Genome-wide association studies have proven to be essential for understanding the genetic basis of disease. However, many complex traits—personality traits, facial features, disease subtyping—are inherently high-dimensional, impeding simple approaches to association mapping. We developed a nonparametric Bayesian reduced rank regression model for multi-SNP, multi-trait association mapping that d...

In this article we propose a generalization of the determinant minimization criterion. The problem of minimizing the determinant of a matrix expression has implicit assumptions that the objective matrix is always nonsingular. In case of singular objective matrix the determinant would be zero and the minimization problem would be meaningless. To be able to handle all possible cases we generalize...

This paper addresses the issue of the blind extraction of a second-order cyclostationary source drowned by an unknown number of interferences and additive noise. It first reviews two recently developed methods based respectively on a subspace decomposition of the observed signals via their cyclic statistics and on multiple cyclic regression (MCR). It then proposes a unifying and refined approac...

This thesis deals with three estimation problems motivated by spatial signal processing using arrays of sensors. All three problems are approached using tools from estimation theory, including asymptotical analysis of performance and Cramér-Rao lower bound; Monte Carlo methods are used to evaluate small sample performance. The first part of this thesis treats direction of arrival estimation for...

BACKGROUND Reduced rank regression (RRR) combines exploratory analysis with a-priori knowledge by including risk factors in the model. Dietary patterns, derived from RRR analysis, can be interpreted by the chosen risk factor profile and give an indication of positive or adverse health effects for a specific disease. Our aim was to assess the stability of dietary patterns derived by RRR over tim...

This paper proposes a new methodology to build composite coincident and leading indexes. Based on a formal definition that requires that the first differences of the leading index is the best linear predictor of the first differences of the coincident index, it is shown that the notion of polynomial serial correlation common features can be used to build these composite variables. Concepts and ...

We consider a multivariate linear response regression in which the number of responses and predictors is large and comparable with the number of observations, and the rank of the matrix of regression coefficients is assumed to be small. We study the distribution of singular values for the matrix of regression coefficients and for the matrix of predicted responses. For both matrices, it is found...

Change detection is an important part of image interpretation and automated geographical data collection. In this paper we show a reduced rank regression mixture model for the verification of image changes detected by a human operator. Maximum likelihood estimators are used to learn the operator behaviour. Then, the operator uses the trained system to validate the image changes found. Computati...

MOTIVATION A typical genome-wide association study searches for associations between single nucleotide polymorphisms (SNPs) and a univariate phenotype. However, there is a growing interest to investigate associations between genomics data and multivariate phenotypes, for example, in gene expression or metabolomics studies. A common approach is to perform a univariate test between each genotype-...

If two wide sense stationary time series are correlated then one can be used to predict the other. The reduced rank Wiener filter is the rank constrained linear operator which maps the current value of one time series to an estimate of the current value of the other time series in an optimal way. A closed form solution exists for the reduced rank Wiener filter. This paper studies the problem of...