Related papers: Introduction to Dynamic Linear Models for Time Ser…

While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…

Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a…

Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…

The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…

Time series modeling and analysis have become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the…

Machine learning can provide deep insights into data, allowing machines to make high-quality predictions and having been widely used in real-world applications, such as text mining, visual classification, and recommender systems. However,…

Large language models (LLMs) have been applied in many fields and have developed rapidly in recent years. As a classic machine learning task, time series forecasting has recently been boosted by LLMs. Recent works treat large language…

In this article, we discuss some of the recent developments in applying machine learning (ML) techniques to nonlinear dynamical systems. In particular, we demonstrate how to build a suitable ML framework for addressing two specific…

Time series modeling holds significant importance in many real-world applications and has been extensively studied. While pre-trained foundation models have made impressive strides in the fields of natural language processing (NLP) and…

Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature…

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in Ref. 15 to…

Many, if not most, systems of interest in science are naturally described as nonlinear dynamical systems. Empirically, we commonly access these systems through time series measurements. Often such time series may consist of discrete random…

The Unit-Lindley is a one-parameter family of distributions in $(0,1)$ obtained from an appropriate transformation of the Lindley distribution. In this work, we introduce a class of dynamical time series models for continuous random…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

Current model structural discovery methods for power system dynamics impose rigid priors on the basis functions and variable sets of dynamic models while often neglecting algebraic constraints, thereby limiting the formulation of…

While anomaly detection in static networks has been extensively studied, only recently, researchers have focused on dynamic networks. This trend is mainly due to the capacity of dynamic networks in representing complex physical, biological,…

We review theory and methodology of the class of simultaneous graphical dynamic linear models (SGDLMs) that provide flexibility, parsimony and scalability of multivariate time series analysis. Discussion includes core theoretical aspects…

Synthetic data is essential for training foundation models for time series (FMTS), but most generators assume static correlations, and are typically missing realistic inter-channel dependencies. We introduce DynLMC, a Dynamic Linear Model…

Significant efforts have gone into the development of statistical models for analyzing data in the form of networks, such as social networks. Most existing work has focused on modeling static networks, which represent either a single time…

The staggering amount of streaming time series coming from the real world calls for more efficient and effective online modeling solution. For time series modeling, most existing works make some unrealistic assumptions such as the input…