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High-dimensional and sparse (HiDS) matrices are omnipresent in a variety of big data-related applications. Latent factor analysis (LFA) is a typical representation learning method that extracts useful yet latent knowledge from HiDS matrices…
Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into…
Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
We study the estimation of risk-sensitive policies in reinforcement learning problems defined by a Markov Decision Process (MDPs) whose state and action spaces are countably finite. Prior efforts are predominately afflicted by computational…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
Here, we introduce a new class of Lindley generated distributions which results in more flexible model with increasing failure rate (IFR), decreasing failure rate(DFR) and up-side down hazard functions for different choices of parametric…
Vehicular communication channels are characterized by a non-stationary time- and frequency-selective fading process due to rapid changes in the environment. The non-stationary fading process can be characterized by assuming local…
Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such remote sensing tool the speckle interference…
Dynamic invariants are often estimated from experimental time series with the aim of differentiating between different physical states in the underlying system. The most popular schemes for estimating dynamic invariants are capable of…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
This paper investigates the stereographic projection of points along the Nyquist plots of single input single output (SISO) linear time invariant (LTI) systems subject to probabilistic uncertainty. At each frequency, there corresponds a…
Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…
The incidence of rare events in fast-slow systems is investigated via analysis of the large deviation principle (LDP) that characterizes the likelihood and pathway of large fluctuations of the slow variables away from their mean behavior --…
This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…
A new concept, called the spatio-temporal transfer function (STTF), is introduced to characterise a class of linear time-invariant (LTI) spatio-temporal dynamical systems. The spatio-temporal transfer function is a natural extension of the…
This paper concerns computation of optimal policies in which the one-step reward function contains a cost term that models Kullback-Leibler divergence with respect to nominal dynamics. This technique was introduced by Todorov in 2007, where…
Large-scale data collection, from national censuses to IoT-enabled smart homes, routinely gathers dozens of attributes per individual. These multi-attribute datasets are crucial for analytics but pose significant privacy risks. Local…
This paper focuses on multiscale dynamics occurring in steam supply systems. The dynamics of interest are originally described by a distributed-parameter model for fast steam flows over a pipe network coupled with a lumped-parameter model…