Related papers: Granger Causality Maps for Langevin Systems
Gaussian process classification (GPC) provides a flexible and powerful statistical framework describing joint distributions over function space. Conventional GPCs however suffer from (i) poor scalability for big data due to the full kernel…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
The periodic Gaussian process (PGP) has been increasingly used to model periodic data due to its high accuracy. Yet, computing the likelihood of PGP has a high computational complexity of $\mathcal{O}\left(n^{3}\right)$ ($n$ is the data…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting…
We present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of…
We introduce the spatial disorder-generalized Langevin equation (SD-GLE), a data-driven method for constructing coarse-grained (CG) dynamics in heterogeneous systems. Unlike conventional CG approaches that rely on a mean-field potential,…
We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the…
We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete time grid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component, or node.…
We study Granger causality testing for high-dimensional time series using regularized regressions. To perform proper inference, we rely on heteroskedasticity and autocorrelation consistent (HAC) estimation of the asymptotic variance and…
Capturing the correct dynamics at the Coarse-Grained (CG) scale remains a central challenge in the advancement of systematic CG models for soft matter simulations. The Generalized Langevin Equation (GLE), rooted in the Mori-Zwanzig…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
Applying Gaussian processes (GPs) to very large datasets remains a challenge due to limited computational scalability. Matrix structures, such as the Kronecker product, can accelerate operations significantly, but their application commonly…
This paper is motivated by studies in neuroscience experiments to understand interactions between nodes in a brain network using different types of data modalities that capture different distinct facets of brain activity. To assess…
Dynamical systems comprising of multiple components that can be partitioned into distinct blocks originate in many scientific areas. A pertinent example is the interactions between financial assets and selected macroeconomic indicators,…
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…
A model-free measure of Granger causality in expectiles is proposed, generalizing the traditional mean-based measure to arbitrary positions of the conditional distribution. Expectiles are the only law-invariant risk measures that are both…
In this work we study linear vector stochastic differential equation (SDE) models driven by the generalised hyperbolic (GH) L\'evy process for inference in continuous-time non-Gaussian filtering problems. The GH family of stochastic…
Modelling time-varying and frequency-specific relationships between two brain signals is becoming an essential methodological tool to answer heoretical questions in experimental neuroscience. In this article, we propose to estimate a…