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We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…

The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and…

A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…

Bayesian inference is an effective approach for solving statistical learning problems especially with uncertainty and incompleteness. However, inference efficiencies are physically limited by the bottlenecks of conventional computing…

Bayesian Optimization is a popular tool for tuning algorithms in automatic machine learning (AutoML) systems. Current state-of-the-art methods leverage Random Forests or Gaussian processes to build a surrogate model that predicts algorithm…

We provide a method to solve optimization problem when objective function is a complex stochastic simulator of an urban transportation system. To reach this goal, a Bayesian optimization framework is introduced. We show how the choice of…

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…

Techniques to reduce the energy burden of an industrial ecosystem often require solving a multiobjective optimization problem. However, collecting experimental data can often be either expensive or time-consuming. In such cases, statistical…

We implement Bayesian model selection and parameter estimation for the case of fractional Brownian motion with measurement noise and a constant drift. The approach is tested on artificial trajectories and shown to make estimates that match…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

Friction modeling has always been a challenging problem due to the complexity of real physical systems. Although a few state-of-the-art structured data-driven methods show their efficiency in nonlinear system modeling, deterministic…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

We introduce a framework for Bayesian experimental design (BED) with implicit models, where the data-generating distribution is intractable but sampling from it is still possible. In order to find optimal experimental designs for such…

We study various models of random non-crossing configurations consisting of diagonals of convex polygons, and focus in particular on uniform dissections and non-crossing trees. For both these models, we prove convergence in distribution…

The gradient boosting machine is one of the powerful tools for solving regression problems. In order to cope with its shortcomings, an approach for constructing ensembles of gradient boosting models is proposed. The main idea behind the…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values…

State engineering of quantum objects is a central requirement in most implementations. In the cases where the quantum dynamics can be described by analytical solutions or simple approximation models, optimal state preparation protocols have…

A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…