Related papers: Manifold-constrained Gaussian process inference fo…
A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of…
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…
System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…
Computer simulations of differential equations require a time discretization, which inhibits to identify the exact solution with certainty. Probabilistic simulations take this into account via uncertainty quantification. The construction of…
Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…
In multivariate time series analysis, understanding the underlying causal relationships among variables is often of interest for various applications. Directed acyclic graphs (DAGs) provide a powerful framework for representing causal…
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…
We investigate the channel estimation for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. We revisit the information geometry approach (IGA) for massive MIMO-OFDM channel estimation. By…
Gait recognition aims to distinguish different walking patterns by analyzing video-level human silhouettes, rather than relying on appearance information. Previous research on gait recognition has primarily focused on extracting local or…
Event-based cameras asynchronously capture individual visual changes in a scene. This makes them more robust than traditional frame-based cameras to highly dynamic motions and poor illumination. It also means that every measurement in a…
Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying, expensive, noisy black-box function $f$. However, most of the asymptotic guarantees offered by TVBO algorithms rely on the assumption that…
Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…
We propose classical interferometry with low-intensity thermal radiation for the estimation of nonclassical independent Gaussian processes in material samples. We generally determine the mean square error of the phase-independent parameters…
Estimating time-varying graphical models are of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies,…
We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…
A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…
The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from noisy and sparse measurements. Here, we introduce…