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/*
* 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.collection.mutable
import breeze.linalg.{DenseVector => BDV}
import breeze.optimize.{CachedDiffFunction, DiffFunction, LBFGS => BreezeLBFGS}
import org.apache.hadoop.fs.Path
import org.apache.spark.SparkException
import org.apache.spark.annotation.{Experimental, Since}
import org.apache.spark.broadcast.Broadcast
import org.apache.spark.internal.Logging
import org.apache.spark.ml.{Estimator, Model}
import org.apache.spark.ml.linalg.{BLAS, Vector, Vectors, VectorUDT}
import org.apache.spark.ml.param._
import org.apache.spark.ml.param.shared._
import org.apache.spark.ml.util._
import org.apache.spark.mllib.linalg.VectorImplicits._
import org.apache.spark.mllib.stat.MultivariateOnlineSummarizer
import org.apache.spark.mllib.util.MLUtils
import org.apache.spark.rdd.RDD
import org.apache.spark.sql.{DataFrame, Dataset, Row}
import org.apache.spark.sql.functions._
import org.apache.spark.sql.types.{DoubleType, StructType}
import org.apache.spark.storage.StorageLevel
/**
* Params for accelerated failure time (AFT) regression.
*/
private[regression] trait AFTSurvivalRegressionParams extends Params
with HasFeaturesCol with HasLabelCol with HasPredictionCol with HasMaxIter
with HasTol with HasFitIntercept with Logging {
/**
* Param for censor column name.
* The value of this column could be 0 or 1.
* If the value is 1, it means the event has occurred i.e. uncensored; otherwise censored.
* @group param
*/
@Since("1.6.0")
final val censorCol: Param[String] = new Param(this, "censorCol", "censor column name")
/** @group getParam */
@Since("1.6.0")
def getCensorCol: String = $(censorCol)
setDefault(censorCol -> "censor")
/**
* Param for quantile probabilities array.
* Values of the quantile probabilities array should be in the range (0, 1)
* and the array should be non-empty.
* @group param
*/
@Since("1.6.0")
final val quantileProbabilities: DoubleArrayParam = new DoubleArrayParam(this,
"quantileProbabilities", "quantile probabilities array",
(t: Array[Double]) => t.forall(ParamValidators.inRange(0, 1, false, false)) && t.length > 0)
/** @group getParam */
@Since("1.6.0")
def getQuantileProbabilities: Array[Double] = $(quantileProbabilities)
setDefault(quantileProbabilities -> Array(0.01, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.99))
/**
* Param for quantiles column name.
* This column will output quantiles of corresponding quantileProbabilities if it is set.
* @group param
*/
@Since("1.6.0")
final val quantilesCol: Param[String] = new Param(this, "quantilesCol", "quantiles column name")
/** @group getParam */
@Since("1.6.0")
def getQuantilesCol: String = $(quantilesCol)
/** Checks whether the input has quantiles column name. */
private[regression] def hasQuantilesCol: Boolean = {
isDefined(quantilesCol) && $(quantilesCol).nonEmpty
}
/**
* Validates and transforms the input schema with the provided param map.
* @param schema input schema
* @param fitting whether this is in fitting or prediction
* @return output schema
*/
protected def validateAndTransformSchema(
schema: StructType,
fitting: Boolean): StructType = {
SchemaUtils.checkColumnType(schema, $(featuresCol), new VectorUDT)
if (fitting) {
SchemaUtils.checkColumnType(schema, $(censorCol), DoubleType)
SchemaUtils.checkNumericType(schema, $(labelCol))
}
if (hasQuantilesCol) {
SchemaUtils.appendColumn(schema, $(quantilesCol), new VectorUDT)
}
SchemaUtils.appendColumn(schema, $(predictionCol), DoubleType)
}
}
/**
* :: Experimental ::
* Fit a parametric survival regression model named accelerated failure time (AFT) model
* ([[https://en.wikipedia.org/wiki/Accelerated_failure_time_model]])
* based on the Weibull distribution of the survival time.
*/
@Experimental
@Since("1.6.0")
class AFTSurvivalRegression @Since("1.6.0") (@Since("1.6.0") override val uid: String)
extends Estimator[AFTSurvivalRegressionModel] with AFTSurvivalRegressionParams
with DefaultParamsWritable with Logging {
@Since("1.6.0")
def this() = this(Identifiable.randomUID("aftSurvReg"))
/** @group setParam */
@Since("1.6.0")
def setFeaturesCol(value: String): this.type = set(featuresCol, value)
/** @group setParam */
@Since("1.6.0")
def setLabelCol(value: String): this.type = set(labelCol, value)
/** @group setParam */
@Since("1.6.0")
def setCensorCol(value: String): this.type = set(censorCol, value)
/** @group setParam */
@Since("1.6.0")
def setPredictionCol(value: String): this.type = set(predictionCol, value)
/** @group setParam */
@Since("1.6.0")
def setQuantileProbabilities(value: Array[Double]): this.type = set(quantileProbabilities, value)
/** @group setParam */
@Since("1.6.0")
def setQuantilesCol(value: String): this.type = set(quantilesCol, value)
/**
* Set if we should fit the intercept
* Default is true.
* @group setParam
*/
@Since("1.6.0")
def setFitIntercept(value: Boolean): this.type = set(fitIntercept, value)
setDefault(fitIntercept -> true)
/**
* Set the maximum number of iterations.
* Default is 100.
* @group setParam
*/
@Since("1.6.0")
def setMaxIter(value: Int): this.type = set(maxIter, value)
setDefault(maxIter -> 100)
/**
* Set the convergence tolerance of iterations.
* Smaller value will lead to higher accuracy with the cost of more iterations.
* Default is 1E-6.
* @group setParam
*/
@Since("1.6.0")
def setTol(value: Double): this.type = set(tol, value)
setDefault(tol -> 1E-6)
/**
* Extract [[featuresCol]], [[labelCol]] and [[censorCol]] from input dataset,
* and put it in an RDD with strong types.
*/
protected[ml] def extractAFTPoints(dataset: Dataset[_]): RDD[AFTPoint] = {
dataset.select(col($(featuresCol)), col($(labelCol)).cast(DoubleType), col($(censorCol)))
.rdd.map {
case Row(features: Vector, label: Double, censor: Double) =>
AFTPoint(features, label, censor)
}
}
@Since("2.0.0")
override def fit(dataset: Dataset[_]): AFTSurvivalRegressionModel = {
transformSchema(dataset.schema, logging = true)
val instances = extractAFTPoints(dataset)
val handlePersistence = dataset.rdd.getStorageLevel == StorageLevel.NONE
if (handlePersistence) instances.persist(StorageLevel.MEMORY_AND_DISK)
val featuresSummarizer = {
val seqOp = (c: MultivariateOnlineSummarizer, v: AFTPoint) => c.add(v.features)
val combOp = (c1: MultivariateOnlineSummarizer, c2: MultivariateOnlineSummarizer) => {
c1.merge(c2)
}
instances.treeAggregate(new MultivariateOnlineSummarizer)(seqOp, combOp)
}
val featuresStd = featuresSummarizer.variance.toArray.map(math.sqrt)
val numFeatures = featuresStd.size
if (!$(fitIntercept) && (0 until numFeatures).exists { i =>
featuresStd(i) == 0.0 && featuresSummarizer.mean(i) != 0.0 }) {
logWarning("Fitting AFTSurvivalRegressionModel without intercept on dataset with " +
"constant nonzero column, Spark MLlib outputs zero coefficients for constant nonzero " +
"columns. This behavior is different from R survival::survreg.")
}
val bcFeaturesStd = instances.context.broadcast(featuresStd)
val costFun = new AFTCostFun(instances, $(fitIntercept), bcFeaturesStd)
val optimizer = new BreezeLBFGS[BDV[Double]]($(maxIter), 10, $(tol))
/*
The parameters vector has three parts:
the first element: Double, log(sigma), the log of scale parameter
the second element: Double, intercept of the beta parameter
the third to the end elements: Doubles, regression coefficients vector of the beta parameter
*/
val initialParameters = Vectors.zeros(numFeatures + 2)
val states = optimizer.iterations(new CachedDiffFunction(costFun),
initialParameters.asBreeze.toDenseVector)
val parameters = {
val arrayBuilder = mutable.ArrayBuilder.make[Double]
var state: optimizer.State = null
while (states.hasNext) {
state = states.next()
arrayBuilder += state.adjustedValue
}
if (state == null) {
val msg = s"${optimizer.getClass.getName} failed."
throw new SparkException(msg)
}
state.x.toArray.clone()
}
bcFeaturesStd.destroy(blocking = false)
if (handlePersistence) instances.unpersist()
val rawCoefficients = parameters.slice(2, parameters.length)
var i = 0
while (i < numFeatures) {
rawCoefficients(i) *= { if (featuresStd(i) != 0.0) 1.0 / featuresStd(i) else 0.0 }
i += 1
}
val coefficients = Vectors.dense(rawCoefficients)
val intercept = parameters(1)
val scale = math.exp(parameters(0))
val model = new AFTSurvivalRegressionModel(uid, coefficients, intercept, scale)
copyValues(model.setParent(this))
}
@Since("1.6.0")
override def transformSchema(schema: StructType): StructType = {
validateAndTransformSchema(schema, fitting = true)
}
@Since("1.6.0")
override def copy(extra: ParamMap): AFTSurvivalRegression = defaultCopy(extra)
}
@Since("1.6.0")
object AFTSurvivalRegression extends DefaultParamsReadable[AFTSurvivalRegression] {
@Since("1.6.0")
override def load(path: String): AFTSurvivalRegression = super.load(path)
}
/**
* :: Experimental ::
* Model produced by [[AFTSurvivalRegression]].
*/
@Experimental
@Since("1.6.0")
class AFTSurvivalRegressionModel private[ml] (
@Since("1.6.0") override val uid: String,
@Since("2.0.0") val coefficients: Vector,
@Since("1.6.0") val intercept: Double,
@Since("1.6.0") val scale: Double)
extends Model[AFTSurvivalRegressionModel] with AFTSurvivalRegressionParams with MLWritable {
/** @group setParam */
@Since("1.6.0")
def setFeaturesCol(value: String): this.type = set(featuresCol, value)
/** @group setParam */
@Since("1.6.0")
def setPredictionCol(value: String): this.type = set(predictionCol, value)
/** @group setParam */
@Since("1.6.0")
def setQuantileProbabilities(value: Array[Double]): this.type = set(quantileProbabilities, value)
/** @group setParam */
@Since("1.6.0")
def setQuantilesCol(value: String): this.type = set(quantilesCol, value)
@Since("2.0.0")
def predictQuantiles(features: Vector): Vector = {
// scale parameter for the Weibull distribution of lifetime
val lambda = math.exp(BLAS.dot(coefficients, features) + intercept)
// shape parameter for the Weibull distribution of lifetime
val k = 1 / scale
val quantiles = $(quantileProbabilities).map {
q => lambda * math.exp(math.log(-math.log(1 - q)) / k)
}
Vectors.dense(quantiles)
}
@Since("2.0.0")
def predict(features: Vector): Double = {
math.exp(BLAS.dot(coefficients, features) + intercept)
}
@Since("2.0.0")
override def transform(dataset: Dataset[_]): DataFrame = {
transformSchema(dataset.schema, logging = true)
val predictUDF = udf { features: Vector => predict(features) }
val predictQuantilesUDF = udf { features: Vector => predictQuantiles(features)}
if (hasQuantilesCol) {
dataset.withColumn($(predictionCol), predictUDF(col($(featuresCol))))
.withColumn($(quantilesCol), predictQuantilesUDF(col($(featuresCol))))
} else {
dataset.withColumn($(predictionCol), predictUDF(col($(featuresCol))))
}
}
@Since("1.6.0")
override def transformSchema(schema: StructType): StructType = {
validateAndTransformSchema(schema, fitting = false)
}
@Since("1.6.0")
override def copy(extra: ParamMap): AFTSurvivalRegressionModel = {
copyValues(new AFTSurvivalRegressionModel(uid, coefficients, intercept, scale), extra)
.setParent(parent)
}
@Since("1.6.0")
override def write: MLWriter =
new AFTSurvivalRegressionModel.AFTSurvivalRegressionModelWriter(this)
}
@Since("1.6.0")
object AFTSurvivalRegressionModel extends MLReadable[AFTSurvivalRegressionModel] {
@Since("1.6.0")
override def read: MLReader[AFTSurvivalRegressionModel] = new AFTSurvivalRegressionModelReader
@Since("1.6.0")
override def load(path: String): AFTSurvivalRegressionModel = super.load(path)
/** [[MLWriter]] instance for [[AFTSurvivalRegressionModel]] */
private[AFTSurvivalRegressionModel] class AFTSurvivalRegressionModelWriter (
instance: AFTSurvivalRegressionModel
) extends MLWriter with Logging {
private case class Data(coefficients: Vector, intercept: Double, scale: Double)
override protected def saveImpl(path: String): Unit = {
// Save metadata and Params
DefaultParamsWriter.saveMetadata(instance, path, sc)
// Save model data: coefficients, intercept, scale
val data = Data(instance.coefficients, instance.intercept, instance.scale)
val dataPath = new Path(path, "data").toString
sparkSession.createDataFrame(Seq(data)).repartition(1).write.parquet(dataPath)
}
}
private class AFTSurvivalRegressionModelReader extends MLReader[AFTSurvivalRegressionModel] {
/** Checked against metadata when loading model */
private val className = classOf[AFTSurvivalRegressionModel].getName
override def load(path: String): AFTSurvivalRegressionModel = {
val metadata = DefaultParamsReader.loadMetadata(path, sc, className)
val dataPath = new Path(path, "data").toString
val data = sparkSession.read.parquet(dataPath)
val Row(coefficients: Vector, intercept: Double, scale: Double) =
MLUtils.convertVectorColumnsToML(data, "coefficients")
.select("coefficients", "intercept", "scale")
.head()
val model = new AFTSurvivalRegressionModel(metadata.uid, coefficients, intercept, scale)
DefaultParamsReader.getAndSetParams(model, metadata)
model
}
}
}
/**
* AFTAggregator computes the gradient and loss for a AFT loss function,
* as used in AFT survival regression for samples in sparse or dense vector in an online fashion.
*
* The loss function and likelihood function under the AFT model based on:
* Lawless, J. F., Statistical Models and Methods for Lifetime Data,
* New York: John Wiley & Sons, Inc. 2003.
*
* Two AFTAggregator can be merged together to have a summary of loss and gradient of
* the corresponding joint dataset.
*
* Given the values of the covariates $x^{'}$, for random lifetime $t_{i}$ of subjects i = 1,..,n,
* with possible right-censoring, the likelihood function under the AFT model is given as
*
* <p><blockquote>
* $$
* L(\beta,\sigma)=\prod_{i=1}^n[\frac{1}{\sigma}f_{0}
* (\frac{\log{t_{i}}-x^{'}\beta}{\sigma})]^{\delta_{i}}S_{0}
* (\frac{\log{t_{i}}-x^{'}\beta}{\sigma})^{1-\delta_{i}}
* $$
* </blockquote></p>
*
* Where $\delta_{i}$ is the indicator of the event has occurred i.e. uncensored or not.
* Using $\epsilon_{i}=\frac{\log{t_{i}}-x^{'}\beta}{\sigma}$, the log-likelihood function
* assumes the form
*
* <p><blockquote>
* $$
* \iota(\beta,\sigma)=\sum_{i=1}^{n}[-\delta_{i}\log\sigma+
* \delta_{i}\log{f_{0}}(\epsilon_{i})+(1-\delta_{i})\log{S_{0}(\epsilon_{i})}]
* $$
* </blockquote></p>
* Where $S_{0}(\epsilon_{i})$ is the baseline survivor function,
* and $f_{0}(\epsilon_{i})$ is corresponding density function.
*
* The most commonly used log-linear survival regression method is based on the Weibull
* distribution of the survival time. The Weibull distribution for lifetime corresponding
* to extreme value distribution for log of the lifetime,
* and the $S_{0}(\epsilon)$ function is
*
* <p><blockquote>
* $$
* S_{0}(\epsilon_{i})=\exp(-e^{\epsilon_{i}})
* $$
* </blockquote></p>
*
* and the $f_{0}(\epsilon_{i})$ function is
*
* <p><blockquote>
* $$
* f_{0}(\epsilon_{i})=e^{\epsilon_{i}}\exp(-e^{\epsilon_{i}})
* $$
* </blockquote></p>
*
* The log-likelihood function for Weibull distribution of lifetime is
*
* <p><blockquote>
* $$
* \iota(\beta,\sigma)=
* -\sum_{i=1}^n[\delta_{i}\log\sigma-\delta_{i}\epsilon_{i}+e^{\epsilon_{i}}]
* $$
* </blockquote></p>
*
* Due to minimizing the negative log-likelihood equivalent to maximum a posteriori probability,
* the loss function we use to optimize is $-\iota(\beta,\sigma)$.
* The gradient functions for $\beta$ and $\log\sigma$ respectively are
*
* <p><blockquote>
* $$
* \frac{\partial (-\iota)}{\partial \beta}=
* \sum_{1=1}^{n}[\delta_{i}-e^{\epsilon_{i}}]\frac{x_{i}}{\sigma} \\
*
* \frac{\partial (-\iota)}{\partial (\log\sigma)}=
* \sum_{i=1}^{n}[\delta_{i}+(\delta_{i}-e^{\epsilon_{i}})\epsilon_{i}]
* $$
* </blockquote></p>
*
* @param bcParameters The broadcasted value includes three part: The log of scale parameter,
* the intercept and regression coefficients corresponding to the features.
* @param fitIntercept Whether to fit an intercept term.
* @param bcFeaturesStd The broadcast standard deviation values of the features.
*/
private class AFTAggregator(
bcParameters: Broadcast[BDV[Double]],
fitIntercept: Boolean,
bcFeaturesStd: Broadcast[Array[Double]]) extends Serializable {
private val length = bcParameters.value.length
// make transient so we do not serialize between aggregation stages
@transient private lazy val parameters = bcParameters.value
// the regression coefficients to the covariates
@transient private lazy val coefficients = parameters.slice(2, length)
@transient private lazy val intercept = parameters(1)
// sigma is the scale parameter of the AFT model
@transient private lazy val sigma = math.exp(parameters(0))
private var totalCnt: Long = 0L
private var lossSum = 0.0
// Here we optimize loss function over log(sigma), intercept and coefficients
private val gradientSumArray = Array.ofDim[Double](length)
def count: Long = totalCnt
def loss: Double = {
require(totalCnt > 0.0, s"The number of instances should be " +
s"greater than 0.0, but got $totalCnt.")
lossSum / totalCnt
}
def gradient: BDV[Double] = {
require(totalCnt > 0.0, s"The number of instances should be " +
s"greater than 0.0, but got $totalCnt.")
new BDV(gradientSumArray.map(_ / totalCnt.toDouble))
}
/**
* Add a new training data to this AFTAggregator, and update the loss and gradient
* of the objective function.
*
* @param data The AFTPoint representation for one data point to be added into this aggregator.
* @return This AFTAggregator object.
*/
def add(data: AFTPoint): this.type = {
val xi = data.features
val ti = data.label
val delta = data.censor
val localFeaturesStd = bcFeaturesStd.value
val margin = {
var sum = 0.0
xi.foreachActive { (index, value) =>
if (localFeaturesStd(index) != 0.0 && value != 0.0) {
sum += coefficients(index) * (value / localFeaturesStd(index))
}
}
sum + intercept
}
val epsilon = (math.log(ti) - margin) / sigma
lossSum += delta * math.log(sigma) - delta * epsilon + math.exp(epsilon)
val multiplier = (delta - math.exp(epsilon)) / sigma
gradientSumArray(0) += delta + multiplier * sigma * epsilon
gradientSumArray(1) += { if (fitIntercept) multiplier else 0.0 }
xi.foreachActive { (index, value) =>
if (localFeaturesStd(index) != 0.0 && value != 0.0) {
gradientSumArray(index + 2) += multiplier * (value / localFeaturesStd(index))
}
}
totalCnt += 1
this
}
/**
* Merge another AFTAggregator, and update the loss and gradient
* of the objective function.
* (Note that it's in place merging; as a result, `this` object will be modified.)
*
* @param other The other AFTAggregator to be merged.
* @return This AFTAggregator object.
*/
def merge(other: AFTAggregator): this.type = {
if (other.count != 0) {
totalCnt += other.totalCnt
lossSum += other.lossSum
var i = 0
while (i < length) {
this.gradientSumArray(i) += other.gradientSumArray(i)
i += 1
}
}
this
}
}
/**
* AFTCostFun implements Breeze's DiffFunction[T] for AFT cost.
* It returns the loss and gradient at a particular point (parameters).
* It's used in Breeze's convex optimization routines.
*/
private class AFTCostFun(
data: RDD[AFTPoint],
fitIntercept: Boolean,
bcFeaturesStd: Broadcast[Array[Double]]) extends DiffFunction[BDV[Double]] {
override def calculate(parameters: BDV[Double]): (Double, BDV[Double]) = {
val bcParameters = data.context.broadcast(parameters)
val aftAggregator = data.treeAggregate(
new AFTAggregator(bcParameters, fitIntercept, bcFeaturesStd))(
seqOp = (c, v) => (c, v) match {
case (aggregator, instance) => aggregator.add(instance)
},
combOp = (c1, c2) => (c1, c2) match {
case (aggregator1, aggregator2) => aggregator1.merge(aggregator2)
})
bcParameters.destroy(blocking = false)
(aftAggregator.loss, aftAggregator.gradient)
}
}
/**
* Class that represents the (features, label, censor) of a data point.
*
* @param features List of features for this data point.
* @param label Label for this data point.
* @param censor Indicator of the event has occurred or not. If the value is 1, it means
* the event has occurred i.e. uncensored; otherwise censored.
*/
private[regression] case class AFTPoint(features: Vector, label: Double, censor: Double) {
require(censor == 1.0 || censor == 0.0, "censor of class AFTPoint must be 1.0 or 0.0")
}
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