Analyzing concentration of large random matrices is a common task in a wide variety of
fields. Given independent random variables, several tools are available to bound the norms …

In [Sau11, SPW13], Saunderson, Parrilo and Willsky asked the following elegant geometric
question: what is the largest $ m= m (d) $ such that there is an ellipsoid in $\mathbb {R}^ d …

We present a general framework for designing efficient algorithms for unsupervised learning
problems, such as mixtures of Gaussians and subspace clustering. Our framework is based …

We present a new method for obtaining norm bounds for random matrices, where each entry
is a low-degree polynomial in an underlying set of independent real-valued random …

We develop new techniques for proving lower bounds on the least singular value of random
matrices with limited randomness. The matrices we consider have entries that are given by …

We show that a large class of secant varieties is nondefective. In particular, we positively
resolve most cases of the Baur-Draisma-de Graaf conjecture on Grassmannian secants in …

We resolve most cases of identifiability from sixth-order moments for Gaussian mixtures on
spaces of large dimensions. Our results imply that the parameters of a generic mixture of …

We consider simultaneous Waring decompositions: Given forms $ f_d $ of degrees $ kd $,
$(d= 2, 3) $, which admit a representation as $ d $-th power sums of $ k $-forms $ q_1,\ldots …

This thesis studies graph matrices. Graph matrices are a type of random matrices that were
invented as a powerful tool for analyzing large and complicated moment matrices which …

Unsupervised Learning via Algebraic Circuit Reconstruction Page 1 Unsupervised Learning via
Algebraic Circuit Reconstruction CS224 Project (Algorithms for Data Science, Fall 2023) …