Related papers: Hierarchical sparse Cholesky decomposition with ap…
Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments,…
We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky…
Smoothness of the subdiagonals of the Cholesky factor of large covariance matrices is closely related to the degrees of nonstationarity of autoregressive models for time series and longitudinal data. Heuristically, one expects for a nearly…
In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as…
Max-stable processes are the most popular models for high-impact spatial extreme events, as they arise as the only possible limits of spatially-indexed block maxima. However, likelihood inference for such models suffers severely from the…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
Incomplete factorizations have long been popular general-purpose algebraic preconditioners for solving large sparse linear systems of equations. Guaranteeing the factorization is breakdown free while computing a high quality preconditioner…
The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the…
Statistical modeling for massive spatial data sets has generated a substantial literature on scalable spatial processes based upon Vecchia's approximation. Vecchia's approximation for Gaussian process models enables fast evaluation of the…
Techniques based on $k$-th order Hodge Laplacian operators $L_k$ are widely used to describe the topology as well as the governing dynamics of high-order systems modeled as simplicial complexes. In all of them, it is required to solve a…
This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability,…
Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that…
We present a new computational approach to approximating a large, noisy data table by a low-rank matrix with sparse singular vectors. The approximation is obtained from thresholded subspace iterations that produce the singular vectors…
We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the…
Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…
This paper explores Vecchia likelihood approximation for modeling physical phenomena sensed by mobile and fixed low-cost sensors in urban environments. A three-level hierarchical model is proposed to simultaneously accounts for the physical…
Gaussian processes are flexible, probabilistic, non-parametric models widely used in machine learning and statistics. However, their scalability to large data sets is limited by computational constraints. To overcome these challenges, we…
Gaussian Processes (GPs) are widely used to model dependencies in spatial statistics and machine learning. However, exact inference is computationally intractable for GP regression, with a time complexity of $O(n^3)$. The Vecchia…
Linear models have found widespread use in statistical investigations. For every linear model there exists a matrix representation for which the ReML (Restricted Maximum Likelihood) can be constructed from the elements of the corresponding…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…