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Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…

This paper introduces a novel multi-stage decision-making model that integrates hypothesis testing and dynamic programming algorithms to address complex decision-making scenarios.Initially,we develop a sampling inspection scheme that…

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…

We present a new molecular-dynamics algorithm for integrating the equations of motion for a system of particles interacting with mixed continuous/impulsive forces. This method, which we call Impulsive Verlet, is constructed using operator…

Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…

Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…

Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world…

We introduce a multivariate hidden Markov model to jointly cluster time-series observations with different support, i.e. circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or…

This work is devoted to the clustering of check-in sequences from a geosocial network. We used the mixture Markov chain process as a mathematical model for time-dependent types of data. For clustering, we adjusted the…

In this paper we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the…

We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to…

A goal of systems biology is to understand the dynamics of intracellular systems. Stochastic chemical kinetic models are often utilized to accurately capture the stochastic nature of these systems due to low numbers of molecules. Collecting…

We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…

This work presents a whole-year simulation study on nonlinear mixed-integer Model Predictive Control (MPC) for a complex thermal energy supply system which consists of a heat pump, stratified water storages, free cooling facilities, and a…

In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim we…

We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible…

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…

We propose two approaches for selecting variables in latent class analysis (i.e.,mixture model assuming within component independence), which is the common model-based clustering method for mixed data. The first approach consists in…

The use of machine learning algorithms is an attractive way to produce very fast detector simulations for scattering reactions that can otherwise be computationally expensive. Here we develop a factorised approach where we deal with each…

For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search space information, can achieve huge gains in iterations…