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Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…
This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…
Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…
State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…
Inference for streaming time-series is tightly coupled with the problem of Bayesian on-line state and parameter inference. In this paper we will introduce Dynamic Generalised Linear Models, the class of models often chosen to model…
We develop algorithms for performing semiparametric regression analysis in real time, with data processed as it is collected and made immediately available via modern telecommunications technologies. Our definition of semiparametric…
We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variables. The high computational cost in running large ensemble…
This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…
Learning the relationships between various entities from time-series data is essential in many applications. Gaussian graphical models have been studied to infer these relationships. However, existing algorithms process data in a batch at a…
We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a…
We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function…
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…