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Multi-output Gaussian process (MGP) is commonly used as a transfer learning method to leverage information among multiple outputs. A key advantage of MGP is providing uncertainty quantification for prediction, which is highly important for…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
We present a method that models the evolution of an unbounded number of time series clusters by switching among an unknown number of regimes with linear dynamics. We develop a Bayesian non-parametric approach using a hierarchical Dirichlet…
This paper studies the unsupervised change point detection problem in time series of networks using the Separable Temporal Exponential-family Random Graph Model (STERGM). Inherently, dynamic network patterns are complex due to dyadic and…
In high-dimensional time series, the component processes are often assembled into a matrix to display their interrelationship. We focus on detecting mean shifts with unknown change point locations in these matrix time series. Series that…
High-dimensional self-exciting point processes have been widely used in many application areas to model discrete event data in which past and current events affect the likelihood of future events. In this paper, we are concerned with…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact…
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…
Recent research on the non-stationary nature of the dynamics of complex systems is reviewed through three specific models. The long time dynamics consists of a slow, decelerating but spasmodic release of generalized intrinsic strain. These…
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…
Dynamic topic models (DTMs) are very effective in discovering topics and capturing their evolution trends in time series data. To do posterior inference of DTMs, existing methods are all batch algorithms that scan the full dataset before…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
We consider an integer-valued time series $Y=(Y_t)_{t\in\Z}$ where the models after a time $k^*$ is Poisson autoregressive with the conditional mean that depends on a parameter $\theta^*\in\Theta\subset\R^d$. The structure of the process…
Continuous-time state estimation is gaining in popularity due to its abilities to provide smooth solutions, handle asynchronous sensors, and interpolate between data points. While there are two main paradigms, parametric (e.g., temporal…
The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for…
Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…