Implement pseudo Huber loss (PseudoHuber) evaluation metric for regression analysis (#58734)

client/rest-high-level/src/main/java/org/elasticsearch/client/ml/dataframe/evaluation/MlEvaluationNamedXContentProvider.java

@@ -23,6 +23,7 @@ import org.elasticsearch.client.ml.dataframe.evaluation.classification.Classific
 import org.elasticsearch.client.ml.dataframe.evaluation.classification.MulticlassConfusionMatrixMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.MeanSquaredErrorMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.MeanSquaredLogarithmicErrorMetric;
+import org.elasticsearch.client.ml.dataframe.evaluation.regression.PseudoHuberMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.RSquaredMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.Regression;
 import org.elasticsearch.client.ml.dataframe.evaluation.softclassification.AucRocMetric;
@@ -102,6 +103,10 @@ public class MlEvaluationNamedXContentProvider implements NamedXContentProvider
                 EvaluationMetric.class,
                 new ParseField(registeredMetricName(Regression.NAME, MeanSquaredLogarithmicErrorMetric.NAME)),
                 MeanSquaredLogarithmicErrorMetric::fromXContent),
+            new NamedXContentRegistry.Entry(
+                EvaluationMetric.class,
+                new ParseField(registeredMetricName(Regression.NAME, PseudoHuberMetric.NAME)),
+                PseudoHuberMetric::fromXContent),
             new NamedXContentRegistry.Entry(
                 EvaluationMetric.class,
                 new ParseField(registeredMetricName(Regression.NAME, RSquaredMetric.NAME)),
@@ -149,6 +154,10 @@ public class MlEvaluationNamedXContentProvider implements NamedXContentProvider
                 EvaluationMetric.Result.class,
                 new ParseField(registeredMetricName(Regression.NAME, MeanSquaredLogarithmicErrorMetric.NAME)),
                 MeanSquaredLogarithmicErrorMetric.Result::fromXContent),
+            new NamedXContentRegistry.Entry(
+                EvaluationMetric.Result.class,
+                new ParseField(registeredMetricName(Regression.NAME, PseudoHuberMetric.NAME)),
+                PseudoHuberMetric.Result::fromXContent),
             new NamedXContentRegistry.Entry(
                 EvaluationMetric.Result.class,
                 new ParseField(registeredMetricName(Regression.NAME, RSquaredMetric.NAME)),

client/rest-high-level/src/main/java/org/elasticsearch/client/ml/dataframe/evaluation/regression/PseudoHuberMetric.java

@@ -0,0 +1,142 @@
+/*
+ * Licensed to Elasticsearch under one or more contributor
+ * license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright
+ * ownership. Elasticsearch licenses this file to you under
+ * the Apache License, Version 2.0 (the "License"); you may
+ * not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://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.
+ */
+package org.elasticsearch.client.ml.dataframe.evaluation.regression;
+
+import org.elasticsearch.client.ml.dataframe.evaluation.EvaluationMetric;
+import org.elasticsearch.common.Nullable;
+import org.elasticsearch.common.ParseField;
+import org.elasticsearch.common.xcontent.ConstructingObjectParser;
+import org.elasticsearch.common.xcontent.XContentBuilder;
+import org.elasticsearch.common.xcontent.XContentParser;
+
+import java.io.IOException;
+import java.util.Objects;
+
+import static org.elasticsearch.common.xcontent.ConstructingObjectParser.constructorArg;
+import static org.elasticsearch.common.xcontent.ConstructingObjectParser.optionalConstructorArg;
+
+/**
+ * Calculates the pseudo Huber loss function.
+ *
+ * equation: pseudohuber = 1/n * Σ(δ^2 * sqrt(1 + a^2 / δ^2) - 1)
+ * where: a = y - y´
+ *        δ - parameter that controls the steepness
+ */
+public class PseudoHuberMetric implements EvaluationMetric {
+
+    public static final String NAME = "pseudo_huber";
+
+    public static final ParseField DELTA = new ParseField("delta");
+
+    private static final ConstructingObjectParser<PseudoHuberMetric, Void> PARSER =
+        new ConstructingObjectParser<>(NAME, true, args -> new PseudoHuberMetric((Double) args[0]));
+
+    static {
+        PARSER.declareDouble(optionalConstructorArg(), DELTA);
+    }
+
+    public static PseudoHuberMetric fromXContent(XContentParser parser) {
+        return PARSER.apply(parser, null);
+    }
+
+    private final Double delta;
+
+    public PseudoHuberMetric(@Nullable Double delta) {
+        this.delta = delta;
+    }
+
+    @Override
+    public String getName() {
+        return NAME;
+    }
+
+    @Override
+    public XContentBuilder toXContent(XContentBuilder builder, Params params) throws IOException {
+        builder.startObject();
+        if (delta != null) {
+            builder.field(DELTA.getPreferredName(), delta);
+        }
+        builder.endObject();
+        return builder;
+    }
+
+    @Override
+    public boolean equals(Object o) {
+        if (this == o) return true;
+        if (o == null || getClass() != o.getClass()) return false;
+        PseudoHuberMetric that = (PseudoHuberMetric) o;
+        return Objects.equals(this.delta, that.delta);
+    }
+
+    @Override
+    public int hashCode() {
+        return Objects.hash(delta);
+    }
+
+    public static class Result implements EvaluationMetric.Result  {
+
+        public static final ParseField VALUE = new ParseField("value");
+        private final double value;
+
+        public static Result fromXContent(XContentParser parser) {
+            return PARSER.apply(parser, null);
+        }
+
+        private static final ConstructingObjectParser<Result, Void> PARSER =
+            new ConstructingObjectParser<>("pseudo_huber_result", true, args -> new Result((double) args[0]));
+
+        static {
+            PARSER.declareDouble(constructorArg(), VALUE);
+        }
+
+        public Result(double value) {
+            this.value = value;
+        }
+
+        @Override
+        public XContentBuilder toXContent(XContentBuilder builder, Params params) throws IOException {
+            builder.startObject();
+            builder.field(VALUE.getPreferredName(), value);
+            builder.endObject();
+            return builder;
+        }
+
+        public double getValue() {
+            return value;
+        }
+
+        @Override
+        public String getMetricName() {
+            return NAME;
+        }
+
+        @Override
+        public boolean equals(Object o) {
+            if (this == o) return true;
+            if (o == null || getClass() != o.getClass()) return false;
+            Result that = (Result) o;
+            return Objects.equals(that.value, this.value);
+        }
+
+        @Override
+        public int hashCode() {
+            return Double.hashCode(value);
+        }
+    }
+}

client/rest-high-level/src/test/java/org/elasticsearch/client/MachineLearningIT.java

@@ -143,6 +143,7 @@ import org.elasticsearch.client.ml.dataframe.evaluation.classification.Classific
 import org.elasticsearch.client.ml.dataframe.evaluation.classification.MulticlassConfusionMatrixMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.MeanSquaredErrorMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.MeanSquaredLogarithmicErrorMetric;
+import org.elasticsearch.client.ml.dataframe.evaluation.regression.PseudoHuberMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.RSquaredMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.Regression;
 import org.elasticsearch.client.ml.dataframe.evaluation.softclassification.AucRocMetric;
@@ -1856,12 +1857,15 @@ public class MachineLearningIT extends ESRestHighLevelClientTestCase {
                 new Regression(
                     actualRegression,
                     predictedRegression,
-                    new MeanSquaredErrorMetric(), new MeanSquaredLogarithmicErrorMetric(1.0), new RSquaredMetric()));
+                    new MeanSquaredErrorMetric(),
+                    new MeanSquaredLogarithmicErrorMetric(1.0),
+                    new PseudoHuberMetric(1.0),
+                    new RSquaredMetric()));
 
         EvaluateDataFrameResponse evaluateDataFrameResponse =
             execute(evaluateDataFrameRequest, machineLearningClient::evaluateDataFrame, machineLearningClient::evaluateDataFrameAsync);
         assertThat(evaluateDataFrameResponse.getEvaluationName(), equalTo(Regression.NAME));
-        assertThat(evaluateDataFrameResponse.getMetrics().size(), equalTo(3));
+        assertThat(evaluateDataFrameResponse.getMetrics().size(), equalTo(4));
 
         MeanSquaredErrorMetric.Result mseResult = evaluateDataFrameResponse.getMetricByName(MeanSquaredErrorMetric.NAME);
         assertThat(mseResult.getMetricName(), equalTo(MeanSquaredErrorMetric.NAME));
@@ -1872,6 +1876,10 @@ public class MachineLearningIT extends ESRestHighLevelClientTestCase {
         assertThat(msleResult.getMetricName(), equalTo(MeanSquaredLogarithmicErrorMetric.NAME));
         assertThat(msleResult.getError(), closeTo(0.02759231770210426, 1e-9));
 
+        PseudoHuberMetric.Result pseudoHuberResult = evaluateDataFrameResponse.getMetricByName(PseudoHuberMetric.NAME);
+        assertThat(pseudoHuberResult.getMetricName(), equalTo(PseudoHuberMetric.NAME));
+        assertThat(pseudoHuberResult.getValue(), closeTo(0.029669771640929276, 1e-9));
+
         RSquaredMetric.Result rSquaredResult = evaluateDataFrameResponse.getMetricByName(RSquaredMetric.NAME);
         assertThat(rSquaredResult.getMetricName(), equalTo(RSquaredMetric.NAME));
         assertThat(rSquaredResult.getValue(), closeTo(-5.1000000000000005, 1e-9));

client/rest-high-level/src/test/java/org/elasticsearch/client/RestHighLevelClientTests.java

@@ -62,6 +62,7 @@ import org.elasticsearch.client.ml.dataframe.evaluation.classification.Classific
 import org.elasticsearch.client.ml.dataframe.evaluation.classification.MulticlassConfusionMatrixMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.MeanSquaredErrorMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.MeanSquaredLogarithmicErrorMetric;
+import org.elasticsearch.client.ml.dataframe.evaluation.regression.PseudoHuberMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.RSquaredMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.Regression;
 import org.elasticsearch.client.ml.dataframe.evaluation.softclassification.AucRocMetric;
@@ -702,7 +703,7 @@ public class RestHighLevelClientTests extends ESTestCase {
 
     public void testProvidedNamedXContents() {
         List<NamedXContentRegistry.Entry> namedXContents = RestHighLevelClient.getProvidedNamedXContents();
-        assertEquals(66, namedXContents.size());
+        assertEquals(68, namedXContents.size());
         Map<Class<?>, Integer> categories = new HashMap<>();
         List<String> names = new ArrayList<>();
         for (NamedXContentRegistry.Entry namedXContent : namedXContents) {
@@ -749,7 +750,7 @@ public class RestHighLevelClientTests extends ESTestCase {
         assertTrue(names.contains(TimeSyncConfig.NAME));
         assertEquals(Integer.valueOf(3), categories.get(org.elasticsearch.client.ml.dataframe.evaluation.Evaluation.class));
         assertThat(names, hasItems(BinarySoftClassification.NAME, Classification.NAME, Regression.NAME));
-        assertEquals(Integer.valueOf(11), categories.get(org.elasticsearch.client.ml.dataframe.evaluation.EvaluationMetric.class));
+        assertEquals(Integer.valueOf(12), categories.get(org.elasticsearch.client.ml.dataframe.evaluation.EvaluationMetric.class));
         assertThat(names,
             hasItems(
                 registeredMetricName(BinarySoftClassification.NAME, AucRocMetric.NAME),
@@ -764,8 +765,9 @@ public class RestHighLevelClientTests extends ESTestCase {
                 registeredMetricName(Classification.NAME, MulticlassConfusionMatrixMetric.NAME),
                 registeredMetricName(Regression.NAME, MeanSquaredErrorMetric.NAME),
                 registeredMetricName(Regression.NAME, MeanSquaredLogarithmicErrorMetric.NAME),
+                registeredMetricName(Regression.NAME, PseudoHuberMetric.NAME),
                 registeredMetricName(Regression.NAME, RSquaredMetric.NAME)));
-        assertEquals(Integer.valueOf(11), categories.get(org.elasticsearch.client.ml.dataframe.evaluation.EvaluationMetric.Result.class));
+        assertEquals(Integer.valueOf(12), categories.get(org.elasticsearch.client.ml.dataframe.evaluation.EvaluationMetric.Result.class));
         assertThat(names,
             hasItems(
                 registeredMetricName(BinarySoftClassification.NAME, AucRocMetric.NAME),
@@ -780,6 +782,7 @@ public class RestHighLevelClientTests extends ESTestCase {
                 registeredMetricName(Classification.NAME, MulticlassConfusionMatrixMetric.NAME),
                 registeredMetricName(Regression.NAME, MeanSquaredErrorMetric.NAME),
                 registeredMetricName(Regression.NAME, MeanSquaredLogarithmicErrorMetric.NAME),
+                registeredMetricName(Regression.NAME, PseudoHuberMetric.NAME),
                 registeredMetricName(Regression.NAME, RSquaredMetric.NAME)));
         assertEquals(Integer.valueOf(4), categories.get(org.elasticsearch.client.ml.inference.preprocessing.PreProcessor.class));
         assertThat(names, hasItems(FrequencyEncoding.NAME, OneHotEncoding.NAME, TargetMeanEncoding.NAME, CustomWordEmbedding.NAME));

client/rest-high-level/src/test/java/org/elasticsearch/client/documentation/MlClientDocumentationIT.java

@@ -162,6 +162,7 @@ import org.elasticsearch.client.ml.dataframe.evaluation.classification.Multiclas
 import org.elasticsearch.client.ml.dataframe.evaluation.classification.MulticlassConfusionMatrixMetric.PredictedClass;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.MeanSquaredErrorMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.MeanSquaredLogarithmicErrorMetric;
+import org.elasticsearch.client.ml.dataframe.evaluation.regression.PseudoHuberMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.regression.RSquaredMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.softclassification.AucRocMetric;
 import org.elasticsearch.client.ml.dataframe.evaluation.softclassification.BinarySoftClassification;
@@ -3572,7 +3573,8 @@ public class MlClientDocumentationIT extends ESRestHighLevelClientTestCase {
                     // Evaluation metrics // <4>
                     new MeanSquaredErrorMetric(), // <5>
                     new MeanSquaredLogarithmicErrorMetric(1.0), // <6>
-                    new RSquaredMetric()); // <7>
+                    new PseudoHuberMetric(1.0), // <7>
+                    new RSquaredMetric()); // <8>
             // end::evaluate-data-frame-evaluation-regression
 
             EvaluateDataFrameRequest request = new EvaluateDataFrameRequest(indexName, null, evaluation);
@@ -3586,12 +3588,16 @@ public class MlClientDocumentationIT extends ESRestHighLevelClientTestCase {
                 response.getMetricByName(MeanSquaredLogarithmicErrorMetric.NAME); // <3>
             double meanSquaredLogarithmicError = meanSquaredLogarithmicErrorResult.getError(); // <4>
 
-            RSquaredMetric.Result rSquaredResult = response.getMetricByName(RSquaredMetric.NAME); // <5>
+            PseudoHuberMetric.Result pseudoHuberResult = response.getMetricByName(PseudoHuberMetric.NAME); // <5>
-            double rSquared = rSquaredResult.getValue(); // <6>
+            double pseudoHuber = pseudoHuberResult.getValue(); // <6>
+
+            RSquaredMetric.Result rSquaredResult = response.getMetricByName(RSquaredMetric.NAME); // <7>
+            double rSquared = rSquaredResult.getValue(); // <8>
             // end::evaluate-data-frame-results-regression
 
             assertThat(meanSquaredError, closeTo(0.021, 1e-3));
             assertThat(meanSquaredLogarithmicError, closeTo(0.003, 1e-3));
+            assertThat(pseudoHuber, closeTo(0.01, 1e-3));
             assertThat(rSquared, closeTo(0.941, 1e-3));
         }
     }

client/rest-high-level/src/test/java/org/elasticsearch/client/ml/dataframe/evaluation/regression/PseudoHuberMetricResultTests.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to Elasticsearch under one or more contributor
+ * license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright
+ * ownership. Elasticsearch licenses this file to you under
+ * the Apache License, Version 2.0 (the "License"); you may
+ * not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://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.
+ */
+package org.elasticsearch.client.ml.dataframe.evaluation.regression;
+
+import org.elasticsearch.client.ml.dataframe.evaluation.MlEvaluationNamedXContentProvider;
+import org.elasticsearch.common.xcontent.NamedXContentRegistry;
+import org.elasticsearch.common.xcontent.XContentParser;
+import org.elasticsearch.test.AbstractXContentTestCase;
+
+import java.io.IOException;
+
+public class PseudoHuberMetricResultTests extends AbstractXContentTestCase<PseudoHuberMetric.Result> {
+
+    public static PseudoHuberMetric.Result randomResult() {
+        return new PseudoHuberMetric.Result(randomDouble());
+    }
+
+    @Override
+    protected PseudoHuberMetric.Result createTestInstance() {
+        return randomResult();
+    }
+
+    @Override
+    protected PseudoHuberMetric.Result doParseInstance(XContentParser parser) throws IOException {
+        return PseudoHuberMetric.Result.fromXContent(parser);
+    }
+
+    @Override
+    protected boolean supportsUnknownFields() {
+        return true;
+    }
+
+    @Override
+    protected NamedXContentRegistry xContentRegistry() {
+        return new NamedXContentRegistry(new MlEvaluationNamedXContentProvider().getNamedXContentParsers());
+    }
+}

client/rest-high-level/src/test/java/org/elasticsearch/client/ml/dataframe/evaluation/regression/PseudoHuberMetricTests.java

@@ -0,0 +1,49 @@
+/*
+ * Licensed to Elasticsearch under one or more contributor
+ * license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright
+ * ownership. Elasticsearch licenses this file to you under
+ * the Apache License, Version 2.0 (the "License"); you may
+ * not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://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.
+ */
+package org.elasticsearch.client.ml.dataframe.evaluation.regression;
+
+import org.elasticsearch.client.ml.dataframe.evaluation.MlEvaluationNamedXContentProvider;
+import org.elasticsearch.common.xcontent.NamedXContentRegistry;
+import org.elasticsearch.common.xcontent.XContentParser;
+import org.elasticsearch.test.AbstractXContentTestCase;
+
+import java.io.IOException;
+
+public class PseudoHuberMetricTests extends AbstractXContentTestCase<PseudoHuberMetric> {
+
+    @Override
+    protected NamedXContentRegistry xContentRegistry() {
+        return new NamedXContentRegistry(new MlEvaluationNamedXContentProvider().getNamedXContentParsers());
+    }
+
+    @Override
+    protected PseudoHuberMetric createTestInstance() {
+        return new PseudoHuberMetric(randomBoolean() ? randomDouble() : null);
+    }
+
+    @Override
+    protected PseudoHuberMetric doParseInstance(XContentParser parser) throws IOException {
+        return PseudoHuberMetric.fromXContent(parser);
+    }
+
+    @Override
+    protected boolean supportsUnknownFields() {
+        return true;
+    }
+}

client/rest-high-level/src/test/java/org/elasticsearch/client/ml/dataframe/evaluation/regression/RegressionTests.java

@@ -44,6 +44,9 @@ public class RegressionTests extends AbstractXContentTestCase<Regression> {
         if (randomBoolean()) {
             metrics.add(new MeanSquaredLogarithmicErrorMetricTests().createTestInstance());
         }
+        if (randomBoolean()) {
+            metrics.add(new PseudoHuberMetricTests().createTestInstance());
+        }
         if (randomBoolean()) {
             metrics.add(new RSquaredMetric());
         }

docs/java-rest/high-level/ml/evaluate-data-frame.asciidoc

@@ -69,7 +69,8 @@ include-tagged::{doc-tests-file}[{api}-evaluation-regression]
 <4> The remaining parameters are the metrics to be calculated based on the two fields described above
 <5> https://en.wikipedia.org/wiki/Mean_squared_error[Mean squared error]
 <6> Mean squared logarithmic error
-<7> https://en.wikipedia.org/wiki/Coefficient_of_determination[R squared]
+<7> https://en.wikipedia.org/wiki/Huber_loss#Pseudo-Huber_loss_function[Pseudo Huber loss]
+<8> https://en.wikipedia.org/wiki/Coefficient_of_determination[R squared]
 
 include::../execution.asciidoc[]
 
@@ -126,5 +127,7 @@ include-tagged::{doc-tests-file}[{api}-results-regression]
 <2> Fetching the actual mean squared error value
 <3> Fetching mean squared logarithmic error metric by name
 <4> Fetching the actual mean squared logarithmic error value
-<5> Fetching R squared metric by name
+<5> Fetching pseudo Huber loss metric by name
-<6> Fetching the actual R squared value
+<6> Fetching the actual pseudo Huber loss value
+<7> Fetching R squared metric by name
+<8> Fetching the actual R squared value

docs/reference/ml/df-analytics/apis/evaluate-dfanalytics.asciidoc

@@ -134,6 +134,10 @@ which outputs a prediction of values.
     (Optional, object) Average squared difference between the logarithm of the predicted values and the logarithm of the actual
     (`ground truth`) value.
 
+  `pseudo_huber`:::
+    (Optional, object) Pseudo Huber loss function.
+    For more information, read https://en.wikipedia.org/wiki/Huber_loss#Pseudo-Huber_loss_function[this wiki article].
+
   `r_squared`:::
     (Optional, object) Proportion of the variance in the dependent variable that is predictable from the independent variables.
     For more information, read https://en.wikipedia.org/wiki/Coefficient_of_determination[this wiki article].

x-pack/plugin/core/src/main/java/org/elasticsearch/xpack/core/ml/dataframe/evaluation/MlEvaluationNamedXContentProvider.java

@@ -14,6 +14,7 @@ import org.elasticsearch.xpack.core.ml.dataframe.evaluation.classification.Class
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.classification.MulticlassConfusionMatrix;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.MeanSquaredError;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.MeanSquaredLogarithmicError;
+import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.PseudoHuber;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.RSquared;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.Regression;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.softclassification.AucRoc;
@@ -99,6 +100,9 @@ public class MlEvaluationNamedXContentProvider implements NamedXContentProvider
             new NamedXContentRegistry.Entry(EvaluationMetric.class,
                 new ParseField(registeredMetricName(Regression.NAME, MeanSquaredLogarithmicError.NAME)),
                 MeanSquaredLogarithmicError::fromXContent),
+            new NamedXContentRegistry.Entry(EvaluationMetric.class,
+                new ParseField(registeredMetricName(Regression.NAME, PseudoHuber.NAME)),
+                PseudoHuber::fromXContent),
             new NamedXContentRegistry.Entry(EvaluationMetric.class,
                 new ParseField(registeredMetricName(Regression.NAME, RSquared.NAME)),
                 RSquared::fromXContent)
@@ -151,6 +155,9 @@ public class MlEvaluationNamedXContentProvider implements NamedXContentProvider
             new NamedWriteableRegistry.Entry(EvaluationMetric.class,
                 registeredMetricName(Regression.NAME, MeanSquaredLogarithmicError.NAME),
                 MeanSquaredLogarithmicError::new),
+            new NamedWriteableRegistry.Entry(EvaluationMetric.class,
+                registeredMetricName(Regression.NAME, PseudoHuber.NAME),
+                PseudoHuber::new),
             new NamedWriteableRegistry.Entry(EvaluationMetric.class,
                 registeredMetricName(Regression.NAME, RSquared.NAME),
                 RSquared::new),
@@ -185,6 +192,9 @@ public class MlEvaluationNamedXContentProvider implements NamedXContentProvider
             new NamedWriteableRegistry.Entry(EvaluationMetricResult.class,
                 registeredMetricName(Regression.NAME, MeanSquaredLogarithmicError.NAME),
                 MeanSquaredLogarithmicError.Result::new),
+            new NamedWriteableRegistry.Entry(EvaluationMetricResult.class,
+                registeredMetricName(Regression.NAME, PseudoHuber.NAME),
+                PseudoHuber.Result::new),
             new NamedWriteableRegistry.Entry(EvaluationMetricResult.class,
                 registeredMetricName(Regression.NAME, RSquared.NAME),
                 RSquared.Result::new)

x-pack/plugin/core/src/main/java/org/elasticsearch/xpack/core/ml/dataframe/evaluation/regression/PseudoHuber.java

@@ -0,0 +1,195 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+package org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression;
+
+import org.elasticsearch.common.Nullable;
+import org.elasticsearch.common.ParseField;
+import org.elasticsearch.common.collect.Tuple;
+import org.elasticsearch.common.io.stream.StreamInput;
+import org.elasticsearch.common.io.stream.StreamOutput;
+import org.elasticsearch.common.xcontent.ConstructingObjectParser;
+import org.elasticsearch.common.xcontent.XContentBuilder;
+import org.elasticsearch.common.xcontent.XContentParser;
+import org.elasticsearch.script.Script;
+import org.elasticsearch.search.aggregations.AggregationBuilder;
+import org.elasticsearch.search.aggregations.AggregationBuilders;
+import org.elasticsearch.search.aggregations.Aggregations;
+import org.elasticsearch.search.aggregations.PipelineAggregationBuilder;
+import org.elasticsearch.search.aggregations.metrics.NumericMetricsAggregation;
+import org.elasticsearch.xpack.core.ml.dataframe.evaluation.EvaluationMetric;
+import org.elasticsearch.xpack.core.ml.dataframe.evaluation.EvaluationMetricResult;
+import org.elasticsearch.xpack.core.ml.dataframe.evaluation.EvaluationParameters;
+
+import java.io.IOException;
+import java.text.MessageFormat;
+import java.util.Arrays;
+import java.util.Collections;
+import java.util.List;
+import java.util.Locale;
+import java.util.Optional;
+
+import static org.elasticsearch.common.xcontent.ConstructingObjectParser.optionalConstructorArg;
+import static org.elasticsearch.xpack.core.ml.dataframe.evaluation.MlEvaluationNamedXContentProvider.registeredMetricName;
+
+/**
+ * Calculates the pseudo Huber loss function.
+ *
+ * equation: pseudohuber = 1/n * Σ(δ^2 * sqrt(1 + a^2 / δ^2) - 1)
+ * where: a = y - y´
+ *        δ - parameter that controls the steepness
+ */
+public class PseudoHuber implements EvaluationMetric {
+
+    public static final ParseField NAME = new ParseField("pseudo_huber");
+
+    public static final ParseField DELTA = new ParseField("delta");
+    private static final double DEFAULT_DELTA = 1.0;
+
+    private static final String PAINLESS_TEMPLATE =
+        "def a = doc[''{0}''].value - doc[''{1}''].value;" +
+        "def delta2 = {2};" +
+        "return delta2 * (Math.sqrt(1.0 + Math.pow(a, 2) / delta2) - 1.0);";
+    private static final String AGG_NAME = "regression_" + NAME.getPreferredName();
+
+    private static String buildScript(Object...args) {
+        return new MessageFormat(PAINLESS_TEMPLATE, Locale.ROOT).format(args);
+    }
+
+    private static final ConstructingObjectParser<PseudoHuber, Void> PARSER =
+        new ConstructingObjectParser<>(NAME.getPreferredName(), true, args -> new PseudoHuber((Double) args[0]));
+
+    static {
+        PARSER.declareDouble(optionalConstructorArg(), DELTA);
+    }
+
+    public static PseudoHuber fromXContent(XContentParser parser) {
+        return PARSER.apply(parser, null);
+    }
+
+    private final double delta;
+    private EvaluationMetricResult result;
+
+    public PseudoHuber(StreamInput in) throws IOException {
+        this.delta = in.readDouble();
+    }
+
+    public PseudoHuber(@Nullable Double delta) {
+        this.delta = delta != null ? delta : DEFAULT_DELTA;
+    }
+
+    @Override
+    public String getName() {
+        return NAME.getPreferredName();
+    }
+
+    @Override
+    public Tuple<List<AggregationBuilder>, List<PipelineAggregationBuilder>> aggs(EvaluationParameters parameters,
+                                                                                  String actualField,
+                                                                                  String predictedField) {
+        if (result != null) {
+            return Tuple.tuple(Collections.emptyList(), Collections.emptyList());
+        }
+        return Tuple.tuple(
+            Arrays.asList(AggregationBuilders.avg(AGG_NAME).script(new Script(buildScript(actualField, predictedField, delta * delta)))),
+            Collections.emptyList());
+    }
+
+    @Override
+    public void process(Aggregations aggs) {
+        NumericMetricsAggregation.SingleValue value = aggs.get(AGG_NAME);
+        result = value == null ? new Result(0.0) : new Result(value.value());
+    }
+
+    @Override
+    public Optional<EvaluationMetricResult> getResult() {
+        return Optional.ofNullable(result);
+    }
+
+    @Override
+    public String getWriteableName() {
+        return registeredMetricName(Regression.NAME, NAME);
+    }
+
+    @Override
+    public void writeTo(StreamOutput out) throws IOException {
+        out.writeDouble(delta);
+    }
+
+    @Override
+    public XContentBuilder toXContent(XContentBuilder builder, Params params) throws IOException {
+        builder.startObject();
+        builder.field(DELTA.getPreferredName(), delta);
+        builder.endObject();
+        return builder;
+    }
+
+    @Override
+    public boolean equals(Object o) {
+        if (this == o) return true;
+        if (o == null || getClass() != o.getClass()) return false;
+        PseudoHuber that = (PseudoHuber) o;
+        return this.delta == that.delta;
+    }
+
+    @Override
+    public int hashCode() {
+        return Double.hashCode(delta);
+    }
+
+    public static class Result implements EvaluationMetricResult {
+
+        private static final String VALUE = "value";
+        private final double value;
+
+        public Result(double value) {
+            this.value = value;
+        }
+
+        public Result(StreamInput in) throws IOException {
+            this.value = in.readDouble();
+        }
+
+        @Override
+        public String getWriteableName() {
+            return registeredMetricName(Regression.NAME, NAME);
+        }
+
+        @Override
+        public String getMetricName() {
+            return NAME.getPreferredName();
+        }
+
+        public double getValue() {
+            return value;
+        }
+
+        @Override
+        public void writeTo(StreamOutput out) throws IOException {
+            out.writeDouble(value);
+        }
+
+        @Override
+        public XContentBuilder toXContent(XContentBuilder builder, Params params) throws IOException {
+            builder.startObject();
+            builder.field(VALUE, value);
+            builder.endObject();
+            return builder;
+        }
+
+        @Override
+        public boolean equals(Object o) {
+            if (this == o) return true;
+            if (o == null || getClass() != o.getClass()) return false;
+            Result other = (Result)o;
+            return value == other.value;
+        }
+
+        @Override
+        public int hashCode() {
+            return Double.hashCode(value);
+        }
+    }
+}

x-pack/plugin/core/src/test/java/org/elasticsearch/xpack/core/ml/action/EvaluateDataFrameActionResponseTests.java

@@ -17,6 +17,7 @@ import org.elasticsearch.xpack.core.ml.dataframe.evaluation.classification.Preci
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.classification.RecallResultTests;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.MeanSquaredError;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.MeanSquaredLogarithmicError;
+import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.PseudoHuber;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.RSquared;
 
 import java.util.List;
@@ -39,6 +40,7 @@ public class EvaluateDataFrameActionResponseTests extends AbstractWireSerializin
                 MulticlassConfusionMatrixResultTests.createRandom(),
                 new MeanSquaredError.Result(randomDouble()),
                 new MeanSquaredLogarithmicError.Result(randomDouble()),
+                new PseudoHuber.Result(randomDouble()),
                 new RSquared.Result(randomDouble()));
         return new Response(evaluationName, randomSubsetOf(metrics));
     }

x-pack/plugin/core/src/test/java/org/elasticsearch/xpack/core/ml/dataframe/evaluation/regression/PseudoHuberTests.java

@@ -0,0 +1,68 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+package org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression;
+
+import org.elasticsearch.common.Strings;
+import org.elasticsearch.common.io.stream.Writeable;
+import org.elasticsearch.common.xcontent.XContentParser;
+import org.elasticsearch.search.aggregations.Aggregations;
+import org.elasticsearch.test.AbstractSerializingTestCase;
+import org.elasticsearch.xpack.core.ml.dataframe.evaluation.EvaluationMetricResult;
+
+import java.io.IOException;
+import java.util.Arrays;
+import java.util.Collections;
+
+import static org.elasticsearch.xpack.core.ml.dataframe.evaluation.MockAggregations.mockSingleValue;
+import static org.hamcrest.Matchers.equalTo;
+
+public class PseudoHuberTests extends AbstractSerializingTestCase<PseudoHuber> {
+
+    @Override
+    protected PseudoHuber doParseInstance(XContentParser parser) throws IOException {
+        return PseudoHuber.fromXContent(parser);
+    }
+
+    @Override
+    protected PseudoHuber createTestInstance() {
+        return createRandom();
+    }
+
+    @Override
+    protected Writeable.Reader<PseudoHuber> instanceReader() {
+        return PseudoHuber::new;
+    }
+
+    public static PseudoHuber createRandom() {
+        return new PseudoHuber(randomBoolean() ? randomDoubleBetween(0.0, 1000.0, false) : null);
+    }
+
+    public void testEvaluate() {
+        Aggregations aggs = new Aggregations(Arrays.asList(
+            mockSingleValue("regression_pseudo_huber", 0.8123),
+            mockSingleValue("some_other_single_metric_agg", 0.2377)
+        ));
+
+        PseudoHuber pseudoHuber = new PseudoHuber((Double) null);
+        pseudoHuber.process(aggs);
+
+        EvaluationMetricResult result = pseudoHuber.getResult().get();
+        String expected = "{\"value\":0.8123}";
+        assertThat(Strings.toString(result), equalTo(expected));
+    }
+
+    public void testEvaluate_GivenMissingAggs() {
+        Aggregations aggs = new Aggregations(Collections.singletonList(
+            mockSingleValue("some_other_single_metric_agg", 0.2377)
+        ));
+
+        PseudoHuber pseudoHuber = new PseudoHuber((Double) null);
+        pseudoHuber.process(aggs);
+
+        EvaluationMetricResult result = pseudoHuber.getResult().get();
+        assertThat(result, equalTo(new PseudoHuber.Result(0.0)));
+    }
+}

x-pack/plugin/ml/qa/native-multi-node-tests/src/test/java/org/elasticsearch/xpack/ml/integration/RegressionEvaluationIT.java

@@ -13,6 +13,7 @@ import org.elasticsearch.xpack.core.ml.action.EvaluateDataFrameAction;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.EvaluationMetricResult;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.MeanSquaredError;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.MeanSquaredLogarithmicError;
+import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.PseudoHuber;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.RSquared;
 import org.elasticsearch.xpack.core.ml.dataframe.evaluation.regression.Regression;
 import org.junit.After;
@@ -95,7 +96,21 @@ public class RegressionEvaluationIT extends MlNativeDataFrameAnalyticsIntegTestC
 
         MeanSquaredLogarithmicError.Result msleResult = (MeanSquaredLogarithmicError.Result) evaluateDataFrameResponse.getMetrics().get(0);
         assertThat(msleResult.getMetricName(), equalTo(MeanSquaredLogarithmicError.NAME.getPreferredName()));
-        assertThat(msleResult.getError(), closeTo(Math.pow(Math.log(1001), 2), 10E-6));
+        assertThat(msleResult.getError(), closeTo(Math.pow(Math.log(1000 + 1), 2), 10E-6));
+    }
+
+    public void testEvaluate_PseudoHuber() {
+        EvaluateDataFrameAction.Response evaluateDataFrameResponse =
+            evaluateDataFrame(
+                HOUSES_DATA_INDEX,
+                new Regression(PRICE_FIELD, PRICE_PREDICTION_FIELD, List.of(new PseudoHuber((Double) null))));
+
+        assertThat(evaluateDataFrameResponse.getEvaluationName(), equalTo(Regression.NAME.getPreferredName()));
+        assertThat(evaluateDataFrameResponse.getMetrics(), hasSize(1));
+
+        PseudoHuber.Result pseudoHuberResult = (PseudoHuber.Result) evaluateDataFrameResponse.getMetrics().get(0);
+        assertThat(pseudoHuberResult.getMetricName(), equalTo(PseudoHuber.NAME.getPreferredName()));
+        assertThat(pseudoHuberResult.getValue(), closeTo(Math.sqrt(1000000 + 1) - 1, 10E-6));
     }
 
     public void testEvaluate_RSquared() {

x-pack/plugin/src/test/resources/rest-api-spec/test/ml/evaluate_data_frame.yml

@@ -849,6 +849,7 @@ setup:
   - match: { regression.mean_squared_error.error: 28.67749840974834 }
   - is_false: regression.mean_squared_logarithmic_error.value
   - is_false: regression.r_squared.value
+  - is_false: regression.pseudo_huber.value
 ---
 "Test regression mean_squared_logarithmic_error":
   - do:
@@ -868,6 +869,27 @@ setup:
   - match: { regression.mean_squared_logarithmic_error.error: 0.08680568028334916 }
   - is_false: regression.mean_squared_error.value
   - is_false: regression.r_squared.value
+  - is_false: regression.pseudo_huber.value
+---
+"Test regression pseudo_huber":
+  - do:
+      ml.evaluate_data_frame:
+        body: >
+          {
+            "index": "utopia",
+            "evaluation": {
+              "regression": {
+                "actual_field": "regression_field_act",
+                "predicted_field": "regression_field_pred",
+                "metrics": { "pseudo_huber": { "delta": 2.0 } }
+              }
+            }
+          }
+
+  - match: { regression.pseudo_huber.value: 3.5088110471730145 }
+  - is_false: regression.mean_squared_logarithmic_error.value
+  - is_false: regression.mean_squared_error.value
+  - is_false: regression.r_squared.value
 ---
 "Test regression r_squared":
   - do:
@@ -886,6 +908,8 @@ setup:
   - match: { regression.r_squared.value: 0.8551031778603486 }
   - is_false: regression.mean_squared_error
   - is_false: regression.mean_squared_logarithmic_error.value
+  - is_false: regression.pseudo_huber.value
+
 ---
 "Test regression with null metrics":
   - do: