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Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
In this paper, we are concerned with nonparametric inference on the volatility of volatility process in stochastic volatility models. We construct several estimators for its integrated version in a high-frequency setting, all based on…
Model Predictive Control (MPC) has shown to be a successful method for many applications that require control. Especially in the presence of prediction uncertainty, various types of MPC offer robust or efficient control system behavior. For…
Multivariate correlation analysis plays an important role in various fields such as statistics, economics, and big data analytics. In this paper, we propose a pair of measures, the unsigned correlation coefficient (UCC) and the unsigned…
In the present paper, the models of structural analysis and evaluation of efficiency indicators (reliability, fault tolerance, viability, and flexibility) of a multi core processor with variable structure, equipped with multi functional…
Decoupling systems into independently evolving components has a long history of simplifying seemingly complex systems. They enable a better understanding of the underlying dynamics and causal structures while providing more efficient means…
Independent Component Analysis (ICA) aims to recover independent latent variables from observed mixtures thereof. Causal Representation Learning (CRL) aims instead to infer causally related (thus often statistically dependent) latent…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
This paper is motivated by modeling the cycle-to-cycle variability associated with the resistive switching operation behind memristors. As the data are by nature curves, functional principal component analysis is a suitable candidate to…
The use of factor stochastic volatility models requires choosing the number of latent factors used to describe the dynamics of the financial returns process; however, empirical evidence suggests that the number and makeup of pertinent…
Computational mechanisms for uncertainty management must support interactive and incremental problem formulation, inference, hypothesis testing, and decision making. However, most current uncertainty inference systems concentrate primarily…
The variational quantum eigensolver has been proposed as a low-depth quantum circuit that can be employed to examine strongly correlated systems on today's noisy intermediate-scale quantum computers. We examine details associated with the…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
An important problem in many domains is to predict how a system will respond to interventions. This task is inherently linked to estimating the system's underlying causal structure. To this end, Invariant Causal Prediction (ICP) (Peters et…
Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both…
We develop a time-dependent variational Monte Carlo (t-VMC) method for quantum dynamics of strongly correlated electrons. The t-VMC method has been recently applied to bosonic systems and quantum spin systems. Here, we propose a…
We propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives. Our model extends the…
The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a…
In this article, we introduce the mean independent component analysis for multivariate time series to reduce the parameter space. In particular, we seek for a contemporaneous linear transformation that detects univariate mean independent…