Related papers: Probabilistic Grammars for Equation Discovery

Statistical model discovery is a challenging search over a vast space of models subject to domain-specific constraints. Efficiently searching over this space requires expertise in modeling and the problem domain. Motivated by the domain…

Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of…

The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through…

Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…

We propose a new statistical model for computational linguistics. Rather than trying to estimate directly the probability distribution of a random sentence of the language, we define a Markov chain on finite sets of sentences with many…

A fundamental challenge in the cognitive sciences is discovering the dynamics that govern behaviour. Take the example of spoken language, which is characterised by a highly variable and complex set of physical movements that map onto the…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…

Automated methods for discovering mechanistic simulator models from observational data offer a promising path toward accelerating scientific progress. Such methods often take the form of agentic-style iterative workflows that repeatedly…

Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to…

Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…

Recent advances in neural symbolic learning, such as DeepProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds,…

Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between…

There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side…

Techniques for plan recognition under uncertainty require a stochastic model of the plan-generation process. We introduce Probabilistic State-Dependent Grammars (PSDGs) to represent an agent's plan-generation process. The PSDG language…

The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression emerged as a…

Probabilistic Law Discovery (PLD) is a logic based Machine Learning method, which implements a variant of probabilistic rule learning. In several aspects, PLD is close to Decision Tree/Random Forest methods, but it differs significantly in…

A causal query will commonly not be identifiable from observed data, in which case no estimator of the query can be contrived without further assumptions or measured variables, regardless of the amount or precision of the measurements of…