Related papers: Phase transitions in spiked matrix estimation: inf…

We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…

We prove the equivalent of the Baik, Ben Arous, P\'ech\'e (2004) phenomenon for a novel, doubly sparse model where both the Wigner noise matrix and signal vector(s) are sparse. Specifically, we consider a deformed sub-Gaussian sparse Wigner…

The problem of low-rank matrix completion with heterogeneous and sub-exponential (as opposed to homogeneous and Gaussian) noise is particularly relevant to a number of applications in modern commerce. Examples include panel sales data and…

In this work we analyse quantitatively the interplay between the loss landscape and performance of descent algorithms in a prototypical inference problem, the spiked matrix-tensor model. We study a loss function that is the negative…

Motivated by applications to group synchronization and quadratic assignment on random data, we study a general problem of Bayesian inference of an unknown ``signal'' belonging to a high-dimensional compact group, given noisy pairwise…

Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…

Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…

Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…

The recent development of compressed sensing has led to spectacular advances in the understanding of sparse linear estimation problems as well as in algorithms to solve them. It has also triggered a new wave of developments in the related…

Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…

Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…

We study a phase transition in parameter learning of Hidden Markov Models (HMMs). We do this by generating sequences of observed symbols from given discrete HMMs with uniformly distributed transition probabilities and a noise level encoded…

This paper deals with the phase noise affecting communication systems, where local oscillators are employed to obtain reference signals for carrier and timing synchronizations. The most common discrete-time phase noise channel model is…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…

We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…

We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance,…

The numerical emulation of quantum physics and quantum chemistry often involves an intractable number of degrees of freedom and admits no known approximation in general form. In practice, representing quantum-mechanical states using…

Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…

The Bayesian and Akaike information criteria aim at finding a good balance between under- and over-fitting. They are extensively used every day by practitioners. Yet we contend they suffer from at least two afflictions: their penalty…