Yanbo Liang commented on SPARK-11918:

Cholesky decomposition is unstable (for near-singular and rank deficient 
matrices), but it was often used when matrix A is very large and sparse due to 
faster calculation. QR decomposition is more stable than Cholesky, I think we 
should switch to it in the future. I will take a look at this issue. For 
temporary fix, I think throwing a better exception to let users know the 
failure cause is OK. Thanks.

> WLS can not resolve some kinds of equation
> ------------------------------------------
>                 Key: SPARK-11918
>                 URL: https://issues.apache.org/jira/browse/SPARK-11918
>             Project: Spark
>          Issue Type: Improvement
>          Components: ML
>            Reporter: Yanbo Liang
>            Priority: Minor
>              Labels: starter
>         Attachments: R_GLM_output
> Weighted Least Squares (WLS) is one of the optimization method for solve 
> Linear Regression (when #feature < 4096). But if the dataset is very ill 
> condition (such as 0-1 based label used for classification and the equation 
> is underdetermined), the WLS failed (But "l-bfgs" can train and get the 
> model). The failure is caused by the underneath lapack library return error 
> value when Cholesky decomposition.
> This issue is easy to reproduce, you can train a LinearRegressionModel by 
> "normal" solver with the example 
> dataset(https://github.com/apache/spark/blob/master/data/mllib/sample_libsvm_data.txt).
>  The following is the exception:
> {code}
> assertion failed: lapack.dpotrs returned 1.
> java.lang.AssertionError: assertion failed: lapack.dpotrs returned 1.
>       at scala.Predef$.assert(Predef.scala:179)
>       at 
> org.apache.spark.mllib.linalg.CholeskyDecomposition$.solve(CholeskyDecomposition.scala:42)
>       at 
> org.apache.spark.ml.optim.WeightedLeastSquares.fit(WeightedLeastSquares.scala:117)
>       at 
> org.apache.spark.ml.regression.LinearRegression.train(LinearRegression.scala:180)
>       at 
> org.apache.spark.ml.regression.LinearRegression.train(LinearRegression.scala:67)
>       at org.apache.spark.ml.Predictor.fit(Predictor.scala:90)
> {code}

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