Related papers: High-Performance Variance-Covariance Matrix Constr…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
High-throughput chromatin conformation capture (Hi-C) data provide insights into the 3D structure of chromosomes, with normalization being a crucial pre-processing step. A common technique for normalization is matrix balancing, which…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
In the realm of high-dimensional data analysis, the estimation of covariance matrices is a fundamental task, and this holds true for interval-valued data as well. However, there is no unified definition for the covariance matrix of…
Calibration of expensive computer models with high-dimensional output fields can be approached via history matching. If the entire output field is matched, with patterns or correlations between locations or time points represented,…
It's regarded as an axiom that a good model is one that compromises between bias and variance. The bias is measured in training cost, while the variance of a (say, regression) model is measure by the cost associated with a validation set.…
We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the…
Employing the framework of regular variation, we propose two decompositions which help to summarize and describel high-dimensional tail dependence. Via transformation, we define a vector space on the positive orthant, yielding the notion of…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
Covariances from categorical variables are defined using a regular simplex expression for categories. The method follows the variance definition by Gini, and it gives the covariance as a solution of simultaneous equations. The calculated…
We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…
While a set of covariance matrices corresponding to different populations are unlikely to be exactly equal they can still exhibit a high degree of similarity. For example, some pairs of variables may be positively correlated across most…
As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and the Bayesian frameworks. Aiming to quantify the uncertainty of the…
We propose a novel variational Bayes approach to estimate high-dimensional vector autoregression (VAR) models with hierarchical shrinkage priors. Our approach does not rely on a conventional structural VAR representation of the parameter…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Nonparametric estimation using uniform-width binning is a standard approach for evaluating the calibration performance of machine learning models. However, existing theoretical analyses of the bias induced by binning are limited to binary…
Explaining generalizations and preventing over-confident predictions are central goals of studies on the loss landscape of neural networks. Flatness, defined as loss invariability on perturbations of a pre-trained solution, is widely…
Many scientific computing problems can be reduced to Matrix-Matrix Multiplications (MMM), making the General Matrix Multiply (GEMM) kernels in the Basic Linear Algebra Subroutine (BLAS) of interest to the high-performance computing…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…