Related papers: Deep Variational Inference Symbolic Regression
We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is…
Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great…
Digital twins (DTs), serving as the core enablers for real-time monitoring and predictive maintenance of complex cyber-physical systems, impose critical requirements on their virtual models: high predictive accuracy, strong…
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…
Discrete probability laws underpin statistical modeling, yet the catalog of interpretable distributions has expanded only gradually through centuries of case-by-case mathematical derivations. We introduce symbolic density estimation (SDE),…
We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…
Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of…
Symbolic regression is a powerful tool for knowledge discovery, enabling the extraction of interpretable mathematical expressions directly from data. However, conventional symbolic discovery typically follows an end-to-end, "one-step"…
Recently, several algorithms for symbolic regression (SR) emerged which employ a form of multiple linear regression (LR) to produce generalized linear models. The use of LR allows the algorithms to create models with relatively small error…
In the context of supervised learning of a function by a neural network, we claim and empirically verify that the neural network yields better results when the distribution of the data set focuses on regions where the function to learn is…
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…
Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems so called recurrent models are used. In this article we…
Similarity analysis is one of the crucial steps in most fMRI studies. Representational Similarity Analysis (RSA) can measure similarities of neural signatures generated by different cognitive states. This paper develops Deep…
Variational inference has been widely used in machine learning literature to fit various Bayesian models. In network analysis, this method has been successfully applied to solve the community detection problems. Although these results are…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new…
Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
Generally, the performance of deep neural networks (DNNs) heavily depends on the quality of data representation learning. Our preliminary work has emphasized the significance of deep representation learning (DRL) in the context of speech…
A conventional Bayesian approach to prediction uses the posterior distribution to integrate out parameters in a density for unobserved data conditional on the observed data and parameters. When the true posterior is intractable, it is…