Related papers: Detection problems in the spiked matrix models
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…
We consider solving the low rank matrix sensing problem with Factorized Gradient Descend (FGD) method when the true rank is unknown and over-specified, which we refer to as over-parameterized matrix sensing. If the ground truth signal…
We consider a statistical model for symmetric matrix factorization with additive Gaussian noise in the high-dimensional regime, where the rank of the signal matrix to infer $M$ scales with its size $N$ as $M=\mathrm{o}(\sqrt{\ln N})$.…
Randomized benchmarking (RB) protocols are standard tools for characterizing quantum devices. Prior analyses of RB protocols have not provided a complete method for analyzing realistic data, resulting in a variety of ad-hoc methods. The…
We study detection of random signals corrupted by noise that over time switch their values (states) from a finite set of possible values, where the switchings occur at unknown points in time. We model such signals by means of a random…
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…
High-dimensional planted problems, such as finding a hidden dense subgraph within a random graph, often exhibit a gap between statistical and computational feasibility. While recovering the hidden structure may be statistically possible, it…
In this article, the joint fluctuations of the extreme eigenvalues and eigenvectors of a large dimensional sample covariance matrix are analyzed when the associated population covariance matrix is a finite-rank perturbation of the identity…
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…
The Border Gateway Protocol (BGP) is a distributed protocol that manages interdomain routing without requiring a centralized record of which autonomous systems (ASes) connect to which others. Many methods have been devised to infer the AS…
We present a simple algorithm for identifying and correcting real-valued noisy labels from a mixture of clean and corrupted sample points using Gaussian process regression. A heteroscedastic noise model is employed, in which additive…
Spiking neural networks are the basis of versatile and power-efficient information processing in the brain. Although we currently lack a detailed understanding of how these networks compute, recently developed optimization techniques allow…
We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex…
Minimax detection of Gaussian stochastic sequences (signals) with unknown covariance matrices is studied. For a fixed false alarm probability (1-st kind error probability), the performance of the minimax detection is being characterized by…
Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of…
We consider an Information-Plus-Noise type matrix where the Information matrix is a spiked matrix. When some eigenvalues of the random matrix separate from the bulk, we study how the corresponding eigenvectors project onto those of the…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
This paper investigates the classical statistical signal processing problem of detecting a signal in the presence of colored noise with an unknown covariance matrix. In particular, we consider a scenario where m-dimensional p possible…
We consider the problem of estimating the state transition matrix of a linear time-invariant (LTI) system, given access to multiple independent trajectories sampled from the system. Several recent papers have conducted a non-asymptotic…
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…