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Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
In this paper a first order analytical system of difference equations is considered. For an asymptotically stable fixed point x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when the matrix…
The Deferred Acceptance Algorithm (DAA) is the most widely accepted and used algorithm to match students, workers, or residents to colleges, firms or hospitals respectively. In this paper, we consider for the first time, the complexity of…
Multivariate function approximation is a fundamental problem in machine learning. Classic multivariate function approximations rely on hand-crafted basis functions (e.g., polynomial basis and Fourier basis), which limits their approximation…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may…
While multiagent systems have shown promise for tackling complex tasks via specialization, finetuning multiple agents simultaneously faces two key challenges: (1) credit assignment across agents, and (2) sample efficiency of expensive…
Car-following behavior modeling is critical for understanding traffic flow dynamics and developing high-fidelity microscopic simulation models. Most existing impulse-response car-following models prioritize computational efficiency and…
Agent technology is a software paradigm that permits to implement large and complex distributed applications. In order to assist the development of multi-agent systems, agent-oriented methodologies (AOM) have been created in the last years…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we…
"Deep Archetypal Analysis" generates latent representations of high-dimensional datasets in terms of fractions of intuitively understandable basic entities called archetypes. The proposed method is an extension of linear "Archetypal…
We introduce a generalized \textit{Probabilistic Approximate Optimization Algorithm (PAOA)}, a classical variational Monte Carlo framework that extends and formalizes prior work by Weitz \textit{et al.}~\cite{Combes_2023}, enabling…
Many complex systems can be modeled as multiagent systems in which the constituent entities (agents) interact with each other. The global dynamics of such a system is determined by the nature of the local interactions among the agents.…
One's ability to learn a generative model of the world without supervision depends on the extent to which one can construct abstract knowledge representations that generalize across experiences. To this end, capturing an accurate…
In this paper, auto-associative models are proposed as candidates to the generalization of Principal Component Analysis. We show that these models are dedicated to the approximation of the dataset by a manifold. Here, the word "manifold"…
Consider a dynamical system $u \mapsto x, \dot{x} = f_{nl}(x,u)$ where $f_{nl}$ is a nonlinear (convex or nonconvex) function, or a combination of nonlinear functions that can eventually switch. We present, in this preliminary work, a…
We propose a novel framework, termed Fourier-Activated Adapter (FAA), for parameter-efficient fine-tuning of large pre-trained language models. By incorporating random Fourier features into lightweight adapter modules, FAA decomposes…