Related papers: Data-driven formulation of natural laws by recursi…

Online decision tree learning algorithms typically examine all features of a new data point to update model parameters. We propose a novel alternative, Reinforcement Learning- based Decision Trees (RLDT), that uses Reinforcement Learning…

We describe a machine learning method for predicting the value of a real-valued function, given the values of multiple input variables. The method induces solutions from samples in the form of ordered disjunctive normal form (DNF) decision…

Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally…

High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise…

Symbolic regression (SR) aims to discover explicit mathematical expressions that explain observed data and is widely used in domains where interpretability is essential. Because interpretability requires expressions to reflect meaningful…

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…

Large Language Models (LLMs) are transformer-based machine learning models that have shown remarkable performance in tasks for which they were not explicitly trained. Here, we explore the potential of LLMs to perform symbolic regression --…

Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…

Designing plausible network models typically requires scholars to form a priori intuitions on the key drivers of network formation. Oftentimes, these intuitions are supported by the statistical estimation of a selection of network evolution…

Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions…

This article will devise data-driven, mathematical laws that generate optimal, statistical classification systems which achieve minimum error rates for data distributions with unchanging statistics. Thereby, I will design learning machines…

Discovering causal relationships between different variables from time series data has been a long-standing challenge for many domains such as climate science, finance, and healthcare. Given the complexity of real-world relationships and…

In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…

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…

Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection…

Accurate and explainable artificial-intelligence (AI) models are promising tools for the acceleration of the discovery of new materials, ore new applications for existing materials. Recently, symbolic regression has become an increasingly…

A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…

We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learned representations meaningful. For this, the typical approach is to regularize the learned…