Github user dbtsai commented on a diff in the pull request:
https://github.com/apache/spark/pull/8013#discussion_r36719346
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/regression/LinearRegression.scala ---
@@ -645,3 +658,80 @@ private class LeastSquaresCostFun(
(leastSquaresAggregator.loss + regVal, new BDV(totalGradientArray))
}
}
+
+/**
+ * HuberCostFun implements Breeze's DiffFunction[T] for Huber cost as used
in Robust regression.
+ * The Huber M-estimator corresponds to a probability distribution for the
errors which is normal
+ * in the centre but like a double exponential distribution in the tails
(Hogg 1979: 109).
+ * L = 1/2 ||A weights-y||^2 if |A weights-y| <= k
+ * L = k |A weights-y| - 1/2 K^2 if |A weights-y| > k
+ * where k = 1.345 which produce 95% efficiency when the errors are normal
and
+ * substantial resistance to outliers otherwise.
+ * See also the documentation for the precise formulation.
+ * It's used in Breeze's convex optimization routines.
+ */
+private class HuberCostFun(
+ data: RDD[(Double, Vector)],
+ labelStd: Double,
+ labelMean: Double,
+ fitIntercept: Boolean,
+ standardization: Boolean,
+ featuresStd: Array[Double],
+ featuresMean: Array[Double],
+ effectiveL2regParam: Double) extends DiffFunction[BDV[Double]] {
+
+ override def calculate(weights: BDV[Double]): (Double, BDV[Double]) = {
+ val w = Vectors.fromBreeze(weights)
+
+ val leastSquaresAggregator = data.treeAggregate(new
LeastSquaresAggregator(w, labelStd,
+ labelMean, fitIntercept, featuresStd, featuresMean))(
--- End diff --
Do you have reference paper of the objective function of robust regression?
My gut feeling is that the condition is per instance, which means if the one
particular sample has high error, we make the impact smaller. But you are still
using `LeastSquaresAggregator`, and have the condition applied in the whole
objective function. I may be wrong. Thanks.
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