Related papers: Generalized front propagation for spatial stochast…

We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using non-symmetric Dirichlet forms and their convergence in a sense close to the Mosco-convergence, we…

We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…

Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or…

Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via Markov chains. We consider stochastic normalizing flows as…

Normalizing flow (NF) has gained popularity over traditional maximum likelihood based methods due to its strong capability to model complex data distributions. However, the standard approach, which maps the observed data to a normal…

Desertification in dryland ecosystems is considered to be a major environmental threat that may lead to devastating consequences. The concern increases when the system admits two alternative steady states and the transition is abrupt and…

This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor…

While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…

This paper introduces a novel framework for causal inference in spatial economics that explicitly models the stochastic transition from partial to general equilibrium effects. We develop a Denoising Diffusion Probabilistic Model (DDPM)…

Recent work has demonstrated the utility of Random Forest (RF) proximities for various supervised machine learning tasks, including outlier detection, missing data imputation, and visualization. However, the utility of the RF proximities…

Machine learning traditionally assumes that the training and testing data are distributed independently and identically. However, in many real-world settings, the data distribution can shift over time, leading to poor generalization of…

Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient…

Conditional Normalizing Flows (CNFs) are flexible generative models capable of representing complicated distributions with high dimensionality and large interdimensional correlations, making them appealing for structured output learning.…

We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation,…

We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival…

Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…

The scope of this paper is generative modeling through diffusion processes. An approach falling within this paradigm is the work of Song et al. (2021), which relies on a time-reversal argument to construct a diffusion process targeting the…

We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…

Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose…

Federated Learning (FL) is a privacy-preserving machine learning framework facilitating collaborative training across distributed clients. However, its performance is often compromised by data heterogeneity among participants, which can…