Post on 18-Jan-2016
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Logistic Regression (Classification Algorithm)
Classification Problem
• Email: Spam/Not Spam?• Online Transactions: Fraudulent (Yes/No)?• Tumor: Malignant/Benign
Classification Problem
• Email: Spam/Not Spam?• Online Transactions: Fraudulent (Yes/No)?• Tumor: Malignant/Benign
Prediction Task:
Classification Problem
• Email: Spam/Not Spam?• Online Transactions: Fraudulent (Yes/No)?• Tumor: Malignant/Benign
Prediction Task:
This is an example of Binary Classification task. A generalized case of classification task in Multi-class Classification
Applying Linear Regression
Applying Linear Regression
hθ(x)
Applying Linear Regression
hθ(x)
Problem in Applying Linear Regression
Yes(1)
No(0)Tumor Size
Problem in Applying Linear Regression
Yes(1)
No(0)Tumor Size
Problem in Applying Linear Regression
Yes(1)
No(0)Tumor Size
Problem in Applying Linear Regression
Yes(1)
No(0)
Benign if tumor size lies in this range
Malignantif tumor size lies in this range
Tumor Size
Problem in Applying Linear Regression
Hypothesis Representation
hθ(x) = θTx
Hypothesis Representation
Sigmoid functionLogistic function
z
g(z)
Interpretation of Hypothesis Output
hθ(x) = P(y=1|x;θ)
Interpretation of Hypothesis Output
Interpretation of Hypothesis Output
z
g(z)
Decision Boundary
Decision Boundary
Decision Boundary
Decision Boundary
Decision Boundary
Decision Boundary
Learning Task
Cost Function
Cost Function
Logistic Regression Cost Function
Logistic Regression Cost Function
Logistic Regression Cost Function
Logistic Regression Cost Function
Logistic Regression Cost Function
Logistic Regression Cost Function
Logistic Regression Cost Function
Logistic Regression Cost Function
Gradient Descent
Gradient Descent
Gradient Descent
Algorithm looks identical to linear regression
Multi-class Classification: One-vs-All Algorithm
Binary vs Multi-class Classification Problem
One-vs-All (one-vs-rest)
One-vs-All (one-vs-rest)
One-vs-All (one-vs-rest)
One-vs-All (one-vs-rest)
One-vs-All Algorithm