Apache Spark 中的线性回归给出错误的截距和权重

对 y = (2*x1) + (3*x2) + 4 的虚拟数据集 (y, x1, x2) 使用 MLLib LinearRegressionWithSGD 会产生错误的截距和权重。实际使用的数据是，

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

我设置了以下输入参数并得到了以下模型输出 [numIterations、step、miniBatchFraction、regParam] [截距、[权重]]

1. [5,9,0.6,5] = [2.36667135839938E13，权重：[1.708772545209758E14，3.849548062850367E13] ]
2. [2，默认，默认，默认] = [-2495.5635231554793，权重：[-19122.41357929275，-4308.224496146531]]
3. [5，默认，默认，默认] = [2.875191315671051E8，权重：[2.2013802074495964E9，4.9593017130199933E8]]
4. [20，默认，默认，默认] = [-8.896967235537095E29，权重：[-6.811932001659158E30，-1.53​​46020624812824E30]]

需要知道，

1. 我如何获得上述虚拟数据的正确截距和权重 [4, [2, 3]]。
2. 调整步长有助于收敛吗？我需要以自动化的方式运行数百个变量，所以不热衷于这样做。
3. 我应该缩放数据吗？会有什么帮助？

以下是用于生成这些结果的代码。

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}")
    })
  }
}

如文档中所述https://spark.apache.org/docs/1.0.2/mllib-optimization.html https://spark.apache.org/docs/1.0.2/mllib-optimization.html选择 SGD 方法的最佳步长通常很微妙。

例如，我会尝试用爱人的价值观

// Build linear regression model
var regression = new LinearRegressionWithSGD().setIntercept(true)
regression.optimizer.setStepSize(0.001)
val model = regression.run(parsedData)