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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