zhengruifeng 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_r341439843
 
 

 ##########
 File path: 
mllib/src/main/scala/org/apache/spark/ml/regression/FMRegressor.scala
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 @@ -0,0 +1,768 @@
+/*
+ * 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.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.regression.{LabeledPoint => OldLabeledPoint}
+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 {
+
+  /**
+   * Param for dimensionality of the factors (>= 0)
+   * @group param
+   */
+  @Since("3.0.0")
+  final val numFactors: IntParam = new IntParam(this, "numFactors",
+    "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 getNumFactors: Int = $(numFactors)
+
+  /**
+   * 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 = $(initStd)
+
+  /** String name for "gd". */
+  private[ml] val GD = "gd"
+
+  /** String name for "adamW". */
+  private[ml] val AdamW = "adamW"
+
+  /** Set of solvers that FactorizationMachines supports. */
+  private[ml] val supportedSolvers = Array(GD, AdamW)
+
+  /**
+   * The solver algorithm for optimization.
+   * Supported options: "gd", "adamW".
+   * Default: "adamW"
+   *
+   * @group param
+   */
+  @Since("3.0.0")
+  final override val solver: Param[String] = new Param[String](this, "solver",
+    "The solver algorithm for optimization. Supported options: " +
+      s"${supportedSolvers.mkString(", ")}. (Default adamW)",
+    ParamValidators.inArray[String](supportedSolvers))
+
+  private[ml] def parseSolver(solver: String, coefficientsSize: Int): Updater 
= {
+    solver match {
+      case GD => new SquaredL2Updater()
+      case AdamW => new AdamWUpdater(coefficientsSize)
+    }
+  }
+}
+
+/**
+ * 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, FMRegressorModel]
+  with FMRegressorParams with DefaultParamsWritable with Logging {
+
+  import 
org.apache.spark.ml.regression.BaseFactorizationMachinesGradient.{SquaredError, 
parseLoss}
+  import org.apache.spark.ml.regression.FMRegressor.initCoefficients
+
+  @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 setNumFactors(value: Int): this.type = set(numFactors, value)
+  setDefault(numFactors -> 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 = {
+    require(value > 0 && value <= 1.0,
 
 Review comment:
   `ParamValidators.inRange(0, 1, false, true)` already checks input value

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