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From "GAURAV BHATIA (JIRA)" <j...@apache.org>
Subject [jira] [Created] (SPARK-26883) Spark MLIB Logistic Regression with heavy class imbalance estimates 0 coefficients
Date Fri, 15 Feb 2019 02:43:00 GMT
```GAURAV BHATIA created SPARK-26883:
-------------------------------------

Summary: Spark MLIB Logistic Regression with heavy class imbalance estimates
0 coefficients
Key: SPARK-26883
URL: https://issues.apache.org/jira/browse/SPARK-26883
Project: Spark
Issue Type: Bug
Components: MLlib
Affects Versions: 2.3.2
Reporter: GAURAV BHATIA

Minimal example is below.

Basically, when the frequency of positives becomes low, the coefficients out of spark.ml.classification.LogisticRegression
become 0, deviating from the corresponding sklearn results.

I have not been able to find any parameter setting or documentation that describes why this
happens or how I can alter the behavior.

I'd appreciate any help in debugging. Thanks in advance!

Here, we set up the code to create the two sample scenarios. In both cases a binary outcome
is fit to a single binary predictor using logistic regression. The effect of the binary predictor
is to approximately 10x the probability of a positive (1) outcome. The only difference between
the "common" and "rare" cases is the base frequency of the positive outcome. In the "common"
case it is 0.01, in the "rare" case it is 1e-4.

{code:java}

import pandas as pd
import numpy as np
import math

def sampleLogistic(p0, p1, p1prev,size):
intercept = -1*math.log(1/p0 - 1)
coefficient = -1*math.log(1/p1 - 1) - intercept

x = np.random.choice([0, 1], size=(size,), p=[1 - p1prev, p1prev])
freq= 1/(1 + np.exp(-1*(intercept + coefficient*x)))
y = (np.random.uniform(size=size) < freq).astype(int)
df = pd.DataFrame({'x':x, 'y':y})
return(df)

df_common = sampleLogistic(0.01,0.1,0.1,100000)
df_rare = sampleLogistic(0.0001,0.001,0.1,100000){code}

Using sklearn:

{code:java}
from sklearn.linear_model import LogisticRegression

l = 0.3
skmodel = LogisticRegression(
fit_intercept=True,
penalty='l2',
C=1/l,
max_iter=100,
tol=1e-11,
solver='lbfgs',verbose=1)

skmodel.fit(df_common[['x']], df_common.y)
print(skmodel.coef_, skmodel.intercept_)
skmodel.fit(df_rare[['x']], df_rare.y)
print(skmodel.coef_, skmodel.intercept_)
{code}
In one run of the simulation, this prints:

{noformat}
[[ 2.39497867]] [-4.58143701] # the common case
[[ 1.84918485]] [-9.05090438] # the rare case{noformat}
Now, using PySpark for the common case:

{code:java}
from pyspark.ml.classification import LogisticRegression
from pyspark.ml.feature import VectorAssembler

n = len(df_common.index)
sdf_common = spark.createDataFrame(df_common)
assembler = VectorAssembler(inputCols=['x'], outputCol="features")
sdf_common = assembler.transform(sdf_common)

# Make regularization 0.3/10=0.03
lr = LogisticRegression(regParam=l/n,labelCol='y',featuresCol='features',tol=1e-11/n,maxIter=100,standardization=False)
model = lr.fit(sdf_common)
print(model.coefficients, model.intercept)
{code}

This prints:

{code:java}
[2.39497214622] -4.5814342575166505 # nearly identical to the common case above
{code}
Pyspark for the rare case:

{code:java}
n = len(df_rare.index)
sdf_rare = spark.createDataFrame(df_rare)
assembler = VectorAssembler(inputCols=['x'], outputCol="features")
sdf_rare = assembler.transform(sdf_rare)

# Make regularization 0.3/10=0.03
lr = LogisticRegression(regParam=l/n,labelCol='y',featuresCol='features',tol=1e-11/n,maxIter=100,standardization=False)
model = lr.fit(sdf_rare)
print(model.coefficients,model.intercept)
{code}
This prints:

{noformat}
[0.0] -8.62237369087212 # where does the 0 come from??
{noformat}

To verify that the data frames have the properties that we discussed:
{code:java}
sdf_common.describe().show()

+-------+------------------+------------------+
|summary|                 x|                 y|
+-------+------------------+------------------+
|  count|            100000|            100000|
|   mean|           0.10055|           0.01927|
| stddev|0.3007334399530905|0.1374731104200414|
|    min|                 0|                 0|
|    max|                 1|                 1|
+-------+------------------+------------------+

sdf_rare.describe().show()

+-------+------------------+--------------------+
|summary|                 x|                   y|
+-------+------------------+--------------------+
|  count|            100000|              100000|
|   mean|           0.09997|              1.8E-4|
| stddev|0.2999614956440055|0.013415267410454295|
|    min|                 0|                   0|
|    max|                 1|                   1|
+-------+------------------+--------------------+

{code}

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