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In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…

The established technique of eliminating upper or lower parameters in a general hypergeometric series is profitably exploited to create pathways among confluent hypergeometric functions, binomial functions, Bessel functions, and exponential…

We consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in…

Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…

We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…

We propose automated augmented conjugate inference, a new inference method for non-conjugate Gaussian processes (GP) models. Our method automatically constructs an auxiliary variable augmentation that renders the GP model conditionally…

Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first principles. Some of these processes can also be successfully…

We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our…

Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…

We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike…

We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…

We propose to approximate the conditional expectation of a spatial random variable given its nearest-neighbour observations by an additive function. The setting is meaningful in practice and requires no unilateral ordering. It is capable of…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…

In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…

There has been a tremendous growth in publicly available digital video footage over the past decade. This has necessitated the development of new techniques in computer vision geared towards efficient analysis, storage and retrieval of such…