- [[linear classifiers]], [[dot product]], [[loss function]], [[Python]] # Idea The [[dot product]] is used to express how [[linear classifiers]] make predictions. Step 1: $prediction = coefficients \cdot features + intercept$ Step 2: If $prediction \geq 0$, predict one class; if $prediction < 0$, predict the other class. These steps are the same for [[logistic regression]] and [[linear support vector machines]]—these two models are fitted differently (i.e., they have different fit functions) but they use the same prediction function. Example logistic regression in [[scikit-learn]]: ```python lr = LogisticRegression() lr.fit(X, y) lr.predict(X)[0] # same as lines below lr.coef_ @ X[0] + lr.intercept_ # raw model prediction/output (lr.coef_ @ X[0] + lr.intercept_) >= 0 # same as 2 lines above ``` # References - https://campus.datacamp.com/courses/linear-classifiers-in-python/loss-functions?ex=1 - https://campus.datacamp.com/courses/linear-classifiers-in-python/loss-functions?ex=3 # Figures - https://campus.datacamp.com/courses/linear-classifiers-in-python/loss-functions?ex=1 ![[Pasted image 44.png]] ![[Pasted image 45.png]] ![[Pasted image 46.png]]