Related papers: System Identification with Copula Entropy
We present a method for the identification of continuous, spatiotemporal dynamics from experimental data. We use a model in the form of a partial differential equation and formulate an optimization problem for its estimation from data. The…
Probability density estimation from observed data constitutes a central task in statistics. In this brief, we focus on the problem of estimating the copula density associated to any observed data, as it fully describes the dependence…
The dynamics of a power system with a significant presence of renewable energy resources are growing increasingly nonlinear. This nonlinearity is a result of the intermittent nature of these resources and the switching behavior of their…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
We reformulate and reframe a series of increasingly complex parametric statistical topics into a framework of response-vs-covariate (Re-Co) dynamics that is described without any explicit functional structures. Then we resolve these topics'…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
Discovering pure causes or driver variables in deterministic LTI systems is of vital importance in the data-driven reconstruction of causal networks. A recent work by Kathari and Tangirala, proposed in 2022, formulated the causal discovery…
In this work, we consider the problem of identifying an unknown linear dynamical system given a finite hypothesis class. In particular, we analyze the effect of the excitation input on the sample complexity of identifying the true system…
Optical Character Recognition (OCR) is fundamental to Vision-Language Models (VLMs) and high-quality data generation for LLM training. Yet, despite progress in average OCR accuracy, state-of-the-art VLMs still struggle with detecting…
'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between…
Cross-entropy method model predictive control (CEM--MPC) is a powerful gradient-free technique for nonlinear optimal control, but its performance is often limited by the reliance on random sampling. This conventional approach can lead to…
The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2011) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
Oscillons are long-lived, spherically-symmetric, attractor scalar field configurations that emerge as certain field configurations evolve in time. It has been known for many years that there is a direct correlation between the initial…
The cross-entropy (CE) method is simple and versatile technique for optimization, based on Kullback-Leibler (or cross-entropy) minimization. The method can be applied to a wide range of optimization tasks, including continuous, discrete,…
This paper addresses the challenge of identifying a minimal subset of discrete, independent variables that best predicts a binary class. We propose an efficient iterative method that sequentially selects variables based on which one…
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…
In this paper, we consider two questions about topological entropy of dynamical systems. We propose to resolve these questions by the same approach of using \'etale analogs of topological and algebraic dynamical systems. The first question…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals,…