1. [k Nearest Neighbors] Consider properties of k-NN models: a. (2 pts) Suppose that we are...

   

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1. [k Nearest Neighbors] Consider properties of k-NN models: a. (2 pts) Suppose that we are using k-NN with just two training points, which have different (binary) labels. Assuming we are using k 1 and Euclidean distance, what = is the decision boundary? Include a drawing with a brief explanation. = b. (2 pts) For binary classification, given infinite data points, can k-NN with k 1 express any decision boundary? If yes, describe the (infinite) dataset you would use to realize a given classification decision boundary. If no, give an example of a decision boundary that cannot be achieved. c. (2 pts) Suppose we take k → ∞; what is the resulting model family? d. (2 pts) What effect does increasing the number of nearest neighbors k have on the bias-variance tradeoff? Explain your answer. [Hint: Use parts (b) and (c) in your explanation.] e. (2 pts) In logistic regression, we learned that we can tune the threshold of the linear classifier to trade off the true negative rate and the true positive rate. Explain how we can do so for k-NNs for binary classification. [Hint: By default, k-NN uses majority vote to aggregate labels of the k nearest neighbors; consider another option.] 1. [k Nearest Neighbors] Consider properties of k-NN models: a. (2 pts) Suppose that we are using k-NN with just two training points, which have different (binary) labels. Assuming we are using k 1 and Euclidean distance, what = is the decision boundary? Include a drawing with a brief explanation. = b. (2 pts) For binary classification, given infinite data points, can k-NN with k 1 express any decision boundary? If yes, describe the (infinite) dataset you would use to realize a given classification decision boundary. If no, give an example of a decision boundary that cannot be achieved. c. (2 pts) Suppose we take k → ∞; what is the resulting model family? d. (2 pts) What effect does increasing the number of nearest neighbors k have on the bias-variance tradeoff? Explain your answer. [Hint: Use parts (b) and (c) in your explanation.] e. (2 pts) In logistic regression, we learned that we can tune the threshold of the linear classifier to trade off the true negative rate and the true positive rate. Explain how we can do so for k-NNs for binary classification. [Hint: By default, k-NN uses majority vote to aggregate labels of the k nearest neighbors; consider another option.]

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SOLUTION Sure Id be happy to help Here are the answers to the questions a 2 pts Suppose we have two training points x1 and x2 with different binary labels y1 and y2 We want to use kNN with k1 and Eucl... View the full answer