arXiv research

The paper provides entrywise bounds for Sparse PCA, improving upon previous results.

The paper proposes methods for predicting missing values in mixed data matrices.

Proposes a new algorithm to estimate invariant subspaces across multilayer networks.

We study the column subset selection problem with respect to the entrywise $\ell_1$-norm loss. It is known that in the worst case, to obtain a good rank-$k$ approximation to a matrix, one needs an arbitrarily large $n^{Ω(1)}$ number of columns to obtain a $(1+ε)$-approximation to the best entrywise $\ell_1$-norm low ra…

Simple method for estimating missing panel data entries with confidence intervals.

Improves detection of low-rank signals from noisy data matrices.

Develops inequalities for high-dimensional linear processes with dependent innovations.

This paper is concerned with the problem of top-$K$ ranking from pairwise comparisons. Given a collection of $n$ items and a few pairwise comparisons across them, one wishes to identify the set of $K$ items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model --- the Bradley-Te…

EPMF factorizes matrices by adjusting their entries to match a specified power.

We develop embeddings for nonlinear subspaces preserving vector norms.

We develop an efficient algorithm for low-rank approximation with improved approximation guarantees.

Optimal transfer learning for missing not-at-random matrix completion using source data.

Spectral clustering achieves strong consistency in the stochastic block model under certain conditions.

The report studies ranking from pairwise comparisons in graphs, achieving optimal error bounds and proposing efficient algorithms.

New method improves subspace iteration for eigenvectors in machine learning.

Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from sparse observations and argue that it achieves sample complexity that nearly matc…

Spectral ranking methods are improved against semi-random graph sampling.

Study heavy-tailed weights' impact on neural network's spectral distribution.

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low rank matrix $Θ^\star$ with a second matrix $Γ^\star$ endowed with a complementary …

Matrices of (approximate) low rank are pervasive in data science, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a vast literature on how to exploit low rank structure in these datasets, there is less attention on explaining why the low rank structure ap…

New method estimates heterogeneous treatment effects with improved guarantees.

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for iterative stochastic procedures in the presence of probabilistic dependency. We demon…

We analyze the eigenvalue distribution of a neural network's kernel under specific scaling.

Paper improves robust spectral clustering for noisy data.

We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not depend on the distribution of the signal or the noise. The test is optimal unde…

A new method for streaming PCA provides confidence intervals for eigenvector entries.

We propose practical algorithms for entrywise $\ell_p$-norm low-rank approximation, for $p = 1$ or $p = \infty$. The proposed framework, which is non-convex and gradient-based, is easy to implement and typically attains better approximations, faster, than state of the art. From a theoretical standpoint, we show that th…

Improved learning of multivariate Gaussians with imperfect advice.

The paper analyzes how random perturbations affect RSVD and its applications.

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle this problem is convex relaxation, which achieves remarkable efficacy in practic…

Adaptive classifier optimizes high-dimensional data with spiked covariance structure.

Develops an ℓ_p theory for PCA and spectral clustering.

New method estimates high-dimensional GoM models efficiently.

Paper tackles matrix estimation under arbitrary noise, achieving minimax optimality.

Q-learning requires more samples than minimax bounds suggest for optimal Q-function approximation.

We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the linear spectral statistics of the data matrix. The test is data-driven and does no…

Asynchronous Q-learning achieves optimal Q-function estimation with reduced sample complexity.

Paper develops methods for PCA inference with missing data and heteroskedastic noise.

We consider the problem of selecting non-zero entries of a matrix $A$ in order to produce a sparse sketch of it, $B$, that minimizes $\|A-B\|_2$. For large $m \times n$ matrices, such that $n \gg m$ (for example, representing $n$ observations over $m$ attributes) we give sampling distributions that exhibit four importa…

A new model integrates covariates with grade of membership analysis for better latent structure recovery.

This work analyzes self-attention matrices using random matrix theory.

New framework detects directional influence in multivariate time series.

Power-law spectrum of random feature model is preserved in neural networks.

The paper addresses statistical inference in matching markets with dependent missingness.

Matrices satisfying the Restricted Isometry Property (RIP) play an important role in the areas of compressed sensing and statistical learning. RIP matrices with optimal parameters are mainly obtained via probabilistic arguments, as explicit constructions seem hard. It is therefore interesting to ask whether a fixed mat…

Unified framework for statistical inference of low-rank tensors.

New method calibrates diffusion models for image regression tasks.

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly perturbed version $\mathbf{M}$ is observed. The noise matrix $\mathbf{M}-\mathbf{M}^{\s…