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org.nd4j.evaluation.regression.RegressionEvaluation Maven / Gradle / Ivy
/*******************************************************************************
* Copyright (c) 2015-2018 Skymind, Inc.
*
* This program and the accompanying materials are made available under the
* terms of the Apache License, Version 2.0 which is available at
* https://www.apache.org/licenses/LICENSE-2.0.
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations
* under the License.
*
* SPDX-License-Identifier: Apache-2.0
******************************************************************************/
package org.nd4j.evaluation.regression;
import lombok.Data;
import lombok.EqualsAndHashCode;
import lombok.val;
import org.nd4j.evaluation.BaseEvaluation;
import org.nd4j.evaluation.IEvaluation;
import org.nd4j.evaluation.IMetric;
import org.nd4j.linalg.api.buffer.DataType;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.api.ops.impl.reduce.same.ASum;
import org.nd4j.linalg.factory.Nd4j;
import org.nd4j.common.primitives.Triple;
import org.nd4j.serde.jackson.shaded.NDArrayTextDeSerializer;
import org.nd4j.serde.jackson.shaded.NDArrayTextSerializer;
import org.nd4j.shade.jackson.databind.annotation.JsonDeserialize;
import org.nd4j.shade.jackson.databind.annotation.JsonSerialize;
import java.io.Serializable;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
/**
* Evaluation method for the evaluation of regression algorithms.http://www.saedsayad.com/model_evaluation_r.htm
* For classification, see {@link Evaluation}
*
* @author Alex Black
*/
@Data
@EqualsAndHashCode(callSuper = true)
public class RegressionEvaluation extends BaseEvaluation {
public enum Metric implements IMetric { MSE, MAE, RMSE, RSE, PC, R2;
@Override
public Class getEvaluationClass() {
return RegressionEvaluation.class;
}
/**
* @return True if the metric should be minimized, or false if the metric should be maximized.
* For example, MSE of 0 is best, but R^2 of 1.0 is best
*/
@Override
public boolean minimize(){
if(this == R2 || this == PC){
return false;
}
return true;
}
}
public static final int DEFAULT_PRECISION = 5;
@EqualsAndHashCode.Exclude //Exclude axis: otherwise 2 Evaluation instances could contain identical stats and fail equality
protected int axis = 1;
private boolean initialized;
private List columnNames;
private long precision;
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray exampleCountPerColumn; //Necessary to account for per-output masking
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray labelsSumPerColumn; //sum(actual) per column -> used to calculate mean
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray sumSquaredErrorsPerColumn; //(predicted - actual)^2
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray sumAbsErrorsPerColumn; //abs(predicted-actial)
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray currentMean;
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray currentPredictionMean;
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray sumOfProducts;
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray sumSquaredLabels;
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray sumSquaredPredicted;
@JsonSerialize(using = NDArrayTextSerializer.class)
@JsonDeserialize(using = NDArrayTextDeSerializer.class)
private INDArray sumLabels;
protected RegressionEvaluation(int axis, List columnNames, long precision){
this.axis = axis;
this.columnNames = columnNames;
this.precision = precision;
}
public RegressionEvaluation() {
this(null, DEFAULT_PRECISION);
}
/** Create a regression evaluation object with the specified number of columns, and default precision
* for the stats() method.
* @param nColumns Number of columns
*/
public RegressionEvaluation(long nColumns) {
this(createDefaultColumnNames(nColumns), DEFAULT_PRECISION);
}
/** Create a regression evaluation object with the specified number of columns, and specified precision
* for the stats() method.
* @param nColumns Number of columns
*/
public RegressionEvaluation(long nColumns, long precision) {
this(createDefaultColumnNames(nColumns), precision);
}
/** Create a regression evaluation object with default precision for the stats() method
* @param columnNames Names of the columns
*/
public RegressionEvaluation(String... columnNames) {
this(columnNames == null || columnNames.length == 0 ? null : Arrays.asList(columnNames), DEFAULT_PRECISION);
}
/** Create a regression evaluation object with default precision for the stats() method
* @param columnNames Names of the columns
*/
public RegressionEvaluation(List columnNames) {
this(columnNames, DEFAULT_PRECISION);
}
/** Create a regression evaluation object with specified precision for the stats() method
* @param columnNames Names of the columns
*/
public RegressionEvaluation(List columnNames, long precision) {
this.precision = precision;
if (columnNames == null || columnNames.isEmpty()) {
initialized = false;
} else {
this.columnNames = columnNames;
initialize(columnNames.size());
}
}
/**
* Set the axis for evaluation - this is the dimension along which the probability (and label classes) are present. createDefaultColumnNames(long nColumns) {
List list = new ArrayList<>((int) nColumns);
for (int i = 0; i < nColumns; i++)
list.add("col_" + i);
return list;
}
@Override
public void eval(INDArray labels, INDArray predictions) {
eval(labels, predictions, (INDArray) null);
}
@Override
public void eval(INDArray labels, INDArray networkPredictions, INDArray maskArray, List recordMetaData) {
eval(labels, networkPredictions, maskArray);
}
@Override
public void eval(INDArray labelsArr, INDArray predictionsArr, INDArray maskArr) {
Triple p = BaseEvaluation.reshapeAndExtractNotMasked(labelsArr, predictionsArr, maskArr, axis);
INDArray labels = p.getFirst();
INDArray predictions = p.getSecond();
INDArray maskArray = p.getThird();
if(labels.dataType() != predictions.dataType())
labels = labels.castTo(predictions.dataType());
if (!initialized) {
initialize((int) labels.size(1));
}
//References for the calculations is this section:
//https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Online_algorithm
//https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient#For_a_sample
//Doing online calculation of means, sum of squares, etc.
if (columnNames.size() != labels.size(1) || columnNames.size() != predictions.size(1)) {
throw new IllegalArgumentException(
"Number of the columns of labels and predictions must match specification ("
+ columnNames.size() + "). Got " + labels.size(1) + " and "
+ predictions.size(1));
}
if (maskArray != null) {
//Handle per-output masking. We are assuming *binary* masks here
labels = labels.mul(maskArray);
predictions = predictions.mul(maskArray);
}
labelsSumPerColumn.addi(labels.sum(0).castTo(labelsSumPerColumn.dataType()));
INDArray error = predictions.sub(labels);
INDArray absErrorSum = Nd4j.getExecutioner().exec(new ASum(error, 0));
INDArray squaredErrorSum = error.mul(error).sum(0);
sumAbsErrorsPerColumn.addi(absErrorSum.castTo(labelsSumPerColumn.dataType()));
sumSquaredErrorsPerColumn.addi(squaredErrorSum.castTo(labelsSumPerColumn.dataType()));
sumOfProducts.addi(labels.mul(predictions).sum(0).castTo(labelsSumPerColumn.dataType()));
sumSquaredLabels.addi(labels.mul(labels).sum(0).castTo(labelsSumPerColumn.dataType()));
sumSquaredPredicted.addi(predictions.mul(predictions).sum(0).castTo(labelsSumPerColumn.dataType()));
val nRows = labels.size(0);
INDArray newExampleCountPerColumn;
if (maskArray == null) {
newExampleCountPerColumn = exampleCountPerColumn.add(nRows);
} else {
newExampleCountPerColumn = exampleCountPerColumn.add(maskArray.sum(0).castTo(labelsSumPerColumn.dataType()));
}
currentMean.muliRowVector(exampleCountPerColumn).addi(labels.sum(0).castTo(labelsSumPerColumn.dataType())).diviRowVector(newExampleCountPerColumn);
currentPredictionMean.muliRowVector(exampleCountPerColumn).addi(predictions.sum(0).castTo(labelsSumPerColumn.dataType()))
.divi(newExampleCountPerColumn);
exampleCountPerColumn = newExampleCountPerColumn;
sumLabels.addi(labels.sum(0).castTo(labelsSumPerColumn.dataType()));
}
@Override
public void merge(RegressionEvaluation other) {
if (other.labelsSumPerColumn == null) {
//Other RegressionEvaluation is empty -> no op
return;
} else if (labelsSumPerColumn == null) {
//This RegressionEvaluation is empty -> just copy over from the other one...
this.columnNames = other.columnNames;
this.precision = other.precision;
this.exampleCountPerColumn = other.exampleCountPerColumn;
this.labelsSumPerColumn = other.labelsSumPerColumn.dup();
this.sumSquaredErrorsPerColumn = other.sumSquaredErrorsPerColumn.dup();
this.sumAbsErrorsPerColumn = other.sumAbsErrorsPerColumn.dup();
this.currentMean = other.currentMean.dup();
this.currentPredictionMean = other.currentPredictionMean.dup();
this.sumOfProducts = other.sumOfProducts.dup();
this.sumSquaredLabels = other.sumSquaredLabels.dup();
this.sumSquaredPredicted = other.sumSquaredPredicted.dup();
return;
}
this.labelsSumPerColumn.addi(other.labelsSumPerColumn);
this.sumSquaredErrorsPerColumn.addi(other.sumSquaredErrorsPerColumn);
this.sumAbsErrorsPerColumn.addi(other.sumAbsErrorsPerColumn);
this.currentMean.muliRowVector(exampleCountPerColumn)
.addi(other.currentMean.mulRowVector(other.exampleCountPerColumn))
.diviRowVector(exampleCountPerColumn.add(other.exampleCountPerColumn));
this.currentPredictionMean.muliRowVector(exampleCountPerColumn)
.addi(other.currentPredictionMean.mulRowVector(other.exampleCountPerColumn))
.diviRowVector(exampleCountPerColumn.add(other.exampleCountPerColumn));
this.sumOfProducts.addi(other.sumOfProducts);
this.sumSquaredLabels.addi(other.sumSquaredLabels);
this.sumSquaredPredicted.addi(other.sumSquaredPredicted);
this.exampleCountPerColumn.addi(other.exampleCountPerColumn);
}
public String stats() {
if (!initialized) {
return "RegressionEvaluation: No Data";
} else {
if (columnNames == null)
columnNames = createDefaultColumnNames(numColumns());
int maxLabelLength = 0;
for (String s : columnNames)
maxLabelLength = Math.max(maxLabelLength, s.length());
int labelWidth = maxLabelLength + 5;
long columnWidth = precision + 10;
String resultFormat = "%-" + labelWidth + "s" +
"%-" + columnWidth + "." + precision + "e" + //MSE
"%-" + columnWidth + "." + precision + "e" + //MAE
"%-" + columnWidth + "." + precision + "e" + //RMSE
"%-" + columnWidth + "." + precision + "e" + //RSE
"%-" + columnWidth + "." + precision + "e" + //PC
"%-" + columnWidth + "." + precision + "e"; //R2
//Print header:
StringBuilder sb = new StringBuilder();
String headerFormat = "%-" + labelWidth + "s" +
"%-" + columnWidth + "s" + // MSE
"%-" + columnWidth + "s" + // MAE
"%-" + columnWidth + "s" + // RMSE
"%-" + columnWidth + "s" + // RSE
"%-" + columnWidth + "s" + // PC
"%-" + columnWidth + "s"; // R2
sb.append(String.format(headerFormat, "Column", "MSE", "MAE", "RMSE", "RSE", "PC", "R^2"));
sb.append("\n");
//Print results for each column:
for (int i = 0; i < columnNames.size(); i++) {
String name = columnNames.get(i);
double mse = meanSquaredError(i);
double mae = meanAbsoluteError(i);
double rmse = rootMeanSquaredError(i);
double rse = relativeSquaredError(i);
double corr = pearsonCorrelation(i);
double r2 = rSquared(i);
sb.append(String.format(resultFormat, name, mse, mae, rmse, rse, corr, r2));
sb.append("\n");
}
return sb.toString();
}
}
public int numColumns() {
if (columnNames == null) {
if (exampleCountPerColumn == null) {
return 0;
}
return (int) exampleCountPerColumn.size(1);
}
return columnNames.size();
}
public double meanSquaredError(int column) {
//mse per column: 1/n * sum((predicted-actual)^2)
return sumSquaredErrorsPerColumn.getDouble(column) / exampleCountPerColumn.getDouble(column);
}
public double meanAbsoluteError(int column) {
//mse per column: 1/n * |predicted-actual|
return sumAbsErrorsPerColumn.getDouble(column) / exampleCountPerColumn.getDouble(column);
}
public double rootMeanSquaredError(int column) {
//rmse per column: sqrt(1/n * sum((predicted-actual)^2)
return Math.sqrt(sumSquaredErrorsPerColumn.getDouble(column) / exampleCountPerColumn.getDouble(column));
}
/**
* Legacy method for the correlation score.
*
* @param column Column to evaluate
* @return Pearson Correlation for the given column
* @see {@link #pearsonCorrelation(int)}
* @deprecated Use {@link #pearsonCorrelation(int)} instead.
* For the R2 score use {@link #rSquared(int)}.
*/
@Deprecated
public double correlationR2(int column) {
return pearsonCorrelation(column);
}
/**
* Pearson Correlation Coefficient for samples
*
* @param column Column to evaluate
* @return Pearson Correlation Coefficient for column with index {@code column}
* @see Wikipedia
*/
public double pearsonCorrelation(int column) {
double sumxiyi = sumOfProducts.getDouble(column);
double predictionMean = currentPredictionMean.getDouble(column);
double labelMean = currentMean.getDouble(column);
double sumSquaredLabels = this.sumSquaredLabels.getDouble(column);
double sumSquaredPredicted = this.sumSquaredPredicted.getDouble(column);
double exampleCount = exampleCountPerColumn.getDouble(column);
double r = sumxiyi - exampleCount * predictionMean * labelMean;
r /= Math.sqrt(sumSquaredLabels - exampleCount * labelMean * labelMean)
* Math.sqrt(sumSquaredPredicted - exampleCount * predictionMean * predictionMean);
return r;
}
/**
* Coefficient of Determination (R^2 Score)
*
* @param column Column to evaluate
* @return R^2 score for column with index {@code column}
* @see Wikipedia
*/
public double rSquared(int column) {
//ss_tot = sum_i (label_i - mean(labels))^2
// = (sum_i label_i^2) + mean(labels) * (n * mean(labels) - 2 * sum_i label_i)
double sumLabelSquared = sumSquaredLabels.getDouble(column);
double meanLabel = currentMean.getDouble(column);
double sumLabel = sumLabels.getDouble(column);
double n = exampleCountPerColumn.getDouble(column);
double sstot = sumLabelSquared + meanLabel * (n * meanLabel - 2 * sumLabel);
double ssres = sumSquaredErrorsPerColumn.getDouble(column);
return (sstot - ssres) / sstot;
}
public double relativeSquaredError(int column) {
// RSE: sum(predicted-actual)^2 / sum(actual-labelsMean)^2
// (sum(predicted^2) - 2 * sum(predicted * actual) + sum(actual ^ 2)) / (sum(actual ^ 2) - n * actualMean)
double numerator = sumSquaredPredicted.getDouble(column) - 2 * sumOfProducts.getDouble(column)
+ sumSquaredLabels.getDouble(column);
double denominator = sumSquaredLabels.getDouble(column) - exampleCountPerColumn.getDouble(column)
* currentMean.getDouble(column) * currentMean.getDouble(column);
if (Math.abs(denominator) > Nd4j.EPS_THRESHOLD) {
return numerator / denominator;
} else {
return Double.POSITIVE_INFINITY;
}
}
/**
* Average MSE across all columns
* @return
*/
public double averageMeanSquaredError() {
double ret = 0.0;
for (int i = 0; i < numColumns(); i++) {
ret += meanSquaredError(i);
}
return ret / (double) numColumns();
}
/**
* Average MAE across all columns
* @return
*/
public double averageMeanAbsoluteError() {
double ret = 0.0;
for (int i = 0; i < numColumns(); i++) {
ret += meanAbsoluteError(i);
}
return ret / (double) numColumns();
}
/**
* Average RMSE across all columns
* @return
*/
public double averagerootMeanSquaredError() {
double ret = 0.0;
for (int i = 0; i < numColumns(); i++) {
ret += rootMeanSquaredError(i);
}
return ret / (double) numColumns();
}
/**
* Average RSE across all columns
* @return
*/
public double averagerelativeSquaredError() {
double ret = 0.0;
for (int i = 0; i < numColumns(); i++) {
ret += relativeSquaredError(i);
}
return ret / (double) numColumns();
}
/**
* Legacy method for the correlation average across all columns.
*
* @return Pearson Correlation averaged over all columns
* @see {@link #averagePearsonCorrelation()}
* @deprecated Use {@link #averagePearsonCorrelation()} instead.
* For the R2 score use {@link #averageRSquared()}.
*/
@Deprecated
public double averagecorrelationR2() {
return averagePearsonCorrelation();
}
/**
* Average Pearson Correlation Coefficient across all columns
*
* @return Pearson Correlation Coefficient across all columns
*/
public double averagePearsonCorrelation() {
double ret = 0.0;
for (int i = 0; i < numColumns(); i++) {
ret += pearsonCorrelation(i);
}
return ret / (double) numColumns();
}
/**
* Average R2 across all columns
*
* @return R2 score accross all columns
*/
public double averageRSquared() {
double ret = 0.0;
for (int i = 0; i < numColumns(); i++) {
ret += rSquared(i);
}
return ret / (double) numColumns();
}
@Override
public double getValue(IMetric metric){
if(metric instanceof Metric){
return scoreForMetric((Metric) metric);
} else
throw new IllegalStateException("Can't get value for non-regression Metric " + metric);
}
public double scoreForMetric(Metric metric){
switch (metric){
case MSE:
return averageMeanSquaredError();
case MAE:
return averageMeanAbsoluteError();
case RMSE:
return averagerootMeanSquaredError();
case RSE:
return averagerelativeSquaredError();
case PC:
return averagePearsonCorrelation();
case R2:
return averageRSquared();
default:
throw new IllegalStateException("Unknown metric: " + metric);
}
}
public static RegressionEvaluation fromJson(String json){
return fromJson(json, RegressionEvaluation.class);
}
@Override
public RegressionEvaluation newInstance() {
return new RegressionEvaluation(axis, columnNames, precision);
}
}
