Related papers: On the connections between the spatial Lambda-Flem…
We study the Tree Builder Random Walk: a randomly growing tree, built by a walker as she is walking around the tree. Namely, at each time $n$, she adds a leaf to her current vertex with probability $p_n \asymp n^{-\gamma}$, $\gamma\in…
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. Aldous's Brownian continuum random tree, the…
Large climate-model ensembles are computationally expensive; yet many downstream analyses would benefit from additional, statistically consistent realizations of spatiotemporal climate variables. We study a generative modeling approach for…
Pedestrian trajectory prediction is a prominent research track that has advanced towards modelling of crowd social and contextual interactions, with extensive usage of Long Short-Term Memory (LSTM) for temporal representation of walking…
Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…
A new dynamic latent space eigenmodel (LSM) is proposed for weighted temporal networks. The model accommodates integer-valued weights, excess of zeros, time-varying node positions (features), and time-varying network sparsity. The latent…
Despite rapid progress, pretrained vision-language models still struggle when answers depend on tiny visual details or on combining clues spread across multiple regions, as in documents and compositional queries. We address this by framing…
The prediction of critical transitions, such as extinction events, is vitally important to preserving vulnerable populations in the face of a rapidly changing climate and continuously increasing human resource usage. Predicting such events…
Statistical models often assume that data are generated near a structured, smooth, or low-dimensional set. A common approach is to use Bayesian latent variable models, in which each observation is associated with a latent coordinate on the…
Missing data imputation is a critical challenge in various domains, such as healthcare and finance, where data completeness is vital for accurate analysis. Large language models (LLMs), trained on vast corpora, have shown strong potential…
The classical multilevel model fails to capture the proximity effect in epidemiological studies, where subjects are nested within geographical units. Multilevel Conditional Autoregressive models are alternatives to help explain the spatial…
Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational…
Using the matrix-forest theorem and the Parisi-Sourlas trick we formulate and solve a one-matrix model with non-polynomial potential which provides perturbation theory for massive spinless fermions on dynamical planar graphs. This is a…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
Most useful weather prediction for the public is near the surface. The processes that are most relevant for near-surface weather prediction are also those that are most interactive and exhibit positive feedback or have key role in energy…
The main goal of machine learning (ML) is to study and improve mathematical models which can be trained with data provided by the environment to infer the future and to make decisions without necessarily having complete knowledge of all…
We survey the theory and applications of mating-of-trees bijections for random planar maps and their continuum analog: the mating-of-trees theorem of Duplantier, Miller, and Sheffield (2014). The latter theorem gives an encoding of a…
The generative modeling of data on manifolds is an important task, for which diffusion models in flat spaces typically need nontrivial adaptations. This article demonstrates how a technique called `trivialization' can transfer the…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…