Related papers: On a low-rank matrix single index model
Many applications of machine learning involve the analysis of large data frames-matrices collecting heterogeneous measurements (binary, numerical, counts, etc.) across samples-with missing values. Low-rank models, as studied by Udell et al.…
We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the…
PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic…
We propose a computational framework for computing low-rank approximations to the ensemble of solutions of a parametrized system of the form $A(\xi)x(\xi)+g(x(\xi))=b(\xi)$ for multiple parameter values. The central idea is to reinterpret…
The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…
We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of…
Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J.…
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors.…
In recent years, with the rapid development of science and technology, heterogeneous treatment effects have emerged as a focal research topic in statistics, econometrics, and sociology. This paper investigates HTE through semiparametric…
The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…
In this paper, we consider the statistical analysis of a protein interaction network. We propose a Bayesian model that uses a hierarchy of probabilistic assumptions about the way proteins interact with one another in order to: (i) identify…
PAC-Bayes is a useful framework for deriving generalization bounds which was introduced by McAllester ('98). This framework has the flexibility of deriving distribution- and algorithm-dependent bounds, which are often tighter than…
Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when…
The statistical modeling of random networks has been widely used to uncover interaction mechanisms in complex systems and to predict unobserved links in real-world networks. In many applications, network connections are collected via…
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…
Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…
This paper focuses on the problem of modeling and estimating interaction effects between covariates and a continuous treatment variable on an outcome, using a single-index regression approach. The primary motivation is to estimate an…
This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear…