Consider a matrix . In general, this matrix has rank Now, suppose we wish to column-center the data. We can do this algebraically by using what is known as the centering matrix, where is the matrix where for all . Multiplying with results to the centering of all the columns. The vector of ones is […]

From: I have this friend who is great at cutting vegetables. You give her whatever you want, she can shred it in seconds. However, when it comes to cooking, she needs to be shown how to combine the vegetables and understand the differences in taste and acidity of each one, etc. Otherwise she can’t […]

This is the second part of the story that I started with the previous post. Wanting to build a quick counterexample, I wondered if I can create a random variable by solving the moment problem with only finite non-zero moments. In the language of the moment problem, my sequence was such that for all greater […]

Yesterday, while trying to build a counter-example for a research problem, I started playing with the idea of designing a random variable, not by picking a vanilla distribution, but by selecting its moments myself. That is, if I pick the moments myself, can I find a distribution that has them? More formally, if I provide […]

The following is from an answer I wrote on Quora. The easiest answer is: “You just can’t cram the research.” Let’s figure it out together, assuming you’ve passed your quals, you are done with classes, and you work in the natural sciences, engineering, or computer science. First, you need to pick a good problem, which […]

Have you ever searched for a calculation on the Internet and then was disappointed when you couldn’t find it? Yeah, me too. I was trying to find the KL divergence between a Gamma and a Normal random distribution, but eventually decided to compute it on my own. So, if we consider the Gamma distribution, , […]