Linear regression in Apache Spark giving wrong intercept and weights - apache-spark

Question

Using MLLib LinearRegressionWithSGD for the dummy data set (y, x1, x2) for y = (2*x1) + (3*x2) + 4 is producing wrong intercept and weights. Actual data used is,
x1 x2 y
1 0.1 6.3
2 0.2 8.6
3 0.3 10.9
4 0.6 13.8
5 0.8 16.4
6 1.2 19.6
7 1.6 22.8
8 1.9 25.7
9 2.1 28.3
10 2.4 31.2
11 2.7 34.1
I set the following input parameters and got the below model outputs
[numIterations, step, miniBatchFraction, regParam] [intercept, [weights]]
[5,9,0.6,5] = [2.36667135839938E13, weights:[1.708772545209758E14, 3.849548062850367E13] ]
[2,default,default,default] = [-2495.5635231554793, weights:[-19122.41357929275,-4308.224496146531]]
[5,default,default,default] = [2.875191315671051E8, weights: [2.2013802074495964E9,4.9593017130199933E8]]
[20,default,default,default] = [-8.896967235537095E29, weights: [-6.811932001659158E30,-1.5346020624812824E30]]
Need to know,
How do i get the correct intercept and weights [4, [2, 3]] for the above mentioned dummy data.
Will tuning the step size help in convergence? I need to run this in a automated manner for several hundred variables, so not keen to do that.
Should I scale the data? How will it help?
Below is the code used to generate these results.
object SciBenchTest {
def main(args: Array[String]): Unit = run
def run: Unit = {
val sparkConf = new SparkConf().setAppName("SparkBench")
val sc = new SparkContext(sparkConf)
// Load and parse the dummy data (y, x1, x2) for y = (2*x1) + (3*x2) + 4
// i.e. intercept should be 4, weights (2, 3)?
val data = sc.textFile("data/dummy.csv")
// LabeledPoint is (label, [features])
val parsedData = data.map { line =>
val parts = line.split(',')
val label = parts(2).toDouble
val features = Array(parts(0), parts(1)) map (_.toDouble)
LabeledPoint(label, Vectors.dense(features))
}
//parsedData.collect().foreach(x => println(x));
// Scale the features
/*val scaler = new StandardScaler(withMean = true, withStd = true)
.fit(parsedData.map(x => x.features))
val scaledData = parsedData
.map(x =>
LabeledPoint(x.label,
scaler.transform(Vectors.dense(x.features.toArray))))
scaledData.collect().foreach(x => println(x));*/
// Building the model: SGD = stochastic gradient descent
val numIterations = 20 //5
val step = 9.0 //9.0 //0.7
val miniBatchFraction = 0.6 //0.7 //0.65 //0.7
val regParam = 5.0 //3.0 //10.0
//val model = LinearRegressionWithSGD.train(parsedData, numIterations, step) //scaledData
val algorithm = new LinearRegressionWithSGD() //train(parsedData, numIterations)
algorithm.setIntercept(true)
algorithm.optimizer
//.setMiniBatchFraction(miniBatchFraction)
.setNumIterations(numIterations)
//.setStepSize(step)
//.setGradient(new LeastSquaresGradient())
//.setUpdater(new SquaredL2Updater()) //L1Updater //SimpleUpdater //SquaredL2Updater
//.setRegParam(regParam)
val model = algorithm.run(parsedData)
println(s">>>> Model intercept: ${model.intercept}, weights: ${model.weights}")
// Evaluate model on training examples
val valuesAndPreds = parsedData.map { point =>
val prediction = model.predict(point.features)
(point.label, point.features, prediction)
}
// Print out features, actual and predicted values...
valuesAndPreds.take(10).foreach({ case (v, f, p) =>
println(s"Features: ${f}, Predicted: ${p}, Actual: ${v}")
})
}
}

Answer 1

As described in the documentation
https://spark.apache.org/docs/1.0.2/mllib-optimization.html
selecting the best step-size for SGD methods can often be delicate.
I would try with lover values, for example
// Build linear regression model
var regression = new LinearRegressionWithSGD().setIntercept(true)
regression.optimizer.setStepSize(0.001)
val model = regression.run(parsedData)

Answer 2

Adding the stepsize did not help us much.
We used the following parameters to calculate the intercept/weights and loss and used the same to construct a linear regression model in order to predict our features. Thanks #selvinsource for pointing me in the correct direction.
val data = sc.textFile("data/dummy.csv")
// LabeledPoint is (label, [features])
val parsedData = data.map { line =>
val parts = line.split(',')
val label = parts(2).toDouble
val features = Array(parts(0), parts(1)) map (_.toDouble)
(label, MLUtils.appendBias(Vectors.dense(features)))
}.cache()
val numCorrections = 5 //10//5//3
val convergenceTol = 1e-4 //1e-4
val maxNumIterations = 20 //20//100
val regParam = 0.00001 //0.1//10.0
val (weightsWithIntercept, loss) = LBFGS.runLBFGS(
parsedData,
new LeastSquaresGradient(),//LeastSquaresGradient
new SquaredL2Updater(), //SquaredL2Updater(),SimpleUpdater(),L1Updater()
numCorrections,
convergenceTol,
maxNumIterations,
regParam,
Vectors.dense(0.0, 0.0, 0.0))//initialWeightsWithIntercept)
loss.foreach(println)
val model = new LinearRegressionModel(
Vectors.dense(weightsWithIntercept.toArray.slice(0, weightsWithIntercept.size - 1)),
weightsWithIntercept(weightsWithIntercept.size - 1))
println(s">>>> Model intercept: ${model.intercept}, weights: ${model.weights}")
// Evaluate model on training examples
val valuesAndPreds = parsedData.collect().map { point =>
var prediction = model.predict(Vectors.dense(point._2.apply(0), point._2.apply(1)))
(prediction, point._1)
}
// Print out features, actual and predicted values...
valuesAndPreds.take(10).foreach({ case (v, f) =>
println(s"Features: ${f}, Predicted: ${v}")//, Actual: ${v}")
})