## [Notes] Cracking the GRE Mathematics Subject Test – Steve Leduc

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## [Notes] Cracking the GRE Mathematics Subject Test – Steve Leduc

## An intuition to an tangent plane to a surface

## Proof of lower-rank matrix factorization

## Entropy 2016, bảng A

## Triplet Loss’ derivative of VGG Face

## [Notes] Learning From Data – A Short Course: e-Chapter 9

## Learning From Data – A Short Course: Exercise 9.6

## Learning From Data – A Short Course: Exercise 9.4

## Protected: Giới thiệu về Support Vector Machine – Phần 1

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Page 172: http://farside.ph.utexas.edu/teaching/sm1/lectures/node36.html#e4.32

To me: Page 126 of Cracking the GRE Math Subject Test. A rigorous proof can be found here (Calculus, Howard Anton). A note of stress should be on “any smooth curve C on the surface”. Below is my attempt interpretation before looking at any proofs. While it cannot be considered as a proof, it shows [...]

Let and and , prove that . We can determine by applying row operations on . First, we will let the second row of after the first row operation be: . Next, the third row of after the second row operation would be: . Soon, we will come to () which is a linear combination [...]

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: [...]

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