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Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To…

Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be…

In recent years, computational power and data availability breakthroughs have revolutionized our ability to analyze complex physical systems through the inverse problem approach. Data-driven techniques like system identification and machine…

Contemporary time series data often feature objects connected by a social network that naturally induces temporal dependence involving connected neighbours. The network vector autoregressive model is useful for describing the influence of…

This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…

We introduce deep switching auto-regressive factorization (DSARF), a deep generative model for spatio-temporal data with the capability to unravel recurring patterns in the data and perform robust short- and long-term predictions. Similar…

We describe a method to construct directed networks from multivariate time series which has several advantages over the widely accepted methods. This method is based on an information theoretic reduction of linear (auto-regressive) models.…

Identifying the topology underlying a set of time series is useful for tasks such as prediction, denoising, and data completion. Vector autoregressive (VAR) model-based topologies capture dependencies among time series and are often…

This paper introduces the NSB-ARDL (Nonlinear Structural Break Autoregressive Distributed Lag) model, a novel econometric framework designed to capture asymmetric and nonlinear dynamics in macroeconomic time series. Traditional ARDL models,…

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…

The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…

The evolution of epidemiological parameters, such as instantaneous reproduction number Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often…

Recent advances in autoregressive (AR) generative models have produced increasingly powerful systems for media synthesis. Among them, next-scale prediction has emerged as a popular paradigm, where models generate images in a coarse-to-fine…

The objective of transfer learning is to enhance estimation and inference in a target data by leveraging knowledge gained from additional sources. Recent studies have explored transfer learning for independent observations in complex,…

Although Transformer has made breakthrough success in widespread domains especially in Natural Language Processing (NLP), applying it to time series forecasting is still a great challenge. In time series forecasting, the autoregressive…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…

High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…

We analyze a varying-coefficient dynamic spatial autoregressive model with spatial fixed effects. One salient feature of the model is the incorporation of multiple spatial weight matrices through their linear combinations with varying…

Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In…