Related papers: Estimation and Prediction using generalized Wendla…
We consider the problem of estimating small ball probabilities $\mathbb P\{f(G) \leqslant \delta \mathbb Ef(G)\}$ for sub-additive,positively homogeneous functions $f$ with respect to the Gaussian measure. We establish estimates that depend…
This paper first strictly proved that the growth of the second moment of a large class of Gaussian processes is not greater than power function and the covariance matrix is strictly positive definite. Under these two conditions, the maximum…
This paper investigates the properties of the Generalized Covariance (GCov) estimator under misspecification and constraints with application to processes with local explosive patterns, such as causal-noncausal and double autoregressive…
Mobility entropy is proposed to measure predictability of human movements, based on which, the upper and lower bound of prediction accuracy is deduced, but corresponding mathematical expressions of prediction accuracy keeps yet open. In…
The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
Generalized linear models (GLMs) are routinely used for modeling relationships between a response variable and a set of covariates. The simple form of a GLM comes with easy interpretability, but also leads to concerns about model…
Distributed estimation methods have recently been used to compute the maximum likelihood estimate of the precision matrix for large graphical Gaussian models. Our aim, in this paper, is to give a Bayesian estimate of the precision matrix…
A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies all parameters of the distribution are…
This work introduces a novel approach for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are jointly…
This work considers estimation and forecasting in a multivariate, possibly high-dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters…
Aggregated data is commonplace in areas such as epidemiology and demography. For example, census data for a population is usually given as averages defined over time periods or spatial resolutions (cities, regions or countries). In this…
We prove a universality theorem for learning with random features. Our result shows that, in terms of training and generalization errors, a random feature model with a nonlinear activation function is asymptotically equivalent to a…
In this paper, we introduce a class of improved estimators for the mean parameter matrix of a multivariate normal distribution with an unknown variance-covariance matrix. In particular, the main results of [D.Ch\'etelat and M. T.…
The Matern family of covariance functions is currently the most commonly used for the analysis of geostatistical data due to its ability to describe different smoothness behaviors. Yet, in many applications the smoothness parameter is set…
Gaussian inference on smooth manifolds is central to robotics, but exact marginalization and conditioning are generally non-Gaussian and geometry-dependent. We study tangent-linearized Gaussian inference and derive explicit non-asymptotic…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not…
The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact computation of GW alignment is NP hard, entropic regularization…
Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…