Related papers: Dimension Reduction for Symbolic Regression

Vertical Symbolic Regression (VSR) recently has been proposed to expedite the discovery of symbolic equations with many independent variables from experimental data. VSR reduces the search spaces following the vertical discovery path by…

The symbolic dynamics technique is well-known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully…

Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…

The growing number of dimensionality reduction methods available for data visualization has recently inspired the development of quality assessment measures, in order to evaluate the resulting low-dimensional representation independently…

Genetic programming is an often-used technique for symbolic regression: finding symbolic expressions that match data from an unknown function. To make the symbolic regression more efficient, one can also use dimensionally-aware genetic…

Visual analytics now plays a central role in decision-making across diverse disciplines, but it can be unreliable: the knowledge or insights derived from the analysis may not accurately reflect the underlying data. In this dissertation, we…

Symbolic regression is a fundamental tool for discovering interpretable mathematical expressions from data, with broad applications across scientific and engineering domains. Recently, large language models (LLMs) have demonstrated strong…

Symbolic Regression aims to automatically identify compact and interpretable mathematical expressions that model the functional relationship between input and output variables. Most existing search-based symbolic regression methods…

Describing the world behavior through mathematical functions help scientists to achieve a better understanding of the inner mechanisms of different phenomena. Traditionally, this is done by deriving new equations from first principles and…

Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…

Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression…

Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human experts. In particular,…

When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…

Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of…

Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems. Computer algebra…

Compact symbolic expressions have been shown to be more efficient than neural network models in terms of resource consumption and inference speed when implemented on custom hardware such as FPGAs, while maintaining comparable…

We propose SatelliteFormula, a novel symbolic regression framework that derives physically interpretable expressions directly from multi-spectral remote sensing imagery. Unlike traditional empirical indices or black-box learning models,…

We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a…

Symbolic regression via genetic programming is a flexible approach to machine learning that does not require up-front specification of model structure. However, traditional approaches to symbolic regression require the use of protected…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…