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We present the Gaussian process dynamical mixture model (GPDMM) and show its utility in single-example learning of human motion data. The Gaussian process dynamical model (GPDM) is a form of the Gaussian process latent variable model…

Many chemical reactions and molecular processes occur on timescales that are significantly longer than those accessible by direct simulation. One successful approach to estimating dynamical statistics for such processes is to use many short…

The combination of new recording techniques in neuroscience and powerful inference methods recently held the promise to recover useful effective models, at the single neuron or network level, directly from observed data. The value of a…

We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…

Latent dynamics models have emerged as powerful tools for modeling and interpreting neural population activity. Recently, there has been a focus on incorporating simultaneously measured behaviour into these models to further disentangle…

Recent large language models (LLMs) have demonstrated remarkable prediction performance for a growing array of tasks. However, their proliferation into high-stakes domains (e.g. medicine) and compute-limited settings has created a…

This work introduces a novel deep learning-based architecture, termed the Deep Belief Markov Model (DBMM), which provides efficient, model-formulation agnostic inference in Partially Observable Markov Decision Process (POMDP) problems. The…

Discrete time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using any of the several variants of the linear state space model that…

We present the Groupwise Diffusion Model (GDM), which divides data into multiple groups and diffuses one group at one time interval in the forward diffusion process. GDM generates data sequentially from one group at one time interval,…

We explore developing rich semantic models of systems. Specifically, we consider structured causal explanations about state changes in those systems. Essentially, we are developing process-based dynamic knowledge graphs. As an example, we…

Estimating the gradients of stochastic nodes in stochastic computational graphs is one of the crucial research questions in the deep generative modeling community, which enables the gradient descent optimization on neural network…

Within the context of event modeling and understanding, we propose a new method for neural sequence modeling that takes partially-observed sequences of discrete, external knowledge into account. We construct a sequential neural variational…

We introduce the Glauber Generative Model (GGM), a new class of discrete diffusion models, to obtain new samples from a distribution given samples from a discrete space. GGM deploys a discrete Markov chain called the heat bath dynamics (or…

The lack of interpretability is an inevitable problem when using neural network models in real applications. In this paper, an explainable neural network based on generalized additive models with structured interactions (GAMI-Net) is…

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

Efficient skill acquisition, representation, and on-line adaptation to different scenarios has become of fundamental importance for assistive robotic applications. In the past decade, dynamical systems (DS) have arisen as a flexible and…

Accurate learning of system dynamics is becoming increasingly crucial for advanced control and decision-making in engineering. However, real-world systems often exhibit multiple channels and highly nonlinear transition dynamics, challenging…

Dependent generalized extreme value (dGEV) models have attracted much attention due to the dependency structure that often appears in real datasets. To construct a dGEV model, a natural approach is to assume that some parameters in the…

Detection and modeling of change-points in time-series can be considerably challenging. In this paper we approach this problem by incorporating the class of Dynamic Generalized Linear Models (DGLM) into the well know class of Product…

We introduce graph gamma process (GGP) linear dynamical systems to model real-valued multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a…