I am a scientist at XTX.
My doctorate was on statistical foundations for learning on graphs and high-dimensional probability, co-advised by Prof Kimon Fountoulakis and Prof Aukosh Jagannath at the Cheriton School of Computer Science, University of Waterloo.
Before that, I did my M.Math. at UWaterloo with Prof Jeffrey Shallit on algorithmic number theory and combinatorics on words, and my undergrad at IIT Jodhpur.
Fun fact: my Erdős number is 2 via Jeffrey Shallit.
Recent Posts
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The Hanson–Wright inequality
Posted on:A quadratic form in independent random variables concentrates around its mean, the trace of the matrix. Hanson–Wright pins down the two-sided tail: a Gaussian regime near the mean set by the Frobenius norm, crossing over to a heavier exponential tail set by the operator norm. For Gaussian inputs it all follows from rotating to the eigenbasis and applying Bernstein.
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Covering the sphere with ε-nets
Posted on:Many quantities in high dimensions are a supremum over all unit vectors, and a union bound cannot reach infinitely many of them. An ε-net replaces the sphere by a finite set of directions: control the quantity there, pay a constant factor to extend back, and the exponentially large net is still no match for a sub-Gaussian tail. The worked example is the operator norm of a random matrix.
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Sudakov minoration, or how big a maximum must be
Posted on:Averages shrink, but maxima grow. Sudakov's minoration inequality is the clean tool for the harder direction: a lower bound on the expected maximum of many Gaussians. As long as no two of them are too alike, that maximum is at least ε times the square root of log N. This is the engine behind a lot of impossibility proofs.
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Voronoi tessellations and Lloyd's algorithm
Posted on:A set of generators in the plane partitions it into regions, each closer to one generator than to any other. Lloyd's algorithm iterates "move each generator to the centroid of its region" and converges to a centroidal Voronoi tessellation (k-means).
Find all posts here.