Related papers: Shape Constraints in Symbolic Regression using Pen…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
Symbolic Regression (SR) is a type of regression analysis to automatically find the mathematical expression that best fits the data. Currently, SR still basically relies on various searching strategies so that a sample-specific model is…
Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap:…
Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications.…
Stochastic constraints, which incorporate both deterministic parameters and random variables, extend classical deterministic constraints by explicitly accounting for uncertainty. These constraints are increasingly prevalent in data science,…
We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of…
Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the…
Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown…
Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search…
Symbolic regression is a machine learning technique, and it has seen many advancements in recent years, especially in genetic programming approaches (GPSR). Furthermore, it has been known for many years that constant optimization of…
Symbolic Regression (SR) is a powerful technique for discovering interpretable mathematical expressions. However, benchmarking SR methods remains challenging due to the diversity of algorithms, datasets, and evaluation criteria. In this…
Symbolic Regression is the study of algorithms that automate the search for analytic expressions that fit data. While recent advances in deep learning have generated renewed interest in such approaches, the development of symbolic…
Symbolic regression (SR) is a powerful technique for discovering symbolic expressions that characterize nonlinear relationships in data, gaining increasing attention for its interpretability, compactness, and robustness. However, existing…