Github user dbtsai commented on a diff in the pull request:
https://github.com/apache/spark/pull/11610#discussion_r55964826
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/optim/WeightedLeastSquares.scala ---
@@ -108,6 +101,57 @@ private[ml] class WeightedLeastSquares(
"Consider setting fitIntercept=true.")
}
}
+ /*
+ * If more than one of the features in the data are constant (i.e.
data matrix has constant
+ * columns), then A^T.A is no longer positive definite and Cholesky
decomposition fails
+ * (because the normal equation does not have a solution).
+ * In order to find a solution, we need to drop constant columns from
the data matrix. Or,
+ * we can drop corresponding column and row from A^T.A matrix.
+ * Once we drop rows/columns from A^T.A matrix, the Cholesky
decomposition will produce
+ * correct coefficients. But, for the final result, we need to add
zeros to the list of
+ * coefficients corresponding to the constant features.
+ */
+ val aVarRaw = summary.aVar.values
+ // this will keep track of features to keep in the model, and remove
+ // features with zero variance.
+ val nzVarIndex = aVarRaw.zipWithIndex.filter(_._1 != 0).map(_._2)
+ val nz = nzVarIndex.length
+ // if there are features with zero variance, then ATA is not positive
definite, and we need to
+ // keep track of that.
+ val singular = summary.k > nz
+ val k = if (fitIntercept) nz + 1 else nz
+ val triK = nz * (nz + 1) / 2
+
+ val aVar = if (singular) {
+ for (i <- nzVarIndex) yield aVarRaw(i)
+ } else {
+ aVarRaw
+ }
+ val aBar = if (singular) {
+ val aBarTemp = summary.aBar.values
+ for (i <- nzVarIndex) yield aBarTemp(i)
+ } else {
+ summary.aBar.values
+ }
+ val abBar = if (singular) {
+ val abBarTemp = summary.abBar.values
--- End diff --
ditto.
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