Related papers: High-dimensional rank-one nonsymmetric matrix deco…
In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
Every sufficiently big matrix with small spectral norm has a nearby low-rank matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the estimate…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…
A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be…
We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions…
We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…
We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…
This paper studies the problem of finding best rank-1 approximations for both symmetric and nonsymmetric tensors. For symmetric tensors, this is equivalent to optimizing homogeneous polynomials over unit spheres; for nonsymmetric tensors,…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
We present a simulation code which can solve broad ranges of partial differential equations in a full sphere. The code expands tensorial variables in a spectral series of spin-weighted spherical harmonics in the angular directions and a…
A Cartan decomposition for symmetric pairs plays an important role to study not only orbit geometry of the symmetric spaces but also harmonic analysis on them. For non-symmetric reductive pairs, there are examples of generalizations of…
We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the…
We study the problem of robust matrix completion (RMC), where the partially observed entries of an underlying low-rank matrix is corrupted by sparse noise. Existing analysis of the non-convex methods for this problem either requires the…
This paper studies how to recover parameters in diagonal Gaussian mixture models using tensors. High-order moments of the Gaussian mixture model are estimated from samples. They form incomplete symmetric tensors generated by hidden…
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…