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Dynamical systems describe how a physical system evolves over time. Physical processes can evolve faster or slower in different environmental conditions. We use time-warping as rescaling the time in a model of a physical system. This thesis…
We study stochastic motion planning problems which involve a controlled process, with possibly discontinuous sample paths, visiting certain subsets of the state-space while avoiding others in a sequential fashion. For this purpose, we first…
Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies…
The accurate prediction of time-changing covariances is an important problem in the modeling of multivariate financial data. However, some of the most popular models suffer from a) overfitting problems and multiple local optima, b) failure…
Latent variable models have accumulated a considerable amount of interest from the industry and academia for their versatility in a wide range of applications. A large amount of effort has been made to develop systems that is able to extend…
In this paper we study the Total Variation Flow (TVF) in metric random walk spaces, which unifies into a broad framework the TVF on locally finite weighted connected graphs, the TVF determined by finite Markov chains and some nonlocal…
We develop a non-parametric multivariate time series model that remains agnostic on the precise relationship between a (possibly) large set of macroeconomic time series and their lagged values. The main building block of our model is a…
We propose a Leaked Motion Video Predictor (LMVP) to predict future frames by capturing the spatial and temporal dependencies from given inputs. The motion is modeled by a newly proposed component, motion guider, which plays the role of…
The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural…
Motion capture from a monocular video is fundamental and crucial for us humans to naturally experience and interact with each other in Virtual Reality (VR) and Augmented Reality (AR). However, existing methods still struggle with…
Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent…
Finite order Markov models are theoretically well-studied models for dependent discrete data. Despite their generality, application in empirical work when the order is large is rare. Practitioners avoid using higher order Markov models…
Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly…
Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…
We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric science applications. The…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
Linear Parameter-Varying (LPV) systems with jumps and piecewise differentiable parameters is a class of hybrid LPV systems for which no tailored stability analysis and stabilization conditions have been obtained so far. We fill this gap…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…