Logistic Regression

Machine Learning with PySpark

Andrew Collier

Data Scientist, Fathom Data

Logistic Curve

A logistic curve.

Machine Learning with PySpark

Logistic Curve

A logistic curve with shading above threshold

Machine Learning with PySpark

Logistic Curve

A logistic curve with shading below threshold

Machine Learning with PySpark

Logistic Curve

A logistic curve shifted to the right

Machine Learning with PySpark

Logistic Curve

A logistic curve shifted to the left

Machine Learning with PySpark

Logistic Curve

A logistic curve with gradual transition

Machine Learning with PySpark

Logistic Curve

A logistic curve with rapid transition

Machine Learning with PySpark

Cars revisited

Prepare for modeling:

  • assemble the predictors into a single column (called features) and
  • split data into training and testing sets.
+---+----+------+------+----+-----------+----------------------------------+-----+
|cyl|size|mass  |length|rpm |consumption|features                          |label|
+---+----+------+------+----+-----------+----------------------------------+-----+
|6  |3.0 |1451.0|4.775 |5200|9.05       |[6.0,3.0,1451.0,4.775,5200.0,9.05]|1.0  |
|4  |2.2 |1129.0|4.623 |5200|6.53       |[4.0,2.2,1129.0,4.623,5200.0,6.53]|0.0  |
|4  |2.2 |1399.0|4.547 |5600|7.84       |[4.0,2.2,1399.0,4.547,5600.0,7.84]|1.0  |
|4  |1.8 |1147.0|4.343 |6500|7.84       |[4.0,1.8,1147.0,4.343,6500.0,7.84]|0.0  |
|4  |1.6 |1111.0|4.216 |5750|9.05       |[4.0,1.6,1111.0,4.216,5750.0,9.05]|0.0  |
+---+----+------+------+----+-----------+----------------------------------+-----+
Machine Learning with PySpark

Build a Logistic Regression model

from pyspark.ml.classification import LogisticRegression

Create a Logistic Regression classifier.

logistic = LogisticRegression()

Learn from the training data.

logistic = logistic.fit(cars_train)
Machine Learning with PySpark

Predictions

prediction = logistic.transform(cars_test)

+-----+----------+---------------------------------------+
|label|prediction|probability                            |
+-----+----------+---------------------------------------+
|0.0  |0.0       |[0.8683802216422138,0.1316197783577862]|
|0.0  |1.0       |[0.1343792056399585,0.8656207943600416]|
|0.0  |0.0       |[0.9773546766387631,0.0226453233612368]|
|1.0  |1.0       |[0.0170508265586195,0.9829491734413806]|
|1.0  |0.0       |[0.6122241729292978,0.3877758270707023]|
+-----+----------+---------------------------------------+
Machine Learning with PySpark

Precision and recall

How well does model work on testing data?

Consult the confusion matrix.

+-----+----------+-----+
|label|prediction|count|
+-----+----------+-----+
|  1.0|       1.0|    8| - TP (true positive)
|  0.0|       1.0|    4| - FP (false positive)
|  1.0|       0.0|    2| - FN (false negative)
|  0.0|       0.0|   10| - TN (true negative)
+-----+----------+-----+

# Precision (positive)
TP / (TP + FP)

0.6666666666666666

# Recall (positive)
TP / (TP + FN)

0.8
Machine Learning with PySpark

Weighted metrics

from pyspark.ml.evaluation import MulticlassClassificationEvaluator

evaluator = MulticlassClassificationEvaluator()

evaluator.evaluate(prediction, {evaluator.metricName: 'weightedPrecision'})

0.7638888888888888

Other metrics:

  • weightedRecall
  • accuracy
  • f1
Machine Learning with PySpark

ROC and AUC

A ROC curve

ROC = "Receiver Operating Characteristic"

  • TP versus FP
  • threshold = 0 (top right)
  • threshold = 1 (bottom left)

AUC = "Area under the curve"

  • ideally AUC = 1
Machine Learning with PySpark

Let's do Logistic Regression!

Machine Learning with PySpark

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