Multi-class logistic regression

Linear Classifiers in Python

Michael (Mike) Gelbart

Instructor, The University of British Columbia

Combining binary classifiers with one-vs-rest

lr0.fit(X, y==0)

lr1.fit(X, y==1)

lr2.fit(X, y==2)

# get raw model output
lr0.decision_function(X)[0]

6.124

lr1.decision_function(X)[0]

-5.429

lr2.decision_function(X)[0]

-7.532

lr = LogisticRegression(multi_class='ovr')
lr.fit(X, y)

lr.predict(X)[0]

0
Linear Classifiers in Python

One-vs-rest:

  • fit a binary classifier for each class
  • predict with all, take largest output
  • pro: simple, modular
  • con: not directly optimizing accuracy
  • common for SVMs as well
  • can produce probabilities

"Multinomial" or "softmax":

  • fit a single classifier for all classes
  • prediction directly outputs best class
  • con: more complicated, new code
  • pro: tackle the problem directly
  • possible for SVMs, but less common
  • can produce probabilities
Linear Classifiers in Python

Model coefficients for multi-class

lr_ovr = LogisticRegression(multi_class='ovr') 

lr_ovr.fit(X,y)

lr_ovr.coef_.shape

(3,13)

lr_ovr.intercept_.shape

(3,)

lr_mn = LogisticRegression(multi_class="multinomial")
lr_mn.fit(X,y)

lr_mn.coef_.shape

(3,13)

lr_mn.intercept_.shape

(3,)
Linear Classifiers in Python

Let's practice!

Linear Classifiers in Python

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