Related papers: Symbolic Density Estimation: A Decompositional App…
Statement autoformalization acts as a critical bridge between human mathematics and formal mathematics by translating natural language problems into formal language. While prior works have focused on data synthesis and diverse training…
We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP.…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
The estimation of probability density functions is a fundamental problem in science and engineering. However, common methods such as kernel density estimation (KDE) have been demonstrated to lack robustness, while more complex methods have…
The 21 cm signal from the Epoch of Reionization will be observed with the up-coming Square Kilometer Array (SKA). SKA should yield a full tomography of the signal which opens the possibility to explore its non-Gaussian properties. How can…
Symbolic regression (SR) is a powerful machine learning approach that searches for both the structure and parameters of algebraic models, offering interpretable and compact representations of complex data. Unlike traditional regression…
In the rapidly advancing field of image generation, Visual Auto-Regressive (VAR) modeling has garnered considerable attention for its innovative next-scale prediction approach. This paradigm offers substantial improvements in efficiency,…
We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the…
This paper presents QDSR, an advanced symbolic Regression (SR) system that integrates genetic programming (GP), a quality-diversity (QD) algorithm, and a dimensional analysis (DA) engine. Our method focuses on exact symbolic recovery of…
Representation learning and unsupervised learning are two central topics of machine learning and signal processing. Deep learning is one of the most effective unsupervised representation learning approach. The main contributions of this…
We explain how to use Kolmogorov Superposition Theorem (KST) to break the curse of dimensionality when approximating a dense class of multivariate continuous functions. We first show that there is a class of functions called…
This paper investigates the estimation of the self-similarity parameter in fractional processes. We re-examine the Kolmogorov-Smirnov (KS) test as a distribution-based method for assessing self-similarity, emphasizing its robustness and…
Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…
While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
Symbolic regression (SR) is a data analysis problem where we search for the mathematical expression that best fits a numerical dataset. It is a global optimization problem. The most popular approach to SR is by genetic programming (SRGP).…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
The highly nonlinear degradation process, complex physical interactions, and various sources of uncertainty render single-image Super-resolution (SR) a particularly challenging task. Existing interpretable SR approaches, whether based on…
There are many problems in physics, biology, and other natural sciences in which symbolic regression can provide valuable insights and discover new laws of nature. A widespread Deep Neural Networks do not provide interpretable solutions.…
Identifying the mathematical relationships that best describe a dataset remains a very challenging problem in machine learning, and is known as Symbolic Regression (SR). In contrast to neural networks which are often treated as black boxes,…