本章节介绍了分类和回归的算法。它还包括讨论特定类别的算法部分，如：线性方法，树和集成。

下面是整个API Doc中的内容框架，这里不会每个都详细介绍，主要会把用到的介绍出来，后续用到的再陆续添加。(下面的链接都是指向官网文档而不是本笔记中的对应内容所在位置，而且有些内容没有出现在本笔记中)

逻辑回归

逻辑回归是预测分类问题的流行算法。它是 广义线性模型的一个特例来预测结果的可能性。 在spark.ml逻辑回归中可以使用二项式Logistic回归来预测二分类问题，也可以通过使用多项Logistic回归来预测多分类问题。 使用family参数在这两种算法之间进行选择，或者不设置它，让Spark自己推断出正确的值。

通过将family参数设置为“多项式”，也可以将多项Logistic回归用于二分类问题。它将产生两个系数的集合和两个intercept。

当在没有intercept的常量非零列的数据集上对LogisticRegressionModel进行拟合时，Spark MLlib为常数非零列输出零系数。此行为与R glmnet相同，但与LIBSVM不同。

二分类逻辑回归

有关二项式逻辑回归实现的更多背景和更多细节，请参阅spark.mllib中逻辑回归的文档。

代码示例：

以下示例显示了如何用elastic net regularization来训练的二项式和多项Logistic的回归模型用于二分类问题。 elasticNetParam对应于α，regParam对应于λ。

public class JavaLogisticRegressionWithElasticNetExample {

public static void main(String[] args) {

SparkSession spark = SparkSession

.builder()

.appName("JavaLogisticRegressionWithElasticNetExample")

.getOrCreate();

// $example on$

// Load training data

Dataset training = spark.read().format("libsvm")

.load("/home/paul/spark/spark-2.1.0-bin-hadoop2.7/data/mllib/sample_libsvm_data.txt");

LogisticRegression lr = new LogisticRegression()

.setMaxIter(10)

.setRegParam(0.3)

.setElasticNetParam(0.8);

// Fit the model

LogisticRegressionModel lrModel = lr.fit(training);

// Print the coefficients and intercept for logistic regression

System.out.println("\n---------- Binomial logistic regression's Coefficients: "

+ lrModel.coefficients() + "\nBinomial Intercept: " + lrModel.intercept());

// We can also use the multinomial family for binary classification

LogisticRegression mlr = new LogisticRegression()

.setMaxIter(10)

.setRegParam(0.3)

.setElasticNetParam(0.8)

.setFamily("multinomial");

// Fit the model

LogisticRegressionModel mlrModel = mlr.fit(training);

// Print the coefficients and intercepts for logistic regression with multinomial family

System.out.println("\n+++++++++ Multinomial coefficients: " + mlrModel.coefficientMatrix()

+ "\nMultinomial intercepts: " + mlrModel.interceptVector());

// $example off$

spark.stop();

}

}

上面代码运行结果，二项式的系数是按照稀疏矩阵格式打印的，多项式的是按照矩阵的格式打印

spark.ml实现的逻辑回归算法也支持提取出训练集上训练后模型的摘要(这有助于分析模型在训练集上的性能)。 需要注意的是预测结果和权值在BinaryLogisticRegressionSummary中被存储为DataFrame类型并且被标注为@transient，所以只能在driver上可用。

LogisticRegressionTrainingSummary是提供给LogisticRegressionModel的摘要。目前只有二分类模型有这个功能，而且必须被显式的强转成类型BinaryLogisticRegressionTrainingSummary。对于多分类模型的摘要的支持将在后续版本中实现。

Java版代码：

public class JavaLogisticRegressionSummaryExample {

public static void main(String[] args) {

SparkSession spark = SparkSession

.builder()

.appName("JavaLogisticRegressionSummaryExample")

.getOrCreate();

// Load training data

Dataset training = spark.read().format("libsvm")

.load("/home/paul/spark/spark-2.1.0-bin-hadoop2.7/data/mllib/sample_libsvm_data.txt");

LogisticRegression lr = new LogisticRegression()

.setMaxIter(10)

.setRegParam(0.3)

.setElasticNetParam(0.8);

// Fit the model

LogisticRegressionModel lrModel = lr.fit(training);

// $example on$

// Extract the summary from the returned LogisticRegressionModel instance trained in the earlier

// example

LogisticRegressionTrainingSummary trainingSummary = lrModel.summary();

// Obtain the loss per iteration.

double[] objectiveHistory = trainingSummary.objectiveHistory();

for (double lossPerIteration : objectiveHistory) {

System.out.println(lossPerIteration);

}

// Obtain the metrics useful to judge performance on test data.

// We cast the summary to a BinaryLogisticRegressionSummary since the problem is a binary

// classification problem.

BinaryLogisticRegressionSummary binarySummary =

(BinaryLogisticRegressionSummary) trainingSummary;

// Obtain the receiver-operating characteristic as a dataframe and areaUnderROC.

Dataset roc = binarySummary.roc();

roc.show();

roc.select("FPR").show();

System.out.println(binarySummary.areaUnderROC());

// Get the threshold corresponding to the maximum F-Measure and rerun LogisticRegression with

// this selected threshold.

Dataset fMeasure = binarySummary.fMeasureByThreshold();

double maxFMeasure = fMeasure.select(functions.max("F-Measure")).head().getDouble(0);

double bestThreshold = fMeasure.where(fMeasure.col("F-Measure").equalTo(maxFMeasure))

.select("threshold").head().getDouble(0);

lrModel.setThreshold(bestThreshold);

// $example off$

spark.stop();

}

}

运行结果为：

0.6833149135741672

0.6662875751473734

0.6217068546034618

0.6127265245887887

0.6060347986802873

0.6031750687571562

0.5969621534836274

0.5940743031983118

0.5906089243339022

0.5894724576491042

0.5882187775729587

17/05/02 22:46:21 WARN Executor: 1 block locks were not released by TID = 25:

[rdd_39_0]

+---+--------------------+

|FPR| TPR|

+---+--------------------+

|0.0| 0.0|

|0.0|0.017543859649122806|

|0.0| 0.03508771929824561|

|0.0| 0.05263157894736842|

|0.0| 0.07017543859649122|

|0.0| 0.08771929824561403|

|0.0| 0.10526315789473684|

|0.0| 0.12280701754385964|

|0.0| 0.14035087719298245|

|0.0| 0.15789473684210525|

|0.0| 0.17543859649122806|

|0.0| 0.19298245614035087|

|0.0| 0.21052631578947367|

|0.0| 0.22807017543859648|

|0.0| 0.24561403508771928|

|0.0| 0.2631578947368421|

|0.0| 0.2807017543859649|

|0.0| 0.2982456140350877|

|0.0| 0.3157894736842105|

|0.0| 0.3333333333333333|

+---+--------------------+

only showing top 20 rows

17/05/02 22:46:22 WARN Executor: 1 block locks were not released by TID = 27:

[rdd_39_0]

+---+

|FPR|

+---+

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

|0.0|

+---+

only showing top 20 rows

1.0