A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New spectral methods improve matrix estimation in RL with low-rank structure.
Novel method for efficient low-rank matrix estimation and bandit algorithms.
We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we rigorously show that under a certain condition on the magnitude of t…
Unified approach for robust low rank matrix estimation with adversaries.
New framework explains why nonconvex methods work well in low-rank matrix estimation.
We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general case with noisy observations, we show that our algorithm is guaranteed to linearl…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is distorted by a (typically unknown) nonlinear transformation. This paper addresses the…
ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.
This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe only a subset of the entries, this is a problem of matrix completion. In both case…
UA-LQE improves value function learning by selectively erasing uncertain entries in Q-matrix.
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion methods often assume a simple uniform missing mechanism. In this work, we study ma…
Characterizes uncertainty in low-rank matrix completion with noisy data.
Paper finds a lower bound for estimating low-rank matrices in logistic regression.
Estimates low-rank distributional matrices from incomplete samples.
Improved matrix completion for non-uniformly sampled data.
New method for robust matrix completion with mixed data types.
A new method for 1-bit matrix completion that is faster and more accurate.
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict inductively on new users/movies. In this paper, we study the problem of inductive matr…
In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to …
Paper explores statistical and computational limits of estimating low-rank Gaussian mixtures.
The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the …
New method predicts binary matrix entries using empirical Bayes and low-rank structure.
We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank components, we propose a sparsity constrained maximum likelihood estimator based on m…
LEARNER improves low-rank matrix estimation using source population data.
We develop a flexible framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple bootstrap algorithm. Effectively, our procedure seeks an autoencoding basis for the observed matrix that is stable with respect to the specified noise model; we call the resul…
Paper proposes a new method to separate low rank and sparse matrices without bias.
We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank structure, wherein each component matrix is low rank and the latent space of th…
Convex optimization method recovers low-rank matrices from rank-one projections efficiently.
New method estimates heterogeneous treatment effects with improved guarantees.
GAME improves matrix completion by considering subgroup-specific latent structures.
Paper tackles matrix estimation under arbitrary noise, achieving minimax optimality.
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence a…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of matrix entries in the context of these low-rank approximations and other sampling-…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-ra…
The paper proposes methods for predicting missing values in mixed data matrices.
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of methods have been developed for this recovery problem. However, a principled meth…
Robust low-rank matrix estimation is a topic of increasing interest, with promising applications in a variety of fields, from computer vision to data mining and recommender systems. Recent theoretical results establish the ability of such data models to recover the true underlying low-rank matrix when a large portion o…
Gradient descent solves asymmetric low-rank matrix sensing without balancing.
New methods recover best rank-r approximations from few entries.
Paper proposes fast, robust methods for low-rank matrix recovery.
Paper studies quantized LRMR with random dithering for correlated tasks.
We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is low--rank, and the measurements consist of a subset, either of the exact individ…
We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set the parameters of the non-convex penalty functions, in order to ensure that the ob…
Paper proposes diagnostics for error and variance estimation in randomized matrix computations.
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming that the underlying matrix has low rank, or is well-approximated by a low rank matr…
A low-rank tensor model simplifies multi-dimensional Markov chains.
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is…
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with tra…