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Unverified Commit eb00378f authored by WeichenXu's avatar WeichenXu Committed by DB Tsai
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[SPARK-20423][ML] fix MLOR coeffs centering when reg == 0

## What changes were proposed in this pull request?

When reg == 0, MLOR has multiple solutions and we need to centralize the coeffs to get identical result.
BUT current implementation centralize the `coefficientMatrix` by the global coeffs means.

In fact the `coefficientMatrix` should be centralized on each feature index itself.
Because, according to the MLOR probability distribution function, it can be proven easily that:
suppose `{ w0, w1, .. w(K-1) }` make up the `coefficientMatrix`,
then `{ w0 + c, w1 + c, ... w(K - 1) + c}` will also be the equivalent solution.
`c` is an arbitrary vector of `numFeatures` dimension.
reference
https://core.ac.uk/download/pdf/6287975.pdf

So that we need to centralize the `coefficientMatrix` on each feature dimension separately.

**We can also confirm this through R library `glmnet`, that MLOR in `glmnet` always generate coefficients result that the sum of each dimension is all `zero`, when reg == 0.**

## How was this patch tested?

Tests added.

Author: WeichenXu <WeichenXu123@outlook.com>

Closes #17706 from WeichenXu123/mlor_center.
parent a750a595
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