Algorithms
Foundations of Data Science – Lecture 6 – Singular Value Decomposition – l
Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science.…
Rapid Analysis of Network Connectivity
Pacific Northwest Probability Seminar: A Characterization Theorem for the Gaussian Free Field
We prove that any random distribution satisfying conformal invariance and a form of domain Markov property and having a finite moment condition must be the Gaussian free field. We also present some open problems regarding…
Pacific Northwest Probability Seminar: Optimal Matching of Gaussian Samples
Optimal matching problems are random variational problems widely investigated in the mathematics and physics literature. We discuss here the optimal matching problem of an empirical measure on a sample of iid random variables to the…
Pacific Northwest Probability Seminar: Random self-similar trees: dynamical pruning and its applications to inviscid Burgers equations
Consider the fractional Brownian motions on the real line. What should we expect if we replace the real line by a manifold M? We will provide an answer to this question, extending work begun by…
Pacific Northwest Probability Seminar: An Analysis of Spatial Mixing
In joint work with Soumik Pal, we study natural mixing processes where cards (or dominoes or mahjong tiles) are ‘smushed’ around on a table with two hands. How long should mixing continue. If things are…
Pacific Northwest Probability Seminar: Gravitational Allocation to Uniform Points on the Sphere
Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them? “Fairly” means that each region has the same area. It turns out that if the…
Foundations of Data Science – Lecture 5 – Length Squared Sampling in Matrices
Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science.…
Economics and Computer Science (EconCS) at MSR-NE
Economics and computer science (EconCS) is at the core of Microsoft Research New England, an interdisciplinary lab of thirty full-time researchers and postdocs working in machine learning, statistics, computational biology, theoretical computer science, algorithmic game…