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Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…

This paper proposes a stochastic model predictive control method for linear systems affected by additive Gaussian disturbances that optimizes over disturbance feedback matrices online. Closed-loop satisfaction of probabilistic constraints…

In recent decades, new methods and approaches have been developed for forecasting intermittent demand series. However, the majority of research has focused on point forecasting, with little exploration into probabilistic intermittent demand…

Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…

The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…

In this paper, a new polynomial chaos based framework for analyzing linear systems with probabilistic parameters is presented. Stability analysis and synthesis of optimal quadratically stabilizing controllers for such systems are presented…

In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric…

We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics induces a distribution over random partitions. The community has therefore assumed that the best…

Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…

Chance-constrained programming (CCP) is one of the most difficult classes of optimization problems that has attracted the attention of researchers since the 1950s. In this survey, we focus on cases when only a limited information on the…

Copulas provide a modular parameterization of multivariate distributions that decouples the modeling of marginals from the dependencies between them. Gaussian Mixture Copula Model (GMCM) is a highly flexible copula that can model many kinds…

Recent work has demonstrated that water supply pumps in the drinking water distribution network can be leveraged to provide flexibility to the power network, but existing approaches are computationally demanding and/or overly conservative.…

The variational autoencoder (VAE) is a generative model with continuous latent variables where a pair of probabilistic encoder (bottom-up) and decoder (top-down) is jointly learned by stochastic gradient variational Bayes. We first…

The growing amount of fluctuating renewable infeeds and market liberalization increases uncertainty in power system operation. To capture the influence of fluctuations in operational planning, we model the forecast errors of the uncertain…

This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given…

Probabilistic forecasts in the form of ensemble of scenarios are required for complex decision making processes. Ensemble forecasting systems provide such products but the spatio-temporal structures of the forecast uncertainty is lost when…

Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model,…

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…

Polynomial chaos expansion (PCE) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying…

Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…