## Learning From Data – A Short Course: Exercise 4.3

Page 125: Deterministic noise depends on , as some models approximate better than others. (a) Assume is fixed and we increase the complexity of . Will deterministic noise in general go up or down? Is there a higher or lower tendency to overfit? Deterministic noise in general will go up because it is harder for [...]

## Learning From Data – A Short Course: Problem 2.22

Page 74: When there is noise in the data, , where . If is a zero-mean noise random variable with variance , show that the bias-variance decomposition becomes     We have: We split the above expression in two sub-expressions, in which: Together, we can derive that:

## Learning From Data – A Short Course: Problem 1.3

Page 33: Prove that the PLA eventually converges to a linear separator for separable data. The following steps will guide you through the proof. Let be an optimal set of weights (one which separates the data). The essential idea in this proof is to show that the PLA weights get “more aligned” with with every [...]

## Learning From Data – A Short Course: Exercise 1.3

Page 8: The weight update rule in (1.3) has the nice interpretation that it moves in the direction of classifying correctly. (a) Show that . [Hint: x(t) is misclassified by .] Because is misclassified by so: : . Hence: . : . Hence: . So: . (b) Show that . [Hint: Use (1.3).] My solution for (b) is wrong. [...]

## Learning From Data – A Short Course: Exercise 3.12

Page 103: We know that in the Euclidean plane, the perceptron model cannot implement all 16 dichotomies on 4 points. That is . Take the feature transform in (3.12). (a) Show that . We have proved (in Exercise 2.4) that the hypothesis set of perceptron model in Euclidean plane has , and by the definition of [...]

## Learning From Data – A Short Course: Exercise 3.10

Page 98: (a) Define an error for a single data point to be     Argue that PLA can be viewed as SGD on with learning rate . when   means that agrees with (no error at that point): . when  and  disagrees (that point is misclassified): . Hence: When there is no error at the [...]