Verify these matrix properties (easy and fun)
I’m looking at products like \(\mat{G}^t \mat{A} \mat{G}\) where the columns of \(\mat{G}\) are (nonisotropic) normal vectors. Specifically, I’d like to know the distribution of the...
View ArticleSampling models and vector sums
What happens when you sample columns from a matrix whose columns all have roughly the same norm? It’s clear that you should have some kind of concentration: say if you sample \(\ell\) of \(n\) columns,...
View ArticleAre there perturbations that preserve incoherence and give nicely conditioned...
Let \(\mat{P}_{\mathcal{U}}\) denote the projection unto a \(k\)-dimensional subspace of \(\C^{n}.\) We say \(\mathcal{U}\) is \(\mu\)-coherent if \((\mat{P}_{\mathcal{U}})_{ii} \leq \mu \frac{k}{n} \)...
View ArticleQOTD: total unimodularity
I started reading Matousek’s discrete geometry book. Specifically, chapter 12 on applications of high-dimensional polytopes. Mostly because he apparently draws a connection between graphs and the...
View ArticleTruncated SVD … how?
This question has been bothering me off and on for several months now: how *exactly* is the truncated SVD computed, and what is the cost? I’ve gathered that most methods are based on Krylov subspaces,...
View ArticleTeaching kernel learning
Here’s a neat approach to teaching kernel learning (for empirical risk minimization), following section 2.2.6 of the book “First-order and Stochastic Optimization Methods for Machine Learning” by...
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