The method of principal components is widely used to estimate common factors in large panels of continuous data. This paper first reviews alternative methods that obtain the common factors by solving a Procrustes problem. While these matrix decomposition methods do not specify the probabilistic structure of the data and hence do not permit statistical evaluations of the estimates, they can be e...

Appropriate precautions in the case of flood occurrence often require long lead times (several days) in hydrological forecasting. This in turn implies large uncertainties that are mainly inherited from the meteorological precipitation forecast. Here we present a case study of the extreme flood event of August 2005 in the Swiss part of the Rhine catchment (total area 34 550 km2). This event caus...

This work presents a novel approach to address challenging and still unsolved problem of neural network based load forecasting systems, that despite the significant results reached in terms prediction error reduction, lack suitable indications regarding sample-wise trustworthiness their predictions. The present is framed on Bayesian Mixture Density Networks, enhancing mapping capabilities netwo...

Many existing approaches to collaborative filtering can neither handle very large datasets nor easily deal with users who have very few ratings. In this paper we present the Probabilistic Matrix Factorization (PMF) model which scales linearly with the number of observations and, more importantly, performs well on the large, sparse, and very imbalanced Netflix dataset. We further extend the PMF ...

We introduce Probabilistic Matrix Addition (PMA) for modeling real-valued data matrices by simultaneously capturing covariance structure among rows and among columns. PMA additively combines two latent matrices drawn from two Gaussian Processes (GPs) respectively over rows and columns. The resulting joint distribution over the observed matrix does not factorize over entries, rows, or columns, a...

We introduce Probabilistic Matrix Addition (PMA) for modeling real-valued data matrices by simultaneously capturing covariance structure among rows and among columns. PMA additively combines two latent matrices drawn from two Gaussian Processes respectively over rows and columns. The resulting joint distribution over the observed matrix does not factorize over entries, rows, or columns, and can...

We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide asymptotic results on the behavior of the eigenvalues of random density matrices, including convergence of the empirical spectral measure. We also study the large...