Related papers: Non-Factorised Variational Inference in Dynamical …
In many real-world dynamical systems, obtaining precise models of system uncertainty remains a challenge. It may be difficult to estimate noise distributions or robustness bounds, especially when the distributions/robustness bounds vary…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…
We propose a discrete-time, finite-state stationary process that can possess long-range dependence. Among the interesting features of this process is that each state can have different long-term dependency, i.e., the indicator sequence can…
We propose a dynamic factor model (DFM) where the latent factors are linked to observed variables with unknown and potentially nonlinear functions. The key novelty and source of flexibility of our approach is a nonparametric observation…
We develop statistical models for samples of distribution-valued stochastic processes featuring time-indexed univariate distributions, with emphasis on functional principal component analysis. The proposed model presents an intrinsic rather…
Deep learning has shown impressive results in a variety of time series forecasting tasks, where modeling the conditional distribution of the future given the past is the essence. However, when this conditional distribution is…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…
This paper discusses the fractional diffusion equation forced by a tempered fractional Gaussian noise. The fractional diffusion equation governs the probability density function of the subordinated killed Brownian motion. The tempered…
Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
This paper focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies…
Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In…
A deterministic temporal process can be determined by its trajectory, an element in the product space of (a) initial condition $z_0 \in \mathcal{Z}$ and (b) transition function $f: (\mathcal{Z}, \mathcal{T}) \to \mathcal{Z}$ often…
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…
We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…
A random walk-based method is proposed to efficiently compute the solution of a large class of fractional in time linear systems of differential equations (linear F-ODE systems), along with the derivatives with respect to the system…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…