Github user yanboliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/15394#discussion_r83006938
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/optim/WeightedLeastSquares.scala ---
@@ -85,73 +101,193 @@ private[ml] class WeightedLeastSquares(
val triK = summary.triK
val wSum = summary.wSum
val bBar = summary.bBar
- val bStd = summary.bStd
+ val bbBar = summary.bbBar
val aBar = summary.aBar
- val aVar = summary.aVar
+ val aStd = summary.aStd
val abBar = summary.abBar
val aaBar = summary.aaBar
- val aaValues = aaBar.values
-
- if (bStd == 0) {
- if (fitIntercept) {
- logWarning(s"The standard deviation of the label is zero, so the
coefficients will be " +
- s"zeros and the intercept will be the mean of the label; as a
result, " +
- s"training is not needed.")
- val coefficients = new DenseVector(Array.ofDim(k-1))
+ val aaBarValues = aaBar.values
+ val numFeatures = abBar.size
+ val rawBStd = summary.bStd
+ // if b is constant (rawBStd is zero), then b cannot be scaled. In
this case
+ // setting bStd=abs(bBar) ensures that b is not scaled anymore in
l-bfgs algorithm.
+ val bStd = if (rawBStd == 0.0) math.abs(bBar) else rawBStd
+
+ if (rawBStd == 0) {
+ if (fitIntercept || bBar == 0.0) {
+ if (bBar == 0.0) {
+ logWarning(s"Mean and standard deviation of the label are zero,
so the coefficients " +
+ s"and the intercept will all be zero; as a result, training is
not needed.")
+ } else {
+ logWarning(s"The standard deviation of the label is zero, so the
coefficients will be " +
+ s"zeros and the intercept will be the mean of the label; as a
result, " +
+ s"training is not needed.")
+ }
+ val coefficients = new DenseVector(Array.ofDim(numFeatures))
val intercept = bBar
val diagInvAtWA = new DenseVector(Array(0D))
- return new WeightedLeastSquaresModel(coefficients, intercept,
diagInvAtWA)
+ return new WeightedLeastSquaresModel(coefficients, intercept,
diagInvAtWA, Array(0D))
+ } else {
+ require(!(regParam > 0.0 && standardizeLabel), "The standard
deviation of the label is " +
+ "zero. Model cannot be regularized with standardization=true")
+ logWarning(s"The standard deviation of the label is zero. Consider
setting " +
+ s"fitIntercept=true.")
+ }
+ }
+
+ val aBarStd = new Array[Double](numFeatures)
+ var j = 0
+ while (j < numFeatures) {
+ if (aStd(j) == 0.0) {
+ aBarStd(j) = 0.0
} else {
- require(!(regParam > 0.0 && standardizeLabel),
- "The standard deviation of the label is zero. " +
- "Model cannot be regularized with standardization=true")
- logWarning(s"The standard deviation of the label is zero. " +
- "Consider setting fitIntercept=true.")
+ aBarStd(j) = aBar(j) / aStd(j)
+ }
+ j += 1
+ }
+
+ val abBarStd = new Array[Double](numFeatures)
+ j = 0
+ while (j < numFeatures) {
+ if (aStd(j) == 0.0) {
+ abBarStd(j) = 0.0
+ } else {
+ abBarStd(j) = abBar(j) / (aStd(j) * bStd)
+ }
+ j += 1
+ }
+
+ val aaBarStd = new Array[Double](triK)
+ j = 0
+ var kk = 0
+ while (j < numFeatures) {
+ val aStdJ = aStd(j)
+ var i = 0
+ while (i <= j) {
+ val aStdI = aStd(i)
+ if (aStdJ == 0.0 || aStdI == 0.0) {
+ aaBarStd(kk) = 0.0
+ } else {
+ aaBarStd(kk) = aaBarValues(kk) / (aStdI * aStdJ)
+ }
+ kk += 1
+ i += 1
}
+ j += 1
}
+ val bBarStd = bBar / bStd
+ val bbBarStd = bbBar / (bStd * bStd)
+
+ val effectiveRegParam = regParam / bStd
+ val effectiveL1RegParam = elasticNetParam * effectiveRegParam
+ val effectiveL2RegParam = (1.0 - elasticNetParam) * effectiveRegParam
+
// add regularization to diagonals
var i = 0
- var j = 2
+ j = 2
while (i < triK) {
- var lambda = regParam
- if (standardizeFeatures) {
- lambda *= aVar(j - 2)
+ var lambda = effectiveL2RegParam
+ if (!standardizeFeatures) {
+ val std = aStd(j - 2)
+ if (std != 0.0) {
+ lambda /= (std * std)
+ } else {
+ lambda = 0.0
+ }
}
- if (standardizeLabel && bStd != 0) {
- lambda /= bStd
+ if (!standardizeLabel) {
+ lambda *= bStd
}
- aaValues(i) += lambda
+ aaBarStd(i) += lambda
i += j
j += 1
}
+ val aa = getAtA(aaBarStd, aBarStd)
+ val ab = getAtB(abBarStd, bBarStd)
- val aa = if (fitIntercept) {
- Array.concat(aaBar.values, aBar.values, Array(1.0))
- } else {
- aaBar.values
- }
- val ab = if (fitIntercept) {
- Array.concat(abBar.values, Array(bBar))
+ val solver = if ((solverType == WeightedLeastSquares.Auto &&
elasticNetParam != 0.0) ||
+ (solverType == WeightedLeastSquares.QuasiNewton)) {
+ val effectiveL1RegFun: Option[(Int) => Double] = if
(effectiveL1RegParam != 0.0) {
+ Some((index: Int) => {
+ if (fitIntercept && index == numFeatures) {
+ 0.0
+ } else {
+ if (standardizeFeatures) {
+ effectiveL1RegParam
+ } else {
+ if (aStd(index) != 0.0) effectiveL1RegParam / aStd(index)
else 0.0
+ }
+ }
+ })
+ } else {
+ None
+ }
+ new QuasiNewtonSolver(fitIntercept, maxIter, tol, effectiveL1RegFun)
} else {
- abBar.values
+ new CholeskySolver(fitIntercept)
}
- val x = CholeskyDecomposition.solve(aa, ab)
+ val solution = solver match {
+ case cholesky: CholeskySolver =>
+ try {
+ cholesky.solve(bBarStd, bbBarStd, ab, aa, new
DenseVector(aBarStd))
+ } catch {
+ // if Auto solver is used and Cholesky fails due to singular
AtA, then fall back to
+ // quasi-newton solver
+ case _: SingularMatrixException if solverType ==
WeightedLeastSquares.Auto =>
+ logWarning("Cholesky solver failed due to singular covariance
matrix. " +
+ "Retrying with Quasi-Newton solver.")
+ // ab and aa were modified in place, so reconstruct them
+ val _aa = getAtA(aaBarStd, aBarStd)
+ val _ab = getAtB(abBarStd, bBarStd)
+ val newSolver = new QuasiNewtonSolver(fitIntercept, maxIter,
tol, None)
+ newSolver.solve(bBarStd, bbBarStd, _ab, _aa, new
DenseVector(aBarStd))
+ }
+ case qn: QuasiNewtonSolver =>
+ qn.solve(bBarStd, bbBarStd, ab, aa, new DenseVector(aBarStd))
+ }
+ val intercept = solution.intercept * bStd
+ val coefficients = solution.coefficients
- val aaInv = CholeskyDecomposition.inverse(aa, k)
+ // convert the coefficients from the scaled space to the original space
+ var ii = 0
--- End diff --
Nit: I'd like to use ```p``` or ```q``` rather than ```ii```.
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