Related papers: Bootstraps Regularize Singular Correlation Matrice…

This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This…

A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample…

A central goal of neuroscience is to understand how activity in the nervous system is related to features of the external world, or to features of the nervous system itself. A common approach is to model neural responses as a weighted…

Suppose that $k$ series, all having the same autocorrelation function, are observed in parallel at $n$ points in time or space. From a single series of moderate length, the autocorrelation parameter $\beta$ can be estimated with limited…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This…

We analyze bias correction methods using jackknife, bootstrap, and Taylor series. We focus on the binomial model, and consider the problem of bias correction for estimating $f(p)$, where $f \in C[0,1]$ is arbitrary. We characterize the…

Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…

We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a…

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…

Few-shot learning with sequence-processing neural networks (NNs) has recently attracted a new wave of attention in the context of large language models. In the standard N-way K-shot learning setting, an NN is explicitly optimised to learn…

Multi-view learning leverages correlations between different sources of data to make predictions in one view based on observations in another view. A popular approach is to assume that, both, the correlations between the views and the…

Inference about a scalar parameter of interest typically relies on the asymptotic normality of common likelihood pivots, such as the signed likelihood root, the score and Wald statistics. Nevertheless, the resulting inferential procedures…

In high-dimensional time series, the component processes are often assembled into a matrix to display their interrelationship. We focus on detecting mean shifts with unknown change point locations in these matrix time series. Series that…

We apply the bootstrap technique to find the moments of certain multi-trace and multi-matrix random matrix models suggested by noncommutative geometry. Using bootstrapping we are able to find the relationships between the coupling constant…

In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of "max statistics" in high-dimensional problems. A leading example of such a statistic is the coordinate-wise maximum of a sample average of…

We consider the properties of the bootstrap as a tool for inference concerning the eigenvalues of a sample covariance matrix computed from an $n\times p$ data matrix $X$. We focus on the modern framework where $p/n$ is not close to 0 but…

Bootstrap percolation on an arbitrary graph has a random initial configuration, where each vertex is occupied with probability p, independently of each other, and a deterministic spreading rule with a fixed parameter k: if a vacant site has…

This paper concerns the facial geometry of the set of $n \times n$ correlation matrices. The main result states that almost every set of $r$ vertices generates a simplicial face, provided that $r \leq \sqrt{\mathrm{c} n}$, where…

Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based…