*
* @param sampleSize
* The number of examples sampled from the dataset on each iteration.
* @param regularizationWeight
* The regularization weight (lambda). Must be positive.
* @param maxIterations
* The maximum number of iterations. Must be positive.
* @param random
* The random number generator to use.
*/
public PrimalEstimatedSubGradient(
final int sampleSize,
final double regularizationWeight,
final int maxIterations,
final Random random)
{
super(maxIterations);
this.setSampleSize(sampleSize);
this.setRegularizationWeight(regularizationWeight);
this.setRandom(random);
}
@Override
protected boolean initializeAlgorithm()
{
// Figure out if there is enough data to run the algorithm.
if (CollectionUtil.isEmpty(this.data))
{
// Can't run the algorithm on empty data.
return false;
}
this.dataSize = this.data.size();
this.dataList = CollectionUtil.asArrayList(this.data);
this.dimensionality = DatasetUtil.getInputDimensionality(this.data);
this.dataSampleSize = Math.min(dataSize, this.sampleSize);
// Compute a vector to store the update that gets reused between steps.
final VectorFactory vectorFactory = VectorFactory.getDenseDefault();
this.update = vectorFactory.createVector(this.dimensionality);
// Create initial random weights.
final double lambda = this.regularizationWeight;
final double sqrtLambda = Math.sqrt(lambda);
final double initializationRange =
1.0 / (this.dimensionality * sqrtLambda);
final Vector initialWeights =
vectorFactory.createUniformRandom(this.dimensionality,
-initializationRange, initializationRange, this.random);
if (initialWeights.norm2() < (1.0 / sqrtLambda))
{
initialWeights.unitVectorEquals();
initialWeights.scaleEquals(1.0 / sqrtLambda);
}
this.result = new LinearBinaryCategorizer(initialWeights, 0.0);
// Compute a vector to store the update that gets reused between steps.
this.update = vectorFactory.createVector(this.dimensionality);
return true;
}
@Override
protected boolean step()
{
// Sample a sub-set of the dataset.
final List>
subSet = DiscreteSamplingUtil.sampleWithoutReplacement(
random, dataList, dataSampleSize);
// Compute the learning rate (eta).
final double lambda = this.regularizationWeight;
final double learningRate = 1.0 / (lambda * this.iteration);
// Compute the update to the weight vector.
this.update.zero();
double biasUpdate = 0.0;
int errorCount = 0;
for (InputOutputPair example : subSet)
{
final boolean output = example.getOutput();
final double actual = output ? +1.0 : -1.0;
final double predicted = this.result.evaluateAsDouble(
example.getInput());
if (actual * predicted < 1.0)
{
// An error occurred.
errorCount++;
// Increment the update vector.
final Vector input = example.getInput().convertToVector();
if (output)
{
this.update.plusEquals(input);
}
else
{
this.update.minusEquals(input);
}
biasUpdate += actual;
}
// else - No update required.
}
// Update the weights.
final Vector weights = this.result.getWeights();
// Regularization shrinkage.
weights.scaleEquals(1.0 - (learningRate * lambda));
// Apply update.
final double stepSize = learningRate / subSet.size();
this.update.scaleEquals(stepSize);
weights.plusEquals(this.update);
// Bias doesn't get regularized or projected.
biasUpdate *= stepSize;
double bias = this.result.getBias() + biasUpdate;
// w_t+1 = min{1, (1 / sqrt(lambda)) / ||w_t+1/2||)} w_t+1/2
final double norm2Squared = weights.norm2Squared();
final double projection = 1.0 / Math.sqrt(lambda * norm2Squared);
if (projection < 1.0)
{
weights.scaleEquals(projection);
}
this.result.setWeights(weights);
this.result.setBias(bias);
return true;
}
@Override
protected void cleanupAlgorithm()
{
this.dataList = null;
this.update = null;
}
@Override
public LinearBinaryCategorizer getResult()
{
return this.result;
}
/**
* Gets the sample size, which is the number of examples sampled without
* replacement on each iteration of the algorithm.
*
* @return
* The sample size. Must be positive.
*/
public int getSampleSize()
{
return this.sampleSize;
}
/**
* Sets the sample size, which is the number of examples sampled without
* replacement on each iteration of the algorithm.
*
* @param sampleSize
* The sample size. Must be positive.
*/
public void setSampleSize(
final int sampleSize)
{
ArgumentChecker.assertIsPositive("sampleSize", sampleSize);
this.sampleSize = sampleSize;
}
/**
* Gets the regularization weight (lambda) assigned to the regularization
* term of the algorithm.
*
* @return
* The regularization weight. Must be positive.
*/
public double getRegularizationWeight()
{
return this.regularizationWeight;
}
/**
* Sets the regularization weight (lambda) assigned to the regularization
* term of the algorithm.
*
* @param regularizationWeight
* The regularization weight. Must be positive.
*/
public void setRegularizationWeight(
final double regularizationWeight)
{
ArgumentChecker.assertIsPositive("regularizationWeight",
regularizationWeight);
this.regularizationWeight = regularizationWeight;
}
public Random getRandom()
{
return this.random;
}
public void setRandom(
final Random random)
{
this.random = random;
}
}