逻辑回归模型原始预测领域背后的 pyspark 2.2.0 概念

Question

我试图理解 Pyspark 中逻辑回归模型生成的输出的概念。

谁能解释一下从逻辑回归模型生成的 rawPrediction 字段计算背后的概念？谢谢

Answer 1

在老版本的Sparkjavadocs中（例如1.5.x），曾有如下解释：

The meaning of a "raw" prediction may vary between algorithms, but it intuitively gives a measure of confidence in each possible label (where larger = more confident).

在以后的版本中没有了，但是在Scala中还是可以找到的source code。

无论如何，撇开任何不幸的措辞不谈，Spark ML 中的 rawPrecictions 对于逻辑回归案例，就是世界其他地方所说的 logits, i.e. the raw output of a logistic regression classifier, which is subsequently transformed into a probability score using the logistic function exp(x)/(1+exp(x)).

这是玩具数据的示例：

spark.version
# u'2.2.0'

from pyspark.ml.classification import LogisticRegression
from pyspark.ml.linalg import Vectors
from pyspark.sql import Row
df = sqlContext.createDataFrame([
     (0.0, Vectors.dense(0.0, 1.0)),
     (1.0, Vectors.dense(1.0, 0.0))], 
     ["label", "features"])
df.show()
# +-----+---------+
# |label| features|
# +-----+---------+
# |  0.0|[0.0,1.0]|
# |  1.0|[1.0,0.0]|
# +-----+---------+

lr = LogisticRegression(maxIter=5, regParam=0.01, labelCol="label")
lr_model = lr.fit(df)

test = sc.parallelize([Row(features=Vectors.dense(0.2, 0.5)),
                       Row(features=Vectors.dense(0.5, 0.2))]).toDF()
lr_result = lr_model.transform(test)
lr_result.show(truncate=False)

结果如下：

+---------+----------------------------------------+----------------------------------------+----------+ 
|features |                          rawPrediction |                            probability |prediction|
+---------+----------------------------------------+----------------------------------------+----------+ 
|[0.2,0.5]|[0.9894187891647654,-0.9894187891647654]|[0.7289731070426124,0.27102689295738763]|      0.0 |
|[0.5,0.2]|[-0.9894187891647683,0.9894187891647683]|[0.2710268929573871,0.728973107042613]  |      1.0 | 
+---------+----------------------------------------+----------------------------------------+----------+

现在让我们确认 rawPrediction 的逻辑函数给出 probability 列：

import numpy as np

x1 = np.array([0.9894187891647654,-0.9894187891647654])
np.exp(x1)/(1+np.exp(x1))
# array([ 0.72897311, 0.27102689])

x2 = np.array([-0.9894187891647683,0.9894187891647683])
np.exp(x2)/(1+np.exp(x2))
# array([ 0.27102689, 0.72897311])

即确实如此

因此，总结所有三 (3) 个输出列：

rawPrediction是逻辑回归分类器的原始输出（长度等于类个数的数组）
probability是对rawPrediction（长度等于rawPrediction的数组）应用logistic函数的结果
prediction是数组probability取最大值的参数，给出最可能的标签（单数）

逻辑回归模型原始预测领域背后的 pyspark 2.2.0 概念

pyspark 2.2.0 concept behind raw predictions field of logistic regression model

machine-learning

logistic-regression

pyspark

apache-spark-ml