spark.mllib中LogisticRegression源代码分析
前言：在用spark编写多分类逻辑回归的不同优化器算法求解时遇到问题，特写此篇。
主要包含LogisticRegressionModel和LogisticRegressionWithLBFGS
直接看源码：注释说明了一些参数的维度
import org.apache.spark.SparkContext
import org.apache.spark.annotation.Since
import org.apache.spark.ml.linalg.DenseMatrix
import org.apache.spark.ml.util.Identifiable
import org.apache.spark.mllib.classification.impl.GLMClassificationModel
import org.apache.spark.mllib.linalg.{DenseVector, Vector, Vectors}
import org.apache.spark.mllib.linalg.BLAS.dot
import org.apache.spark.mllib.optimization._
import org.apache.spark.mllib.pmml.PMMLExportable
import org.apache.spark.mllib.regression._
import org.apache.spark.mllib.util.{DataValidators, Loader, Saveable}
import org.apache.spark.rdd.RDD
import org.apache.spark.sql.SparkSession
import org.apache.spark.storage.StorageLevel
/**
* Classification model trained using Multinomial/Binary Logistic Regression.
*
* @param weights Weights computed for every feature.
* @param intercept Intercept computed for this model. (Only used in Binary Logistic Regression.
* In Multinomial Logistic Regression, the intercepts will not be a single value,
* so the intercepts will be part of the weights.)
* @param numFeatures the dimension of the features.
* @param numClasses the number of possible outcomes for k classes classification problem in
* Multinomial Logistic Regression. By default, it is binary logistic regression
* so numClasses will be set to 2.
*/
@Since("0.8.0")
class LogisticRegressionModel @Since("1.3.0") (
@Since("1.0.0") override val weights: Vector, // 不带bias时(numClasses - 1)*numFeatures 或 带bias时(numClasses - 1)*(numFeatures+1)
@Since("1.0.0") override val intercept: Double, // 1
@Since("1.3.0") val numFeatures: Int,
@Since("1.3.0") val numClasses: Int)
extends GeneralizedLinearModel(weights, intercept) with ClassificationModel with Serializable
with Saveable with PMMLExportable {
if (numClasses == 2) {
require(weights.size == numFeatures,
s"LogisticRegressionModel with numClasses = 2 was given non-matching values:" +
s" numFeatures = $numFeatures, but weights.size = ${weights.size}")
} else {
val weightsSizeWithoutIntercept = (numClasses - 1) * numFeatures //
val weightsSizeWithIntercept = (numClasses - 1) * (numFeatures + 1) // 即带bias时的大小为(numClasses*numFeatures + numClasses) - numFeatures - 1
// InterceptSize = (numClasses - 1)
require(weights.size == weightsSizeWithoutIntercept || weights.size == weightsSizeWithIntercept,
s"LogisticRegressionModel.load with numClasses = $numClasses and numFeatures = $numFeatures" +
s" expected weights of length $weightsSizeWithoutIntercept (without intercept)" +
s" or $weightsSizeWithIntercept (with intercept)," +
s" but was given weights of length ${weights.size}")
}
private val dataWithBiasSize: Int = weights.size / (numClasses - 1) // 不带bias时：numFeatures；带bias时：numFeatures + 1
private val weightsArray: Array[Double] = weights match { // 不带bias时：(numClasses - 1)*numFeatures；带bias时：(numClasses - 1)*(numFeatures+1)
case dv: DenseVector => dv.values
case _ =>
throw new IllegalArgumentException(
s"weights only supports dense vector but got type ${weights.getClass}.")
}
/**
* Constructs a [[LogisticRegressionModel]] with weights and intercept for binary classification.
*/
@Since("1.0.0")
def this(weights: Vector, intercept: Double) = this(weights, intercept, weights.size, 2)
private var threshold: Option[Double] = Some(0.5)
/**
* Sets the threshold that separates positive predictions from negative predictions
* in Binary Logistic Regression. An example with prediction score greater than or equal to
* this threshold is identified as a positive, and negative otherwise. The default value is 0.5.
* It is only used for binary classification.
*/
@Since("1.0.0")
def setThreshold(threshold: Double): this.type = {
this.threshold = Some(threshold)
this
}
/**
* Returns the threshold (if any) used for converting raw prediction scores into 0/1 predictions.
* It is only used for binary classification.
*/
@Since("1.3.0")
def getThreshold: Option[Double] = threshold
/**
* Clears the threshold so that `predict` will output raw prediction scores.
* It is only used for binary classification.
*/
@Since("1.0.0")
def clearThreshold(): this.type = {
threshold = None
this
}
override protected def predictPoint(
dataMatrix: Vector,
weightMatrix: Vector,
intercept: Double) = {
require(dataMatrix.size == numFeatures) // 确保dataMatrix == numFeatures
// If dataMatrix and weightMatrix have the same dimension, it's binary logistic regression.
if (numClasses == 2) {
val margin = dot(weightMatrix, dataMatrix) + intercept
val score = 1.0 / (1.0 + math.exp(-margin))
threshold match {
case Some(t) => if (score > t) 1.0 else 0.0
case None => score
}
} else {
/**
* Compute and find the one with maximum margins. If the maxMargin is negative, then the
* prediction result will be the first class.
*
* PS, if you want to compute the probabilities for each outcome instead of the outcome
* with maximum probability, remember to subtract the maxMargin from margins if maxMargin
* is positive to prevent overflow.
*/
var bestClass = 0
var maxMargin = 0.0
val withBias = dataMatrix.size + 1 == dataWithBiasSize // numFeatures + 1 == dataWithBiasSize --> 看52行，若成立则为带bias。
(0 until numClasses - 1).foreach { i => // i：类别索引
var margin = 0.0
dataMatrix.foreachNonZero { (index, value) => // index: 特征索引 0 -> numFeatures-1
margin += value * weightsArray((i * dataWithBiasSize) + index)
}
// Intercept is required to be added into margin.
if (withBias) {
margin += weightsArray((i * dataWithBiasSize) + dataMatrix.size) // index = numFeatures的特征
}
if (margin > maxMargin) {
maxMargin = margin
bestClass = i + 1
}
}
bestClass.toDouble
}
}
@Since("1.3.0")
override def save(sc: SparkContext, path: String): Unit = {
GLMClassificationModel.SaveLoadV1_0.save(sc, path, this.getClass.getName,
numFeatures, numClasses, weights, intercept, threshold)
}
override def toString: String = {
s"${super.toString}, numClasses = ${numClasses}, threshold = ${threshold.getOrElse("None")}"
}
}
@Since("1.3.0")
object LogisticRegressionModel extends Loader[LogisticRegressionModel] {
@Since("1.3.0")
override def load(sc: SparkContext, path: String): LogisticRegressionModel = {
val (loadedClassName, version, metadata) = Loader.loadMetadata(sc, path)
// Hard-code class name string in case it changes in the future
val classNameV1_0 = "org.apache.spark.mllib.classification.LogisticRegressionModel"
(loadedClassName, version) match {
case (className, "1.0") if className == classNameV1_0 =>
val (numFeatures, numClasses) = ClassificationModel.getNumFeaturesClasses(metadata)
val data = GLMClassificationModel.SaveLoadV1_0.loadData(sc, path, classNameV1_0)
// numFeatures, numClasses, weights are checked in model initialization
val model =
new LogisticRegressionModel(data.weights, data.intercept, numFeatures, numClasses)
data.threshold match {
case Some(t) => model.setThreshold(t)
case None => model.clearThreshold()
}
model
case _ => throw new Exception(
s"LogisticRegressionModel.load did not recognize model with (className, format version):" +
s"($loadedClassName, $version). Supported:\n" +
s" ($classNameV1_0, 1.0)")
}
}
}
@Since("0.8.0")
class LogisticRegressionWithSGD private[mllib] (
private var stepSize: Double,
private var numIterations: Int,
private var regParam: Double,
private var miniBatchFraction: Double)
extends GeneralizedLinearAlgorithm[LogisticRegressionModel] with Serializable {
private val gradient = new LogisticGradient()
private val updater = new SquaredL2Updater()
@Since("0.8.0")
override val optimizer = new GradientDescent(gradient, updater)
.setStepSize(stepSize)
.setNumIterations(numIterations)
.setRegParam(regParam)
.setMiniBatchFraction(miniBatchFraction)
override protected val validators = List(DataValidators.binaryLabelValidator)
override protected[mllib] def createModel(weights: Vector, intercept: Double) = {
new LogisticRegressionModel(weights, intercept)
}
}
/**
* Train a classification model for Multinomial/Binary Logistic Regression using
* Limited-memory BFGS. Standard feature scaling and L2 regularization are used by default.
*
* Earlier implementations of LogisticRegressionWithLBFGS applies a regularization
* penalty to all elements including the intercept. If this is called with one of
* standard updaters (L1Updater, or SquaredL2Updater) this is translated
* into a call to ml.LogisticRegression, otherwise this will use the existing mllib
* GeneralizedLinearAlgorithm trainer, resulting in a regularization penalty to the
* intercept.
*
* @note Labels used in Logistic Regression should be {0, 1, ..., k - 1}
* for k classes multi-label classification problem.
*/
@Since("1.1.0")
class LogisticRegressionWithLBFGS
extends GeneralizedLinearAlgorithm[LogisticRegressionModel] with Serializable {
this.setFeatureScaling(true)
@Since("1.1.0")
override val optimizer = new LBFGS(new LogisticGradient, new SquaredL2Updater)
override protected val validators = List(multiLabelValidator)
private def multiLabelValidator: RDD[LabeledPoint] => Boolean = { data =>
if (numOfLinearPredictor > 1) { // 多分类，numOfLinearPredictor=numClasses-1
DataValidators.multiLabelValidator(numOfLinearPredictor + 1)(data)
} else {
DataValidators.binaryLabelValidator(data)
}
}
/**
* Set the number of possible outcomes for k classes classification problem in
* Multinomial Logistic Regression.
* By default, it is binary logistic regression so k will be set to 2.
*/
@Since("1.3.0")
def setNumClasses(numClasses: Int): this.type = {
require(numClasses > 1)
numOfLinearPredictor = numClasses - 1 // 为类别-1
if (numClasses > 2) {
optimizer.setGradient(new LogisticGradient(numClasses))
}
this
}
override protected def createModel(weights: Vector, intercept: Double) = {
if (numOfLinearPredictor == 1) {
new LogisticRegressionModel(weights, intercept)
} else { // 多分类，numOfLinearPredictor = numClasses-1
new LogisticRegressionModel(weights, intercept, numFeatures, numOfLinearPredictor + 1) // 这里传入的最后一个参数为numClasses
}
}
/**
* Run Logistic Regression with the configured parameters on an input RDD
* of LabeledPoint entries.
*
* If a known updater is used calls the ml implementation, to avoid
* applying a regularization penalty to the intercept, otherwise
* defaults to the mllib implementation. If more than two classes
* or feature scaling is disabled, always uses mllib implementation.
* If using ml implementation, uses ml code to generate initial weights.
*/
override def run(input: RDD[LabeledPoint]): LogisticRegressionModel = {
run(input, generateInitialWeights(input), userSuppliedWeights = false)
}
/**
* Run Logistic Regression with the configured parameters on an input RDD
* of LabeledPoint entries starting from the initial weights provided.
*
* If a known updater is used calls the ml implementation, to avoid
* applying a regularization penalty to the intercept, otherwise
* defaults to the mllib implementation. If more than two classes
* or feature scaling is disabled, always uses mllib implementation.
* Uses user provided weights.
*
* In the ml LogisticRegression implementation, the number of corrections
* used in the LBFGS update can not be configured. So `optimizer.setNumCorrections()`
* will have no effect if we fall into that route.
*/
override def run(input: RDD[LabeledPoint], initialWeights: Vector): LogisticRegressionModel = {
run(input, initialWeights, userSuppliedWeights = true)
}
private def run(input: RDD[LabeledPoint], initialWeights: Vector, userSuppliedWeights: Boolean):
LogisticRegressionModel = {
// ml's Logistic regression only supports binary classification currently.
if (numOfLinearPredictor == 1) {
def runWithMlLogisticRegression(elasticNetParam: Double) = {
// Prepare the ml LogisticRegression based on our settings
val lr = new org.apache.spark.ml.classification.LogisticRegression()
lr.setRegParam(optimizer.getRegParam())
lr.setElasticNetParam(elasticNetParam)
lr.setStandardization(useFeatureScaling)
if (userSuppliedWeights) {
val uid = Identifiable.randomUID("logreg-static")
lr.setInitialModel(new org.apache.spark.ml.classification.LogisticRegressionModel(uid,
new DenseMatrix(1, initialWeights.size, initialWeights.toArray),
Vectors.dense(1.0).asML, 2, false))
}
lr.setFitIntercept(addIntercept)
lr.setMaxIter(optimizer.getNumIterations())
lr.setTol(optimizer.getConvergenceTol())
// Convert our input into a DataFrame
val spark = SparkSession.builder().sparkContext(input.context).getOrCreate()
val df = spark.createDataFrame(input.map(_.asML))
// Determine if we should cache the DF
val handlePersistence = input.getStorageLevel == StorageLevel.NONE
// Train our model
val mlLogisticRegressionModel = lr.train(df, handlePersistence)
// convert the model
val weights = Vectors.dense(mlLogisticRegressionModel.coefficients.toArray)
createModel(weights, mlLogisticRegressionModel.intercept)
}
optimizer.getUpdater() match {
case x: SquaredL2Updater => runWithMlLogisticRegression(0.0)
case x: L1Updater => runWithMlLogisticRegression(1.0)
case _ => super.run(input, initialWeights)
}
} else {
super.run(input, initialWeights)
}
}
}对于多分类的逻辑回归的计算，这里先挖个坑。
因为比较奇怪的点是LogisticRegressionModel这个类接收四个参数（多分类时），第一个参数weights接收的类型为Vector[Double]，而第二个参数intercept接收的类型为Double，
42行说明了：
val weightsSizeWithoutIntercept = (numClasses - 1) * numFeatures
val weightsSizeWithIntercept = (numClasses - 1) * (numFeatures + 1) // numFeatures + 1个特征，分成numClasses - 1个类，剩下的那个类可由 1- 导出weights的两种情况：不带bias和带bias，这里我们考虑带bias。
所以，weights的维度应该为：(numClasses*numFeatures + numClasses) - numFeatures - 1
老师给的程序中，初始化权重时：
val weightsWithIntercept = Vectors.dense( new Array[Double]( (numFeatuews+1)*numClass) )可以看成一个神经网络：输入层的神经元个数为numFeatures+1，输出层神经元个数我
所以由权重构建LR模型时：
val model = new LogisticRegeressionModel(
Vectors.dense(weightsWithIntercept.toArray.slice(0, weightsWithIntercept.size - numFeatures - 1)),
weightsWithIntercept(weightsWithIntercept.size - 1), // 参数表里的最后一个参数
numFeatures, numClasses
)注意：slice(0, weightsWithIntercept.size - numFeatures - 1)), 不包含第weightsWithIntercept.size - numFeatures - 1。
所以 weightsWithIntercept.size - numFeatures - 1得到的值才能与前面的weights=(numClasses - 1) * (numFeatures + 1)相等。
但这样weights与intercept就连不上了？。。weightsWithIntercept中间还有numFeatures个数未用上。
考虑到输入模型的权重连接不上，于是将权重初始化修改为：
val initialWeightsWithIntercept = Vectors.dense(new Array[Double]( (numFeatures + 1)*numClass - numFeatures) )
模型为：
val model = new LogisticRegressionModel(
Vectors.dense(weightsWithIntercept.toArray.slice(0, weightsWithIntercept.size-1)), // numFeatures*numClass+numClass-numFeatures-1
weightsWithIntercept(weightsWithIntercept.size - 1), // 参数表里的最后一个参数
numFeatures, numClass)验证(numFeatures + 1)*numClass - numFeatures = (numFeatures + 1)*(numClass - 1) + 1也成立，而且weights与intercept就连接上了。
但这样用LBFGS训练权重的时候直接报错。
正确的权重初始化：
突然灵感一现，回想之前上吴恩达的机器学习课时，当时将逻辑回归推广到广义线性模型中的softmax回归，输出单元只用了numClass-1个单元，权重矩阵的大小为(numFeatures + 1)*(numClass - 1)
val initialWeightsWithIntercept = Vectors.dense(new Array[Double]( (numFeatures + 1)*(numClass - 1)) )
这样维数才更加正确：(numFeatures + 1)*(numClass - 1)，因为要分为numClass个类别，类之间满足softmax关系，即只要计算numClass - 1个类别的概率即可，剩下的那个类别的概率可由1减前面的概率得到。
另外 weights = (numFeatures + 1)*(numClass - 1) 条件也满足。
用LBFGS和splash优化求解都能正确求解！
构建模型：
val model = new LogisticRegressionModel(
Vectors.dense(weightsWithIntercept.toArray.slice(0, weightsWithIntercept.size)), // numFeatures*numClass+numClass-numFeatures-1
weightsWithIntercept(weightsWithIntercept.size - 1), // 参数表里的最后一个参数
numFeatures, numClass)类似python，dense vector是从0开始，到dv.size结束，右开。这样weights与intercept就连接上了。
下面填前面挖的一个坑：关于多分类的逻辑回归的计算：
权重矩阵为(numFeatures + 1)*(numClass - 1)，计算时，对于从0到numClass-1的类别i，都可以算一个概率：
var margin = 0.0
dataMatrix.foreachNonZero { (index, value) => // index: 特征索引 0 -> numFeatures-1
margin += value * weightsArray((i * dataWithBiasSize) + index) // 对权重矩阵的第i列
}
// Intercept is required to be added into margin.
if (withBias) {
margin += weightsArray((i * dataWithBiasSize) + dataMatrix.size) // index = numFeatures的特征
}margin += value * weightsArray((i * dataWithBiasSize) + index) 就是对权重矩阵的第i行的权重相乘累加。
而margin += weightsArray((i * dataWithBiasSize) + dataMatrix.size)，就是1*第i行的最后一个权重（最后一个权重为第numFeatures列(从0开始数) ）。
ie：对于一个样本有：W[c-1, f+1] * x[f+1, 1] = p[c-1, 1]，方括号表示该变量的维度。
发现构建模型的第二个参数intercept: Double并没有用到，注意Vectors.dense(weightsWithIntercept.toArray.slice(0, weightsWithIntercept.size)) 时，已经把weightsWithIntercept的所有元素都传入了weight，在模型内部，这个weight就是带bias的weight，而不是不带bias的weight，所以第二个参数可以直接给0。
Summary
作者这样写代码也真是奇葩。。。非得把参数中的特征权重和偏置权重这两个分开，引起歧义。。。还是得结合理论知识才能弄清楚到底在干嘛呀。
所以这个interpret在多分类时根本就没起到作用，而且在二分类时，可以将weightsWithIncerpet拆成两份，也可以全部写入第一个参数，第二个置0即可。