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Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations
Parallel Gaussian Process Regression Low-Rank Covariance Matrix Approximations
2013/6/14
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due ...
Covariance inflation in the ensemble Kalman filter: a residual nudging perspective and some implications
Covariance inflation ensemble Kalman filter residual nudging perspective some implications
2013/6/17
This note examines the influence of covariance inflation on the distance between the measured observation and the simulated (or predicted) observation with respect to the state estimate. In order for ...
Evolution of Covariance Functions for Gaussian Process Regression using Genetic Programming
Gaussian Process Genetic Programming Structure Identification
2013/6/14
In this contribution we describe an approach to evolve composite covariance functions for Gaussian processes using genetic programming. A critical aspect of Gaussian processes and similar kernel-based...
Stable Estimation of a Covariance Matrix Guided by Nuclear Norm Penalties
Covariance estimation Regularization Condition number Canonical correlation analysis Discriminant analysis Clustering
2013/6/14
Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-c...
Relative Performance of Expected and Observed Fisher Information in Covariance Estimation for Maximum Likelihood Estimates
Relative Performance Expected and Observed Fisher Information Covariance Estimation Maximum Likelihood Estimates
2013/6/13
Maximum likelihood estimation is a popular method in statistical inference. As a way of assessing the accuracy of the maximum likelihood estimate (MLE), the calculation of the covariance matrix of the...
High Dimensional Covariance Matrix Estimation in Approximate Factor Models
sparse estimation thresholding cross-sectional correlation common factors idiosyncratic seemingly unrelated regression
2011/6/20
The variance covariance matrix plays a central role in the inferential theories
of high dimensional factor models in finance and economics. Popular
regularization methods of directly exploiting spar...
Geometric sensitivity of random matrix results: consequences for shrinkage estimators of covariance and related statistical methods
random matrix related statistical shrinkage estimators
2011/6/16
Shrinkage estimators of covariance are an important tool in modern applied and theoretical statistics.
They play a key role in regularized estimation problems, such as ridge regression (aka Tykhonov
...
First of all we want to thank the editor, Michael Newton, for leading the review and discussion of our work.
A Random Matrix--Theoretic Approach to Handling Singular Covariance Estimates
Random Matrix--Theoretic Approach Handling Singular Covariance Estimates
2010/10/19
In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identica...
Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation...