Related papers: Bayesian Inference in Recurrent Explicit Duration …

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that…

Classification of sequence data is the topic of interest for dynamic Bayesian models and Recurrent Neural Networks (RNNs). While the former can explicitly model the temporal dependencies between class variables, the latter have a capability…

In this paper, we investigate the parameter identification problem in dynamical systems through a deep learning approach. Focusing mainly on second-order, linear time-invariant dynamical systems, the topic of damping factor identification…

This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

Time series datasets are often composed of a variety of sequences from the same domain, but from different entities, such as individuals, products, or organizations. We are interested in how time series models can be specialized to…

Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods…

Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and…

Probabilistic models such as logistic regression, Bayesian classification, neural networks, and models for natural language processing, are increasingly more present in both undergraduate and graduate statistics and data science curricula…

Sequential processes in real-world often carry a combination of simple subsystems that interact with each other in certain forms. Learning such a modular structure can often improve the robustness against environmental changes. In this…

We propose a generative model for single-channel EEG that incorporates the constraints experts actively enforce during visual scoring. The framework takes the form of a dynamic Bayesian network with depth in both the latent variables and…

Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…

A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional…

This paper explores the duration dynamics modelling under the Autoregressive Conditional Durations (ACD) framework (Engle and Russell 1998). I test different distributions assumptions for the durations. The empirical results suggest…

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…

Early work on narrative modeling used explicit plans and goals to generate stories, but the language generation itself was restricted and inflexible. Modern methods use language models for more robust generation, but often lack an explicit…

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…

Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have…

The aim of this work is to investigate the use of Incrementally Input-to-State Stable ($\delta$ISS) deep Long Short Term Memory networks (LSTMs) for the identification of nonlinear dynamical systems. We show that suitable sufficient…