🌏 中文版
The official handout is titled Homework 3: Decision Trees, K-NN, Perceptron, Regression and is entirely written. Its sections are decision tree revisited, regression tree, k-nearest neighbors, perceptron, and linear regression, with overfitting, error rates, and model selection inside them. The ZIP contains the PDF, LaTeX template, and figures—no starter code, dataset, or reference output.
Do not read it as four formula sheets
The common question is which model fails first when representation or decision boundaries change. K-NN distance, perceptron separability, regression loss, and tree split preferences encode different assumptions.
First check and completion
There is no necessary safe command. Open the PDF/LaTeX bundle and list the assumptions behind all five sections before calculating. Completion means pairing every result with its assumption and predicting model behavior on XOR, an outlier-contaminated line, and sparse high-dimensional points. With no official answers, do not label your derivations officially verified.
How XOR exposes a linear-boundary limit
This is an invented teaching example, not an official assignment solution.
Four invented points implement XOR: (0,0) and (1,1) have label 0; (0,1) and (1,0) have label 1. A strict linear separation requires b<0, w₁+b>0, w₂+b>0, and w₁+w₂+b<0. Adding the positive-side requirements gives w₁+w₂+b>-b>0, contradicting the last condition.
Check and answer: Can adding feature x₁x₂ help? Yes: score=x₁+x₂-2x₁x₂-0.5 yields -0.5,-0.5,0.5,0.5 in the listed point order. Changing representation changes separability.
Changelog
- 2026-10-11: Added an invented example, worked calculation or reasoning, and a comprehension check with an answer.
References
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