Multi-task learning aims at transferring knowledge between similar tasks. The multi-task Gaussian process framework of Bonilla et al. models (incomplete) responses of C data points for R tasks (e.g., the responses are given by an R×C matrix) by using a Gaussian process; the covariance function takes its form as the product of a covariance function defined on input-specific features and an inter...

This paper generalizes the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar Gaussian Random Field (GRF) models, to the multivariate, second-order stationary case under a separable covariance function. Theoretical convergence rates for the estimated covariance matrix and for the estimated parameters of the correlation function are establ...

We consider the problem of specifying the design-based error covariance structure in small area modeling with survey data because of too many unknown design parameters. As a compromise, it is customary to treat the estimated covariance as known although undesirable because of its instability, i.e., relative variance of this estimate could be high, and as a result, it could cause serious underes...

Abstract A two-step estimator of a nonparametric regression function via Kernel regularized least squares (KRLS) with parametric error covariance is proposed. The KRLS, not considering any information in the covariance, improved by incorporating allowing for both heteroskedasticity and autocorrelation, estimating function. two step procedure used, where first step, estimated using KRLS residual...

We propose a method to discriminatively train acoustic models with sparse inverse covariance (precision) matrices in order to improve the model robustness when training data is insufficient. Acoustic models with sparse inverse covariance matrices were previously proposed to address the problem of over-fitting when training data is inadequate. Since many of the entries of the inverse covariance ...

rational functions are of great interest to engineers and geoscientists. the rational polynomial coefficient (rpc) model as a generalized sensor model has been introduced as an alternative for the rigorous sensor model of the satellite imaging. numerical instability of normal equations is the only single obstacle to the implementation of these functions. practically, estimating rational functio...