Logistic Regression-Machine Learning and Artificial Intelligence-Lecture Slides, Slides of Machine Learning

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Logis&c

Regression

Classifica&on

Machine Learning

Classifica(on Email: Spam / Not Spam? Online Transac&ons: Fraudulent (Yes / No)? Tumor: Malignant / Benign? 0: “Nega&ve Class” (e.g., benign tumor) 1: “Posi&ve Class” (e.g., malignant tumor)

Classifica&on: y = 0 or 1

can be > 1 or < 0

Logis&c Regression:

Logis&c Regression Hypothesis Representa&on Machine Learning

Interpreta(on of Hypothesis Output = es&mated probability that y = 1 on input x Tell pa&ent that 70% chance of tumor being malignant Example: If “probability that y = 1, given x, parameterized by ”

Logis&c Regression Decision boundary Machine Learning

x 1 x 2 Decision Boundary 1 2 3 1 2 3

Predict “ “ if

Non-­‐linear decision boundaries x 1 x 2

Predict “ “ if

x 1 x 2 -­‐1^1 -­‐ 1

Training

set:

How to choose parameters?

m examples

Cost func(on Linear regression: “non-­‐convex” “convex”

Logis(c regression cost func(on If y = 0 (^01)

Logis&c Regression Simplified cost func&on and gradient descent Machine Learning

Output Logis(c regression cost func(on To fit parameters : To make a predic&on given new :

Gradient Descent Want : Repeat (simultaneously update all )