Github user iyounus commented on a diff in the pull request:
https://github.com/apache/spark/pull/10274#discussion_r50060828
--- Diff:
mllib/src/test/scala/org/apache/spark/ml/optim/WeightedLeastSquaresSuite.scala
---
@@ -74,6 +89,35 @@ class WeightedLeastSquaresSuite extends SparkFunSuite
with MLlibTestSparkContext
}
}
+ test("WLS against lm when label is constant") {
+ /*
+ R code:
+ # here b is constant
+ df <- as.data.frame(cbind(A, b))
+ for (formula in c(b ~ . -1, b ~ .)) {
+ model <- lm(formula, data=df, weights=w)
+ print(as.vector(coef(model)))
+ }
+
+ [1] -9.221298 3.394343
+ [1] 17 0 0
+ */
+
+ val expected = Seq(
+ Vectors.dense(0.0, -9.221298, 3.394343),
+ Vectors.dense(17.0, 0.0, 0.0))
+
+ var idx = 0
+ for (fitIntercept <- Seq(false, true)) {
+ val wls = new WeightedLeastSquares(
+ fitIntercept, regParam = 0.0, standardizeFeatures = false,
standardizeLabel = true)
+ .fit(instancesConstLabel)
--- End diff --
@dbtsai I've implemented normal equation with regularization in R. Here is
my code:
```
ridge_regression <- function(A, b, lambda, intercept=TRUE){
if (intercept) {
A = cbind(rep(1.0, length(b)), A)
I = diag(ncol(A))
I[1,1] = 0.0
} else {
I = diag(ncol(A))
}
R = chol( t(A) %*% A + lambda*I )
z = solve(t(R), t(A) %*% b)
w = solve(R, z)
return(w)
}
```
And here are the results I get using this function.
```
A <- matrix(c(0, 1, 2, 3, 5, 7, 11, 13), 4, 2)
b <- c(17, 19, 23, 29)
ridge_regression(A, b, 0.1)
[,1]
[1,] 12.9048179
[2,] 2.1151586
[3,] 0.6580494
```
The problem is that these don't quite match with `glmnet`. The difference
can be at few percent level:
```
> model <- glmnet(A, b, intercept=TRUE, lambda=0.1, standardize=FALSE,
+ alpha=0, thresh=1E-20)
> print(as.vector(coef(model)))
[1] 13.1018870 2.2362361 0.6159732
```
But, my results match exactly with what I get from ridge regression in
sklearn:
```
from sklearn.linear_model import Ridge
import numpy as np
A = np.array([[0, 1, 2, 3],[5, 7, 11, 13]]).T
b = np.array([17.0, 19.0, 23.0, 29.0])
model = Ridge(alpha=0.1, solver='cholesky', fit_intercept=True)
model.fit(A, b)
print model.intercept_
print model.coef_
12.9048178613
[ 2.11515864 0.65804935]
```
Even if I use other solvers (`svd`, `lsqr`, `sparse_cg`) in
`sklearn.linear_model.Ridge`, I get exactly the same results.
If I don't use regularization by setting `lambda=0`, then the results from
`glmnet` are identical to what I get from normal equation and
`sklearn.linear_model.Ridge`.
Have you observed such differences before? Is `glmnet` making some other
corrections or its just numerical precision issue? I can't seem to reproduce
`glmnet` results.
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