mob-ai commented on a change in pull request #26124: [SPARK-29224][ML]Implement Factorization Machines as a ml-pipeline component URL: https://github.com/apache/spark/pull/26124#discussion_r355913166
########## File path: mllib/src/main/scala/org/apache/spark/ml/regression/FMRegressor.scala ########## @@ -0,0 +1,826 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to You under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package org.apache.spark.ml.regression + +import scala.util.Random + +import breeze.linalg.{axpy => brzAxpy, norm => brzNorm, Vector => BV} +import breeze.numerics.{sqrt => brzSqrt} +import org.apache.hadoop.fs.Path + +import org.apache.spark.annotation.Since +import org.apache.spark.internal.Logging +import org.apache.spark.ml.{PredictionModel, Predictor, PredictorParams} +import org.apache.spark.ml.linalg._ +import org.apache.spark.ml.linalg.BLAS._ +import org.apache.spark.ml.param._ +import org.apache.spark.ml.param.shared._ +import org.apache.spark.ml.regression.FactorizationMachines._ +import org.apache.spark.ml.util._ +import org.apache.spark.ml.util.Instrumentation.instrumented +import org.apache.spark.mllib.{linalg => OldLinalg} +import org.apache.spark.mllib.linalg.{Vector => OldVector, Vectors => OldVectors} +import org.apache.spark.mllib.linalg.VectorImplicits._ +import org.apache.spark.mllib.optimization.{Gradient, GradientDescent, SquaredL2Updater, Updater} +import org.apache.spark.mllib.util.MLUtils +import org.apache.spark.rdd.RDD +import org.apache.spark.sql.{Dataset, Row} +import org.apache.spark.sql.functions.col +import org.apache.spark.storage.StorageLevel + +/** + * Params for Factorization Machines + */ +private[ml] trait FactorizationMachinesParams + extends PredictorParams + with HasMaxIter with HasStepSize with HasTol with HasSolver with HasSeed { + + /** + * Param for dimensionality of the factors (>= 0) + * @group param + */ + @Since("3.0.0") + final val factorSize: IntParam = new IntParam(this, "factorSize", + "Dimensionality of the factor vectors, " + + "which are used to get pairwise interactions between variables", + ParamValidators.gt(0)) + + /** @group getParam */ + @Since("3.0.0") + final def getFactorSize: Int = $(factorSize) + + /** + * Param for whether to fit global bias term + * @group param + */ + @Since("3.0.0") + final val fitBias: BooleanParam = new BooleanParam(this, "fitBias", + "whether to fit global bias term") + + /** @group getParam */ + @Since("3.0.0") + final def getFitBias: Boolean = $(fitBias) + + /** + * Param for whether to fit linear term (aka 1-way term) + * @group param + */ + @Since("3.0.0") + final val fitLinear: BooleanParam = new BooleanParam(this, "fitLinear", + "whether to fit linear term (aka 1-way term)") + + /** @group getParam */ + @Since("3.0.0") + final def getFitLinear: Boolean = $(fitLinear) + + /** + * Param for L2 regularization parameter (>= 0) + * @group param + */ + @Since("3.0.0") + final val regParam: DoubleParam = new DoubleParam(this, "regParam", + "the magnitude of L2-regularization", ParamValidators.gtEq(0)) + + /** @group getParam */ + @Since("3.0.0") + final def getRegParam: Double = $(regParam) + + /** + * Param for mini-batch fraction, must be in range (0, 1] + * @group param + */ + @Since("3.0.0") + final val miniBatchFraction: DoubleParam = new DoubleParam(this, "miniBatchFraction", + "fraction of the input data set that should be used for one iteration of gradient descent", + ParamValidators.inRange(0, 1, false, true)) + + /** @group getParam */ + @Since("3.0.0") + final def getMiniBatchFraction: Double = $(miniBatchFraction) + + /** + * Param for standard deviation of initial coefficients + * @group param + */ + @Since("3.0.0") + final val initStd: DoubleParam = new DoubleParam(this, "initStd", + "standard deviation of initial coefficients", ParamValidators.gt(0)) + + /** @group getParam */ + @Since("3.0.0") + final def getInitStd: Double = $(initStd) + + /** + * The solver algorithm for optimization. + * Supported options: "gd", "adamW". + * Default: "adamW" + * + * @group param + */ + @Since("3.0.0") + final override val solver: Param[String] = new Param[String](this, "solver", + "The solver algorithm for optimization. Supported options: " + + s"${supportedSolvers.mkString(", ")}. (Default adamW)", + ParamValidators.inArray[String](supportedSolvers)) +} + +private[ml] trait FactorizationMachines extends FactorizationMachinesParams { + + private[ml] def initCoefficients(numFeatures: Int): OldVector = { + val rnd = new Random($(seed)) + val initialCoefficients = + OldVectors.dense( + Array.fill($(factorSize) * numFeatures)(rnd.nextGaussian() * $(initStd)) ++ + (if ($(fitLinear)) new Array[Double](numFeatures) else Array.emptyDoubleArray) ++ + (if ($(fitBias)) new Array[Double](1) else Array.emptyDoubleArray)) + initialCoefficients + } + + private[ml] def trainImpl( + data: RDD[(Double, OldVector)], + numFeatures: Int, + loss: String + ): Vector = { + + // initialize coefficients + val initialCoefficients = initCoefficients(numFeatures) + val coefficientsSize = initialCoefficients.size + + // optimize coefficients with gradient descent + val gradient = parseLoss(loss, $(factorSize), $(fitBias), $(fitLinear), numFeatures) + + val updater = parseSolver($(solver), coefficientsSize) + + val optimizer = new GradientDescent(gradient, updater) + .setStepSize($(stepSize)) + .setNumIterations($(maxIter)) + .setRegParam($(regParam)) + .setMiniBatchFraction($(miniBatchFraction)) + .setConvergenceTol($(tol)) + val coefficients = optimizer.optimize(data, initialCoefficients) + coefficients.asML + } +} + +private[ml] object FactorizationMachines { + + /** String name for "gd". */ + val GD = "gd" + + /** String name for "adamW". */ + val AdamW = "adamW" + + /** Set of solvers that FactorizationMachines supports. */ + val supportedSolvers = Array(GD, AdamW) + + /** String name for "logisticLoss". */ + val LogisticLoss = "logisticLoss" + + /** String name for "squaredError". */ + val SquaredError = "squaredError" + + /** Set of loss function names that FactorizationMachines supports. */ + val supportedRegressorLosses = Array(SquaredError) + val supportedClassifierLosses = Array(LogisticLoss) + val supportedLosses = supportedRegressorLosses ++ supportedClassifierLosses + + def parseSolver(solver: String, coefficientsSize: Int): Updater = { + solver match { + case GD => new SquaredL2Updater() + case AdamW => new AdamWUpdater(coefficientsSize) + } + } + + def parseLoss( + lossFunc: String, + factorSize: Int, + fitBias: Boolean, + fitLinear: Boolean, + numFeatures: Int + ): BaseFactorizationMachinesGradient = { + + lossFunc match { + case LogisticLoss => + new LogisticFactorizationMachinesGradient(factorSize, fitBias, fitLinear, numFeatures) + case SquaredError => + new MSEFactorizationMachinesGradient(factorSize, fitBias, fitLinear, numFeatures) + case _ => throw new IllegalArgumentException(s"loss function type $lossFunc is invalidation") + } + } + + def splitCoefficients( + coefficients: Vector, + numFeatures: Int, + factorSize: Int, + fitBias: Boolean, + fitLinear: Boolean + ): (Double, Vector, Matrix) = { + + val coefficientsSize = numFeatures * factorSize + + (if (fitLinear) numFeatures else 0) + (if (fitBias) 1 else 0) + require(coefficientsSize == coefficients.size, + s"coefficients.size did not match the excepted size ${coefficientsSize}") + + val bias = if (fitBias) coefficients(coefficients.size - 1) else 0.0 + val linear: Vector = if (fitLinear) { + new DenseVector(coefficients.toArray.slice( + numFeatures * factorSize, numFeatures * factorSize + numFeatures)) + } else { + Vectors.sparse(numFeatures, Seq.empty) + } + val factors = new DenseMatrix(numFeatures, factorSize, + coefficients.toArray.slice(0, numFeatures * factorSize), true) + (bias, linear, factors) + } + + def combineCoefficients( + bias: Double, + linear: Vector, + factors: Matrix, + fitBias: Boolean, + fitLinear: Boolean + ): Vector = { + + val coefficients = factors.toDense.values ++ + (if (fitLinear) linear.toArray else Array.emptyDoubleArray) ++ + (if (fitBias) Array(bias) else Array.emptyDoubleArray) + new DenseVector(coefficients) + } + + def getRawPrediction( + features: Vector, + bias: Double, + linear: Vector, + factors: Matrix + ): Double = { + var rawPrediction = bias + features.dot(linear) + (0 until factors.numCols).foreach { f => + var sumSquare = 0.0 + var sum = 0.0 + features.foreachActive { case (index, value) => + val vx = factors(index, f) * value + sumSquare += vx * vx + sum += vx + } + rawPrediction += 0.5 * (sum * sum - sumSquare) + } + + rawPrediction + } +} + +/** + * Params for FMRegressor + */ +private[regression] trait FMRegressorParams extends FactorizationMachinesParams { +} + +/** + * Factorization Machines learning algorithm for regression. + * It supports normal gradient descent and AdamW solver. + * + * The implementation is based upon: + * <a href="https://www.csie.ntu.edu.tw/~b97053/paper/Rendle2010FM.pdf";> + * S. Rendle. "Factorization machines" 2010</a>. + * + * FM is able to estimate interactions even in problems with huge sparsity + * (like advertising and recommendation system). + * FM formula is: + * {{{ + * y = w_0 + \sum\limits^n_{i-1} w_i x_i + + * \sum\limits^n_{i=1} \sum\limits^n_{j=i+1} \langle v_i, v_j \rangle x_i x_j + * }}} + * First two terms denote global bias and linear term (as same as linear regression), + * and last term denotes pairwise interactions term. {{{v_i}}} describes the i-th variable + * with k factors. + * + * FM regression model uses MSE loss which can be solved by gradient descent method, and + * regularization terms like L2 are usually added to the loss function to prevent overfitting. + */ +@Since("3.0.0") +class FMRegressor @Since("3.0.0") ( + @Since("3.0.0") override val uid: String) + extends Predictor[Vector, FMRegressor, FMRegressionModel] + with FactorizationMachines with FMRegressorParams with DefaultParamsWritable with Logging { + + @Since("3.0.0") + def this() = this(Identifiable.randomUID("fmr")) + + /** + * Set the dimensionality of the factors. + * Default is 8. + * + * @group setParam + */ + @Since("3.0.0") + def setFactorSize(value: Int): this.type = set(factorSize, value) + setDefault(factorSize -> 8) + + /** + * Set whether to fit global bias term. + * Default is true. + * + * @group setParam + */ + @Since("3.0.0") + def setFitBias(value: Boolean): this.type = set(fitBias, value) + setDefault(fitBias -> true) + + /** + * Set whether to fit linear term. + * Default is true. + * + * @group setParam + */ + @Since("3.0.0") + def setFitLinear(value: Boolean): this.type = set(fitLinear, value) + setDefault(fitLinear -> true) + + /** + * Set the L2 regularization parameter. + * Default is 0.0. + * + * @group setParam + */ + @Since("3.0.0") + def setRegParam(value: Double): this.type = set(regParam, value) + setDefault(regParam -> 0.0) + + /** + * Set the mini-batch fraction parameter. + * Default is 1.0. + * + * @group setParam + */ + @Since("3.0.0") + def setMiniBatchFraction(value: Double): this.type = set(miniBatchFraction, value) + setDefault(miniBatchFraction -> 1.0) + + /** + * Set the standard deviation of initial coefficients. + * Default is 0.01. + * + * @group setParam + */ + @Since("3.0.0") + def setInitStd(value: Double): this.type = set(initStd, value) + setDefault(initStd -> 0.01) + + /** + * Set the maximum number of iterations. + * Default is 100. + * + * @group setParam + */ + @Since("3.0.0") + def setMaxIter(value: Int): this.type = set(maxIter, value) + setDefault(maxIter -> 100) + + /** + * Set the initial step size for the first step (like learning rate). + * Default is 1.0. + * + * @group setParam + */ + @Since("3.0.0") + def setStepSize(value: Double): this.type = set(stepSize, value) + setDefault(stepSize -> 1.0) + + /** + * Set the convergence tolerance of iterations. + * Default is 1E-6. + * + * @group setParam + */ + @Since("3.0.0") + def setTol(value: Double): this.type = set(tol, value) + setDefault(tol -> 1E-6) + + /** + * Set the solver algorithm used for optimization. + * Supported options: "gd", "adamW". + * Default: "adamW" + * + * @group setParam + */ + @Since("3.0.0") + def setSolver(value: String): this.type = set(solver, value) + setDefault(solver -> AdamW) + + /** + * Set the random seed for weight initialization. + * + * @group setParam + */ + @Since("3.0.0") + def setSeed(value: Long): this.type = set(seed, value) + + override protected[spark] def train( + dataset: Dataset[_] + ): FMRegressionModel = instrumented { instr => + + val handlePersistence = dataset.storageLevel == StorageLevel.NONE + val data: RDD[(Double, OldVector)] = + dataset.select(col($(labelCol)), col($(featuresCol))).rdd.map { + case Row(label: Double, features: Vector) => + (label, features) + } + + if (handlePersistence) data.persist(StorageLevel.MEMORY_AND_DISK) + + instr.logPipelineStage(this) + instr.logDataset(dataset) + instr.logParams(this, factorSize, fitBias, fitLinear, regParam, + miniBatchFraction, initStd, maxIter, stepSize, tol, solver) + + val numFeatures = data.first()._2.size + instr.logNumFeatures(numFeatures) + + val coefficients = trainImpl(data, numFeatures, SquaredError) + + val (bias, linear, factors) = splitCoefficients( + coefficients, numFeatures, $(factorSize), $(fitBias), $(fitLinear)) + + if (handlePersistence) data.unpersist() + + copyValues(new FMRegressionModel(uid, bias, linear, factors)) + } + + @Since("3.0.0") + override def copy(extra: ParamMap): FMRegressor = defaultCopy(extra) +} + +@Since("3.0.0") +object FMRegressor extends DefaultParamsReadable[FMRegressor] { + + @Since("3.0.0") + override def load(path: String): FMRegressor = super.load(path) +} + +/** + * Model produced by [[FMRegressor]]. + */ +@Since("3.0.0") +class FMRegressionModel private[regression] ( + @Since("3.0.0") override val uid: String, + @Since("3.0.0") val bias: Double, + @Since("3.0.0") val linear: Vector, + @Since("3.0.0") val factors: Matrix) + extends PredictionModel[Vector, FMRegressionModel] + with FMRegressorParams with MLWritable { + + @Since("3.0.0") + override val numFeatures: Int = linear.size + + override def predict(features: Vector): Double = { + getRawPrediction(features, bias, linear, factors) + } + + @Since("3.0.0") + override def copy(extra: ParamMap): FMRegressionModel = { + copyValues(new FMRegressionModel(uid, bias, linear, factors), extra) + } + + @Since("3.0.0") + override def write: MLWriter = + new FMRegressionModel.FMRegressionModelWriter(this) + + override def toString: String = { + s"FMRegressionModel: " + + s"uid = ${super.toString}, numFeatures = $numFeatures, " + + s"factorSize = ${$(factorSize)}, fitLinear = ${$(fitLinear)}, fitBias = ${$(fitBias)}" + } +} + +@Since("3.0.0") +object FMRegressionModel extends MLReadable[FMRegressionModel] { + + @Since("3.0.0") + override def read: MLReader[FMRegressionModel] = new FMRegressionModelReader + + @Since("3.0.0") + override def load(path: String): FMRegressionModel = super.load(path) + + /** [[MLWriter]] instance for [[FMRegressionModel]] */ + private[FMRegressionModel] class FMRegressionModelWriter( + instance: FMRegressionModel) extends MLWriter with Logging { + + private case class Data( + bias: Double, + linear: Vector, + factors: Matrix) + + override protected def saveImpl(path: String): Unit = { + DefaultParamsWriter.saveMetadata(instance, path, sc) + val data = Data(instance.bias, instance.linear, instance.factors) + val dataPath = new Path(path, "data").toString + sparkSession.createDataFrame(Seq(data)).repartition(1).write.parquet(dataPath) + } + } + + private class FMRegressionModelReader extends MLReader[FMRegressionModel] { + + private val className = classOf[FMRegressionModel].getName + + override def load(path: String): FMRegressionModel = { + val metadata = DefaultParamsReader.loadMetadata(path, sc, className) + val dataPath = new Path(path, "data").toString + val data = sparkSession.read.format("parquet").load(dataPath) + + val Row(bias: Double, linear: Vector, factors: Matrix) = data + .select("bias", "linear", "factors").head() + val model = new FMRegressionModel(metadata.uid, bias, linear, factors) + metadata.getAndSetParams(model) + model + } + } +} + +/** + * Factorization Machines base gradient class + * Implementing the raw FM formula, include raw prediction and raw gradient, + * then inherit the base class to implement special gradient class(like logloss, mse). + * + * Factorization Machines raw formula: + * {{{ + * y_{fm} = w_0 + \sum\limits^n_{i-1} w_i x_i + + * \sum\limits^n_{i=1} \sum\limits^n_{j=i+1} \langle v_i, v_j \rangle x_i x_j + * }}} + * the pairwise interactions (2-way term) can be reformulated: + * {{{ + * \sum\limits^n_{i=1} \sum\limits^n_{j=i+1} \langle v_i, v_j \rangle x_i x_j + * = \frac{1}{2}\sum\limits^k_{f=1} + * \left(\left( \sum\limits^n_{i=1}v_{i,f}x_i \right)^2 - + * \sum\limits^n_{i=1}v_{i,f}^2x_i^2 \right) + * }}} + * and the gradients are: + * {{{ + * \frac{\partial}{\partial\theta}y_{fm} = \left\{ + * \begin{align} + * &1, & if\ \theta\ is\ w_0 \\ + * &x_i, & if\ \theta\ is\ w_i \\ + * &x_i{\sum}^n_{j=1}v_{j,f}x_j - v_{i,f}x_i^2, & if\ \theta\ is\ v_{i,j} \\ + * \end{align} + * \right. + * }}} + * + * Factorization Machines formula with prediction task: + * {{{ + * \hat{y} = p\left( y_{fm} \right) + * }}} + * p is the prediction function, for binary classification task is sigmoid. + * The loss funcation gradient formula: + * {{{ + * \frac{\partial}{\partial\theta} l\left( \hat{y},y \right) = + * \frac{\partial}{\partial\theta} l\left( p\left( y_{fm} \right),y \right) = + * \frac{\partial l}{\partial \hat{y}} \cdot + * \frac{\partial \hat{y}}{\partial y_{fm}} \cdot + * \frac{\partial y_{fm}}{\partial\theta} + * }}} + * Last term is same for all task, so be implemented in base gradient class. + * last term named rawGradient in following code, and first two term named multiplier. + */ +private[ml] abstract class BaseFactorizationMachinesGradient( + factorSize: Int, + fitBias: Boolean, + fitLinear: Boolean, + numFeatures: Int) extends Gradient { + + override def compute( + data: OldVector, + label: Double, + weights: OldVector, + cumGradient: OldVector): Double = { + val (rawPrediction, sumVX) = getRawPrediction(data, weights) + val rawGradient = getRawGradient(data, weights, sumVX) + val multiplier = getMultiplier(rawPrediction, label) + axpy(multiplier, rawGradient, cumGradient) + val loss = getLoss(rawPrediction, label) + loss + } + + def getPrediction(rawPrediction: Double): Double + + protected def getMultiplier(rawPrediction: Double, label: Double): Double + + protected def getLoss(rawPrediction: Double, label: Double): Double + + def getRawPrediction(data: OldVector, weights: OldVector): (Double, Array[Double]) = { + val sumVX = new Array[Double](factorSize) + var rawPrediction = 0.0 + val vWeightsSize = numFeatures * factorSize + + if (fitBias) rawPrediction += weights(weights.size - 1) + if (fitLinear) { + data.foreachActive { case (index, value) => + rawPrediction += weights(vWeightsSize + index) * value + } + } + (0 until factorSize).foreach { f => + var sumSquare = 0.0 + var sum = 0.0 + data.foreachActive { case (index, value) => + val vx = weights(index * factorSize + f) * value + sumSquare += vx * vx + sum += vx + } + sumVX(f) = sum + rawPrediction += 0.5 * (sum * sum - sumSquare) + } + + (rawPrediction, sumVX) + } + + private def getRawGradient( + data: OldVector, + weights: OldVector, + sumVX: Array[Double] + ): OldVector = { + data match { + // Usually Factorization Machines is used, there will be a lot of sparse features. + // So need to optimize the gradient descent of sparse vector. + case data: OldLinalg.SparseVector => + val gardSize = data.indices.length * factorSize + + (if (fitLinear) data.indices.length else 0) + + (if (fitBias) 1 else 0) + val gradIndex = Array.fill(gardSize)(0) + val gradValue = Array.fill(gardSize)(0.0) + var gradI = 0 + val vWeightsSize = numFeatures * factorSize + + data.foreachActive { case (index, value) => + (0 until factorSize).foreach { f => + gradIndex(gradI) = index * factorSize + f + gradValue(gradI) = value * sumVX(f) - weights(index * factorSize + f) * value * value + gradI += 1 + } + } + if (fitLinear) { + data.foreachActive { case (index, value) => + gradIndex(gradI) = vWeightsSize + index + gradValue(gradI) = value + gradI += 1 + } + } + if (fitBias) { + gradIndex(gradI) = weights.size - 1 + gradValue(gradI) = 1.0 + } + + OldVectors.sparse(weights.size, gradIndex, gradValue) + case data: OldLinalg.DenseVector => + val gradient = Array.fill(weights.size)(0.0) + val vWeightsSize = numFeatures * factorSize + + if (fitBias) gradient(weights.size - 1) += 1.0 + if (fitLinear) { + data.foreachActive { case (index, value) => + gradient(vWeightsSize + index) += value + } + } + (0 until factorSize).foreach { f => + data.foreachActive { case (index, value) => + gradient(index * factorSize + f) += + value * sumVX(f) - weights(index * factorSize + f) * value * value + } + } + + OldVectors.dense(gradient) + } + } +} + +/** + * FM with logistic loss + * prediction formula: + * {{{ + * \hat{y} = \sigmoid(y_{fm}) + * }}} + * loss formula: + * {{{ + * - y * log(\hat{y}) - (1 - y) * log(1 - \hat{y}) + * }}} + * multiplier formula: + * {{{ + * \frac{\partial l}{\partial \hat{y}} \cdot + * \frac{\partial \hat{y}}{\partial y_{fm}} = + * \hat{y} - y + * }}} + */ +private[ml] class LogisticFactorizationMachinesGradient( + factorSize: Int, + fitBias: Boolean, + fitLinear: Boolean, + numFeatures: Int) + extends BaseFactorizationMachinesGradient( + factorSize: Int, + fitBias: Boolean, + fitLinear: Boolean, + numFeatures: Int) with Logging { + + override def getPrediction(rawPrediction: Double): Double = { + 1.0 / (1.0 + math.exp(-rawPrediction)) + } + + override protected def getMultiplier(rawPrediction: Double, label: Double): Double = { + getPrediction(rawPrediction) - label + } + + override protected def getLoss(rawPrediction: Double, label: Double): Double = { + if (label > 0) MLUtils.log1pExp(-rawPrediction) + else MLUtils.log1pExp(rawPrediction) + } +} + +/** + * FM with mse + * prediction formula: + * {{{ + * \hat{y} = y_{fm} + * }}} + * loss formula: + * {{{ + * (\hat{y} - y) ^ 2 + * }}} + * multiplier formula: + * {{{ + * \frac{\partial l}{\partial \hat{y}} \cdot + * \frac{\partial \hat{y}}{\partial y_{fm}} = + * 2 * (\hat{y} - y) + * }}} + */ +private[ml] class MSEFactorizationMachinesGradient( + factorSize: Int, + fitBias: Boolean, + fitLinear: Boolean, + numFeatures: Int) + extends BaseFactorizationMachinesGradient( + factorSize: Int, + fitBias: Boolean, + fitLinear: Boolean, + numFeatures: Int) with Logging { + + override def getPrediction(rawPrediction: Double): Double = { + rawPrediction + } + + override protected def getMultiplier(rawPrediction: Double, label: Double): Double = { + 2 * (rawPrediction - label) + } + + override protected def getLoss(rawPrediction: Double, label: Double): Double = { + (rawPrediction - label) * (rawPrediction - label) + } +} + +private[ml] class AdamWUpdater(weightSize: Int) extends Updater with Logging { Review comment: > this regparam is appled to all coefficients, right? yes, RegParam will apply to all coefficients. 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