It took me quite a lot of time to understand the question, though. I do not post the test here as I am not sure if I am permitted to do that. This post serves for my personal use. Even though the original questions are written in Vietnamese, I will be writing my solutions in [...]
We starts with the formula (1) of the paper. We have: By chain rule, we have: We also have: – the th element of . – the th element of . So:
Page 30: Why ? My understanding: as the events and are independent, the same goes for the event . Note that both data points and may exist in dataset so if is a deterministic hypothesis then it is obviously as . If is a non-deterministic hypothesis, is still independent from the random target function (even “ are [...]
Try to build some intuition for what the rotation is doing by using the illustrations in Figure 9.1 to qualitatively answer these questions. (a) If there is a large offset (or bias) in both measured variables, how will this affect the ‘natural axes’, the ones to which the data will be rotated? Should you perform [...]
Let and be independent with zero mean and unit variance. You measure inputs and . (a) What are variance (), variance () and covariance ? First, we have: Now, we consider and get: Expected values: Variance: [...]
There is no excerpt because this is a protected post.
Consider two finite-dimensional feature transforms and and their corresponding kernels and . (a) Define . Express the corresponding kernel of in terms of and . (b) Consider the matrix and let be the vector representation of the matrix (say, by concatenating all the rows). Express the corresponding kernel of in terms of and [...]
Suppose that we removed a data point with . (a) Show that the previous optimal solution remains feasible for the new dual problem (8.21) (after removing ). is the old dual problem while is the new dual problem. Because appears when appears and reverse. So when we replace the value of into (8.21), there is [...]
Page 29 “Then, at least one of the will be strictly positive.”. Please refer to the constraint .
(a) Show that the problem in (8.21) is a standard QP-problem: where and ( for dual) are given by: It is easy to show this, what should be noted here is that: (b) The matrix of quadratic coefficients is . Show that , where is the ‘signed data matrix’, Hence, show that is [...]