Related papers: Gaussian Approximation for High Dimensional Time S…
Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…
We present a test for independence of two strictly stationary time series based on a bootstrap procedure for the distance covariance. Our test detects any kind of dependence between the two time series within an arbitrary maximum lag $L$.…
The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics,…
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…
In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, then link the theory to multivariate approximation theory, and…
The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…
We present an estimator of the covariance matrix $\Sigma$ of random $d$-dimensional vector from an i.i.d. sample of size $n$. Our sole assumption is that this vector satisfies a bounded $L^p-L^2$ moment assumption over its one-dimensional…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
Resampling methods such as the bootstrap have proven invaluable in the field of machine learning. However, the applicability of traditional bootstrap methods is limited when dealing with large streams of dependent data, such as time series…
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…
We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich probability space, a Gaussian process that uniformly…
We consider the famous Rasch model, which is applied to psychometric surveys when n persons under test answer m questions. The score is given by a realization of a random binary (n,m)-matrix. Its (j,k)th component indicates whether or not…
This paper considers a new bootstrap procedure to estimate the distribution of high-dimensional $\ell_p$-statistics, i.e. the $\ell_p$-norms of the sum of $n$ independent $d$-dimensional random vectors with $d \gg n$ and $p \in [1,…
The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is…
Efficient sampling from a high-dimensional Gaussian distribution is an old but high-stake issue. Vanilla Cholesky samplers imply a computational cost and memory requirements which can rapidly become prohibitive in high dimension. To tackle…
We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…
A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in…
High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable…