Related papers: A Riemannian Approach to Multivariate Geostatistic…

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…

The Linear Model of Co-regionalization (LMC) is a very general multitask gaussian process model for regression or classification. While its expressiveness and conceptual simplicity are appealing, naive implementations have cubic complexity…

This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…

Matrix-valued covariance functions are crucial to geostatistical modeling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overlay restrictive and has been considered as unrealistic…

Geodesic Monte Carlo (gMC) is a powerful algorithm for Bayesian inference on non-Euclidean manifolds. The original gMC algorithm was cleverly derived in terms of its progenitor, the Riemannian manifold Hamiltonian Monte Carlo (RMHMC). Here,…

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…

Deep Neural Networks are widely used for solving complex problems in several scientific areas, such as speech recognition, machine translation, image analysis. The strategies employed to investigate their theoretical properties mainly rely…

Single-cell data analysis seeks to characterize cellular heterogeneity based on high-dimensional gene expression profiles. Conventional approaches represent each cell as a vector in Euclidean space, which limits their ability to capture…

Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention…

Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…

This paper introduces a method for studying the correlation structure of a range of responses modelled by a multivariate generalised linear mixed model (MGLMM). The methodology requires the existence of clusters of observations and that…

We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

We construct a generalization of the Ornstein-Uhlenbeck processes on the cone of covariance matrices endowed with the Log-Euclidean and the Affine-Invariant metrics. Our development exploits the Riemannian geometric structure of symmetric…

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…

Linear discriminant analysis (LDA) is a widely used algorithm in machine learning to extract a low-dimensional representation of high-dimensional data, it features to find the orthogonal discriminant projection subspace by using the Fisher…

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…

Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random…

This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic on a suitable Riemannian manifold. We then combine the notion…