#33 Machine Learning Specialization [Course 1, Week 3, Lesson 1] | Summary and Q&A

TL;DR

Logistic regression uses the sigmoid function to compute predictions. The decision boundary determines when to predict a value of 0 or 1.

Key Insights

• 🖱️ Logistic regression uses the sigmoid function to compute predictions based on the calculated value of Z.
• 😃 The decision boundary separates the predicted values of 0 and 1, determined by whether w dot X plus b is greater than or equal to 0 or less than 0.
• ❓ Polynomial features can be introduced to create more complex decision boundaries in logistic regression.
• ❓ The threshold of 0.5 is commonly used to determine the predicted value of 0 or 1.
• ✋ Logistic regression can fit complex data by including higher-order polynomial terms.
• 🫥 Without higher-order polynomials, the decision boundary in logistic regression will always be a straight line.
• 🫥 The decision boundary can be visualized as lines or curves in two-feature examples.

Transcript

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Questions & Answers

Q: How does logistic regression compute predictions?

Logistic regression computes predictions in two steps: computing Z as w dot X plus b, then applying the sigmoid function to Z. The resulting value represents the probability of Y being equal to 1 given X and the parameters W and B.

Q: How does logistic regression decide whether to predict 0 or 1?

Logistic regression sets a threshold, usually 0.5, above which it predicts Y as 1 and below which it predicts Y as 0. If the sigmoid function output (f of X) is greater than or equal to 0.5, it predicts 1; otherwise, it predicts 0.

Q: What is the decision boundary in logistic regression?

The decision boundary is the line or curve that separates the predicted values of 0 and 1. It is determined by the value of w dot X plus b, where values greater than or equal to 0 predict 1 and values less than 0 predict 0.

Q: Can logistic regression have complex decision boundaries?

Yes, logistic regression can have complex decision boundaries by including higher-order polynomial terms in the model. By introducing additional features and adjusting the parameter values, the decision boundary can take various shapes, such as ellipses or curves.

Summary & Key Takeaways

• Logistic regression models compute outputs in two steps: computing Z as w dot X plus b, then applying the sigmoid function to Z.

• The sigmoid function, or logistic function, determines the probability that Y is equal to 1 given X and parameters W and B.

• A threshold of 0.5 is commonly used to decide whether to predict 0 or 1, with values above the threshold predicting 1.