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Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs. Existing methods for diffusion models typically require access to model gradients or retraining, limiting their…
Multi-task learning aims to acquire a set of functions, either regressors or classifiers, that perform well for diverse tasks. At its core, the idea behind multi-task learning is to exploit the intrinsic similarity across data sources to…
Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing…
Distributed multi-task adaptive strategies are useful to estimate multiple parameter vectors simultaneously in a collaborative manner. The existed distributed multi-task strategies use diffusion mode of cooperation in which during…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To…
Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive…
When Perturbation Analysis (PA) yields unbiased sensitivity estimators for expected-value performance functions in discrete event dynamic systems, it can be used for performance optimization of those functions. However, when PA is known to…
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…
While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose…
We present the first part of an efficient framework for nonlinear beam dynamics, termed Approximate Invariant Analysis (AIA). The framework is based on the construction of approximate invariants~[Y.~Li, D.~Xu, and Y.~Hao, Phys.\ Rev.\…
Dynamic discrete choice models are widely employed to answer substantive and policy questions in settings where individuals' current choices have future implications. However, estimation of these models is often computationally intensive…
Archetypal analysis (AA) is a matrix decomposition method that identifies distinct patterns using convex combinations of the data points denoted archetypes with each data point in turn reconstructed as convex combinations of the archetypes.…
Hyper-parameter Tuning is among the most critical stages in building machine learning solutions. This paper demonstrates how multi-agent systems can be utilized to develop a distributed technique for determining near-optimal values for any…
Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…
This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational…
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Many problems within personalized medicine and digital health rely on the analysis of continuous-time functional biomarkers and other complex data structures emerging from high-resolution patient monitoring. In this context, this work…