Github user sethah commented on a diff in the pull request:
https://github.com/apache/spark/pull/11610#discussion_r55909205
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/optim/WeightedLeastSquares.scala ---
@@ -108,6 +101,53 @@ private[ml] class WeightedLeastSquares(
"Consider setting fitIntercept=true.")
}
}
+ /*
+ If more than 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
+ for (i <- nzVarIndex) yield {abBarTemp(i)}
+ } else {
+ summary.abBar.values
+ }
+ val aaBar = if (singular) {
--- End diff --
Though you mentioned it, subtly, in the comment above, it is not clear what
is going on here. It would be nice to add a more thorough comment that you are
removing a row and column of the ATA matrix here and why.
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