arXiv research

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

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughou…

Paper studies tensor models using random matrix theory.

Study on signal-plus-noise decomposition in nonlinear spiked random matrices.

This paper analyzes generalization for linear models with spiked covariance structures.

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Pé…

Estimates rank-one spikes from heavy-tailed noise using self-avoiding walks.

Optimal spectral method found for inhomogeneous spiked Wigner model.

We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit. This setup includes Johnstone's spiked covariance model. We analyze the likelihood ratio …

We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. When the spike comes from a prior that is i.i.d. across coordinates, we prove that the log-likelihood ratio of the spiked model against the non-spiked one is asymptotically normal below a certai…

Using a low-dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference. A very popular and widely explored type of dimensionality reduction is sparsity; another type is generative modelling of signal distributions. Generative models based o…

PLS-SVD struggles with missing data in multimodal datasets, showing a phase transition in performance.

Improved LDA method for better classification and dimensionality reduction.

Study on complexity of random polynomials with deterministic spikes, identifying phase transitions.

Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.

Develops path integral for spiked tensor model dynamics.

New estimator for tensor weights with improved bias.

New theory for eigenvectors of generalized Laplacian matrices, addressing dependency issues.

In this article, we study spectral methods for community detection based on $α$-parametrized normalized modularity matrix hereafter called ${\bf L}_α$ in heterogeneous graph models. We show, in a regime where community detection is not asymptotically trivial, that ${\bf L}_α$ can be well approximated by a more tract…

Study reveals limits of PLS in multi-modal learning with correlated signals.

Consistent model selection for spiked Wigner model via AIC-type criteria.

Study on Langevin dynamics for recovering planted signals in spiked matrix models.

Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how probabilistic inference can be implemented by a network of spiking neurons in th…

Study eigenvalues and eigenvectors in neural networks, focusing on signal propagation.

Randomized SVD shows phase transitions in noisy data.

SGD recovers multiple signal vectors in noisy tensor PCA.

SPQR improves Q-ensemble diversity in reinforcement learning.

New algorithm for signal estimation in noisy matrix models.

Simple AMP algorithm robust to adversarial corruption.

Spectral clustering performance depends on eigenvector fluctuations, shown to be Gaussian.

Study of eigenvalues in nonlinear kernels for classification of separable data.

Neuronal circuits formed in the brain are complex with intricate connection patterns. Such complexity is also observed in the retina as a relatively simple neuronal circuit. A retinal ganglion cell receives excitatory inputs from neurons in previous layers as driving forces to fire spikes. Analytical methods are requir…

New algorithm optimizes positions of CountSketch non-zero entries for better data compression.

Neurons perform computations, and convey the results of those computations through the statistical structure of their output spike trains. Here we present a practical method, grounded in the information-theoretic analysis of prediction, for inferring a minimal representation of that structure and for characterizing its…

Study uses random matrix theory to improve tensor approximation accuracy.

Study optimal algorithms for recovering signals through inhomogeneous low-rank channels.

The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.

Random matrix theory explains transient signal detectability in early-stopped gradient flow.

Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.

We propose reinforcement learning on simple networks consisting of random connections of spiking neurons (both recurrent and feed-forward) that can learn complex tasks with very little trainable parameters. Such sparse and randomly interconnected recurrent spiking networks exhibit highly non-linear dynamics that transf…

Random matrix theory explains how neural networks adapt to data.

We study the problem of detecting an abrupt change to the signal covariance matrix. In particular, the covariance changes from a "white" identity matrix to an unknown spiked or low-rank matrix. Two sequential change-point detection procedures are presented, based on the largest and the smallest eigenvalues of the sampl…

Paper proposes a new method for PCA using generative models.

Develops a new point process model for detecting neural spike sequences.

Improves signal detection in non-Gaussian noise using transformed data.

Model improves covariance estimation from shared and distinct datasets.

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…

Paper finds formulas for mutual information and MMSE in matrix tensor product problems.