Third week of the IBM internship
I’m working on an internal project that motivated me to look into survival analysis. Cool stuff, that. Essentially, you have a bunch of data about the lifetimes of the some objects and potentially...
View Articlenew reading blog
I’ve started a separate blog to track my mathematical reading. Check it out, comment, and suggest material I might find interesting.
View ArticleSummer of languages
This summer’s the summer of languages for me. I’m learning R piecemeal, because I’m working on a data analytics project that requires a lot of statistical analysis: learning a new language is a bother,...
View Articlewhen do \(A\) and \(AA^T\) have the same spectrum?
There are matrices for which the spectrum of \(\mat{A}\) and \(\mat{A}\mat{A}^T\) are identical. As an example, take \[ \mat{A} = \begin{pmatrix} \frac{1}{2} & 0 & \frac{1}{2} & 0 \\ 0...
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Problem: another inequality
Let \(\mat{F},\mat{G}\) be positive definite matrices (do they have to be definite?) and \(0 \leq p \leq 2.\) Show that \[ \tr\left(\mat{F}^{p/2} - \mat{G}^{p/2}\right) \leq \frac{p}{2}...
View ArticleDrawing to a close at IBM
Well damn. It’s been a long while. Time for another post about my not having posted in a while. I’m wrapping up my internship here at IBM, preparing the exit talk on my research. It’s entitled “New...
View ArticleA list of \(\|\cdot\|_{\infty \rightarrow 1}^*\) problems
Recall our old friend the \(\|\cdot\|_{\infty \rightarrow 1}^*\) norm (from the first version of this website, which I still haven’t gotten around to merging into the current iteration). Given a matrix...
View ArticleMonument
Jeff Salyards is doing an Ask Me Anything (AMA) on Reddit tonight at 5 PCT. I started reading his debut novel, Scourge of the Betrayer, a couple of weeks ago, but couldn’t get into it for one reason or...
View ArticleRoll On
I was reading, of all things, a romance novel when I came across this famous excerpt from Childe Harold’s Pilgrimage: Roll on, thou deep and dark blue Ocean – roll! Ten thousand fleets sweep over thee...
View ArticleWe play the long game here
I’ve been off Being Human (the original UK version) for a while now. I stopped watching after the first episode of season 3, in part because the American version came out and I got into that before it...
View ArticleThe convergence rate of the OLS estimator for linear regression
A lot of machine learning and modern statistics concerns the rate at which certain statistical estimators converge to the quantities they are estimating. For instance, in classification, you use a...
View ArticleI miss Mathematica
Why? Because Mathics is not up to helping me determine if indeed \[ f(\{A_1, \ldots, A_p\}) = \frac{(n-p)!^2}{n! p!} \left(\frac{1}{p} \right)^{n-p} \frac{|A_1|^2 \cdots |A_p|^2}{|A_1|!\cdots |A_p|!}...
View ArticleSampling uniformly from the set of partitions into a fixed number of nonempty...
It’s easy to sample uniformly from the set of partitions of a set: you pick a number of bins using an appropriate exponential distribution, then randomly i.i.d. toss each element of the set into one of...
View ArticleQuick note on the Chen, Chi, Goldsmith covariance sketching paper
NB: I will update this post as I read the paper, in case it turns out that the first issue I raised is not legitimately a concern. Covariance estimation (and the natural extension, precision...
View ArticleA workaround for installing SQBLib
I spent about an hour today getting Carlos Becker’s SQBLib package for gradient boosted tree regression in matlab working. The issue is that it depends on liblbfgs, and following the instruction Carlos...
View ArticleA useful trick for computing gradients w.r.t. matrix arguments, with some...
I’ve spent hours this week and last week computing, recomputing, and checking expressions for matrix gradients of functions. It turns out that except in the simplest of cases, the most painfree method...
View ArticleBack of the envelope calculations of how fast your computer can do linear...
Let’s talk about CPU speed, practically. By practically, I mean, how fast can your CPU do linear algebra operations. And by linear algebra operations, I mean matrix-matrix multiplies. First, you need...
View ArticleAdagrad and projections onto ellipsoids
((Caveat! I am not sure the manipulations done in this post are correct, but the gist is certainly there.)) One of my favorite optimization techniques is Adagrad, a first-order technique that...
View ArticleDecision time: MacPorts vs Homebrew vs Fink
My work macbook pro recently crapped out on me during an update of the OS (apparently something has a tendency to go wrong with the video card or its driver or something similar during this particular...
View ArticleCanonical Correlation Analysis (CCA)
I am not completely satisfied with the expositions of CCA that I’ve come across, so I decided to write one that reflects my own intuition. CCA is useful in the case where you observe two random...
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