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Logistic Regression (Classification Algorithm)
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Classification Problem
• Email: Spam/Not Spam?• Online Transactions: Fraudulent (Yes/No)?• Tumor: Malignant/Benign
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Classification Problem
• Email: Spam/Not Spam?• Online Transactions: Fraudulent (Yes/No)?• Tumor: Malignant/Benign
Prediction Task:
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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
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Applying Linear Regression
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Applying Linear Regression
hθ(x)
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Applying Linear Regression
hθ(x)
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Problem in Applying Linear Regression
Yes(1)
No(0)Tumor Size
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Problem in Applying Linear Regression
Yes(1)
No(0)Tumor Size
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Problem in Applying Linear Regression
Yes(1)
No(0)Tumor Size
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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
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Problem in Applying Linear Regression
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Hypothesis Representation
hθ(x) = θTx
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Hypothesis Representation
Sigmoid functionLogistic function
z
g(z)
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Interpretation of Hypothesis Output
hθ(x) = P(y=1|x;θ)
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Interpretation of Hypothesis Output
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Interpretation of Hypothesis Output
z
g(z)
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Decision Boundary
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Decision Boundary
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Decision Boundary
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Decision Boundary
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Decision Boundary
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Decision Boundary
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Learning Task
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Cost Function
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Cost Function
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Logistic Regression Cost Function
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Logistic Regression Cost Function
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Logistic Regression Cost Function
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Logistic Regression Cost Function
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Logistic Regression Cost Function
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Logistic Regression Cost Function
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Logistic Regression Cost Function
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Logistic Regression Cost Function
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Gradient Descent
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Gradient Descent
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Gradient Descent
Algorithm looks identical to linear regression
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Multi-class Classification: One-vs-All Algorithm
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Binary vs Multi-class Classification Problem
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One-vs-All (one-vs-rest)
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One-vs-All (one-vs-rest)
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One-vs-All (one-vs-rest)
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One-vs-All (one-vs-rest)
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One-vs-All Algorithm