Related papers: Probabilistic Grammars for Equation Discovery

When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…

Common wisdom has it that the bias of stochastic grammars in favor of shorter derivations of a sentence is harmful and should be redressed. We show that the common wisdom is wrong for stochastic grammars that use elementary trees instead of…

Reasoning is key to many decision making processes. It requires consolidating a set of rule-like premises that are often associated with degrees of uncertainty and observations to draw conclusions. In this work, we address both the case…

The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…

The inside-outside probabilities are typically used for reestimating Probabilistic Context Free Grammars (PCFGs), just as the forward-backward probabilities are typically used for reestimating HMMs. I show several novel uses, including…

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least…

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…

Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines. However, discovering such insightful equations from data presents significant challenges due to the…

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…

Causal modeling has long been an attractive topic for many researchers and in recent decades there has seen a surge in theoretical development and discovery algorithms. Generally discovery algorithms can be divided into two approaches:…

Scientists have long aimed to discover meaningful formulae which accurately describe experimental data. A common approach is to manually create mathematical models of natural phenomena using domain knowledge, and then fit these models to…

Machine learning algorithms such as linear regression, SVM and neural network have played an increasingly important role in the process of scientific discovery. However, none of them is both interpretable and accurate on nonlinear datasets.…

Recent research in molecular discovery has primarily been devoted to small, drug-like molecules, leaving many similarly important applications in material design without adequate technology. These applications often rely on more complex…

Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y =…

The primary use of any probabilistic model involving a set of random variables is to run inference and sampling queries on it. Inference queries in classical probabilistic models is concerned by the computation of marginal or conditional…

Autoregressive models use chain rule to define a joint probability distribution as a product of conditionals. These conditionals need to be normalized, imposing constraints on the functional families that can be used. To increase…

Understanding how systems evolve over time often requires discovering the differential equations that govern their behavior. Automatically learning these equations from experimental data is challenging when the data are noisy or limited,…

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically…

We present new results on the relation between purely symbolic context-free parsing strategies and their probabilistic counter-parts. Such parsing strategies are seen as constructions of push-down devices from grammars. We show that…

Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…