Related papers: Neural Continuous-Discrete State Space Models for …

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…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…

Continuous-time (CT) modeling has proven to provide improved sample efficiency and interpretability in learning the dynamical behavior of physical systems compared to discrete-time (DT) models. However, even with numerous recent…

Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under-explored. In…

We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et…

Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…

State-space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Several…

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…

Modern technological advances have expanded the scope of applications requiring analysis of large-scale datastreams that comprise multiple indefinitely long time series. There is an acute need for statistical methodologies that perform…

Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In…

Modern time series data often display complex nonlinear dependencies along with irregular regime-switching behaviors. These features present technical challenges in modeling, inference, and in offering insightful understanding into the…

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world…

Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…

Irregularly sampled time series with missing values are often observed in multiple real-world applications such as healthcare, climate and astronomy. They pose a significant challenge to standard deep learning models that operate only on…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…