Related papers: Symbolic Density Estimation: A Decompositional App…
We propose a way of transforming the problem of conditional density estimation into a single nonparametric regression task via the introduction of auxiliary samples. This allows leveraging regression methods that work well in high…
Symbolic Regression (SR) is a machine learning approach that explores the space of mathematical expressions to identify those that best fit a given dataset, balancing both accuracy and simplicity. We apply SR to the study of Gray-Body…
High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most…
This work approximates high-dimensional density functions with an ANOVA-like sparse structure by the mixture of wrapped Gaussian and von Mises distributions. When the dimension $d$ is very large, it is complex and impossible to train the…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
Relational data mining is becoming ubiquitous in many fields of study. It offers insights into behaviour of complex, real-world systems which cannot be modeled directly using propositional learning. We propose Symbolic Graph Embedding…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
Physics-informed Neural Networks (PINNs) have been widely used to obtain accurate neural surrogates for a system of Partial Differential Equations (PDE). One of the major limitations of PINNs is that the neural solutions are challenging to…
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…
Simulation-based techniques such as variants of stochastic Runge-Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and…
Decentralized sparsity learning has attracted a significant amount of attention recently due to its rapidly growing applications. To obtain the robust and sparse estimators, a natural idea is to adopt the non-smooth median loss combined…
Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…
We introduce 'Class Symbolic Regression' (Class SR) a first framework for automatically finding a single analytical functional form that accurately fits multiple datasets - each realization being governed by its own (possibly) unique set of…
Analytical solutions to differential equations offer exact, interpretable insight but are rarely available because discovering them requires expert intuition or exhaustive search of combinatorial spaces. We introduce SIGS, a neuro-symbolic…
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…
Our goal is to develop stable, accurate, and robust semantic scene understanding methods for wide-area scene perception and understanding, especially in challenging outdoor environments. To achieve this, we are exploring and evaluating a…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
Recent self-supervised models have demonstrated equal or better performance than supervised methods, opening for AI systems to learn visual representations from practically unlimited data. However, these methods are typically…
Kolmogorov GAM (K-GAM) networks are shown to be an efficient architecture for training and inference. They are an additive model with an embedding that is independent of the function of interest. They provide an alternative to the…