[jira] [Comment Edited] (SPARK-11918) WLS can not resolve some kinds of equation

["Yanbo Liang (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/SPARK-11918?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15021729#comment-15021729 ] 

Yanbo Liang edited comment on SPARK-11918 at 11/23/15 8:31 AM:
---------------------------------------------------------------

Further more, I use the breeze library to train the model by local normal equation method.
{code}
    import sqlCtx.implicits._
    import org.apache.spark.mllib.linalg.Vector
    import breeze.linalg.DenseMatrix
    import breeze.linalg._

    val df = MLUtils.loadLibSVMFile(sqlCtx.sparkContext, "/Users/yanboliang/data/trunk/spark/data/mllib/sample_libsvm_data.txt").toDF()


    val features = df.select(col("features")).map { r =>
      r.getAs[Vector](0)
    }.collect().flatMap { v => v.toArray }
    val labelArray = df.select(col("label")).map { r =>
      r.getDouble(0)
    }.collect()

    val Xt = new DenseMatrix[Double](692, 100, features)
    val X = Xt.t

    val y = new DenseMatrix[Double](100, 1, labelArray)

    val XtXi = inv(Xt * X)
    val XtY = Xt * y

    val coefs = XtXi * XtY

    println(coefs.toString)
{code}
It also throw exception like:
{code}
breeze.linalg.MatrixSingularException: 
	at breeze.linalg.inv$$anon$1.apply(inv.scala:36)
	at breeze.linalg.inv$$anon$1.apply(inv.scala:19)
	at breeze.generic.UFunc$class.apply(UFunc.scala:48)
	at breeze.linalg.inv$.apply(inv.scala:17)
{code}
The breeze.linalg.inv is also call netlib LAPACK package which is the same library as Spark. Tracking the breeze code, we can get this exception is thrown at here (https://github.com/scalanlp/breeze/blob/master/math/src/main/scala/breeze/linalg/functions/inv.scala#L33) which is also caused by the underneath lapack error. 


was (Author: yanboliang):
Further more, I use the breeze library to train the model by local normal equation method.
{code}
    import sqlCtx.implicits._
    import org.apache.spark.mllib.linalg.Vector
    import breeze.linalg.DenseMatrix
    import breeze.linalg._

    val df = MLUtils.loadLibSVMFile(sqlCtx.sparkContext, "/Users/yanboliang/data/trunk/spark/data/mllib/sample_libsvm_data.txt").toDF()


    val features = df.select(col("features")).map { r =>
      r.getAs[Vector](0)
    }.collect().flatMap { v => v.toArray }
    val labelArray = df.select(col("label")).map { r =>
      r.getDouble(0)
    }.collect()

    val Xt = new DenseMatrix[Double](692, 100, features)
    val X = Xt.t

    val y = new DenseMatrix[Double](100, 1, labelArray)

    val XtXi = inv(Xt * X)
    val XtY = Xt * y

    val coefs = XtXi * XtY

    println(coefs.toString)
{code}
It also throw exception

> WLS can not resolve some kinds of equation
> ------------------------------------------
>
>                 Key: SPARK-11918
>                 URL: https://issues.apache.org/jira/browse/SPARK-11918
>             Project: Spark
>          Issue Type: Bug
>          Components: ML
>            Reporter: Yanbo Liang
>         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. The failure is caused by the underneath 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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