Linear classifiers: prediction equations

Klasifikator Linear di Python

Michael (Mike) Gelbart

Instructor, The University of British Columbia

Dot Products

x = np.arange(3)
x

array([0, 1, 2])

y = np.arange(3,6)
y

array([3, 4, 5])

x*y

array([0, 4, 10])

np.sum(x*y)

14

x@y

14
  • x@y is called the dot product of x and y, and is written $x \cdot y$.
Klasifikator Linear di Python

Linear classifier prediction

  • $\textrm{raw model output} = \textrm{coefficients} \cdot \textrm{features} + \textrm{intercept}$
  • Linear classifier prediction: compute raw model output, check the sign
    • if positive, predict one class
    • if negative, predict the other class
  • This is the same for logistic regression and linear SVM
    • fit is different but predict is the same
Klasifikator Linear di Python

How LogisticRegression makes predictions

$\textrm{raw model output} = \textrm{coefficients} \cdot \textrm{features} + \textrm{intercept}$

lr = LogisticRegression()

lr.fit(X,y)

lr.predict(X)[10]

0

lr.predict(X)[20]

1
Klasifikator Linear di Python

How LogisticRegression makes predictions (cont.)

lr.coef_ @ X[10] + lr.intercept_ # raw model output

array([-33.78572166])

lr.coef_ @ X[20] + lr.intercept_ # raw model output

array([ 0.08050621])
Klasifikator Linear di Python

The raw model output

Klasifikator Linear di Python

The raw model output

Klasifikator Linear di Python

The raw model output

Klasifikator Linear di Python

Let's practice!

Klasifikator Linear di Python

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