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Probabilistic context-free grammars (PCFGs), which are commonly used to generate trees randomly, have been well analyzed theoretically, leading to applications in various domains. Despite their utility, the distributions that the grammar…
Traditional Linear Genetic Programming (LGP) algorithms are based only on the selection mechanism to guide the search. Genetic operators combine or mutate random portions of the individuals, without knowing if the result will lead to a…
We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models. PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to…
Understanding how the structure of language can be learned from sentences alone is a central question in both cognitive science and machine learning. Studies of the internal representations of Large Language Models (LLMs) support their…
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…
Human cognition excels at transcending sensory input and forming latent representations that structure our understanding of the world. While Large Language Model (LLM) agents demonstrate emergent reasoning and decision-making abilities,…
Grammar-based sentence generation has been thoroughly explored for Context-Free Grammars (CFGs), but remains unsolved for recognition-based approaches such as Parsing Expression Grammars (PEGs). Lacking tool support, language designers…
We describe a generative probabilistic model of natural language, which we call HBG, that takes advantage of detailed linguistic information to resolve ambiguity. HBG incorporates lexical, syntactic, semantic, and structural information…
We study the problem of computing the probability that a given stochastic context-free grammar (SCFG), G, generates a string in a given regular language L(D) (given by a DFA, D). This basic problem has a number of applications in…
Syntactic Transformer language models aim to achieve better generalization through simultaneously modeling syntax trees and sentences. While prior work has been focusing on adding constituency-based structures to Transformers, we introduce…
Probabilistic programming languages represent complex data with intermingled models in a few lines of code. Efficient inference algorithms in probabilistic programming languages make possible to build unified frameworks to compute…
We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a…
The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness…
The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness…
The grammars used in grammar-based Genetic Programming (GP) methods have a significant impact on the quality of the solutions generated since they define the search space by restricting the solutions to its syntax. In this work, we propose…
Dependency parsing aims to extract syntactic dependency structure or semantic dependency structure for sentences. Existing methods suffer the drawbacks of lacking universality or highly relying on the auxiliary decoder. To remedy these…
Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this…
Synchronous languages are now a standard industry tool for critical embedded systems. Designers write high-level specifications by composing streams of values using block diagrams. These languages have been extended with Bayesian reasoning…
This paper presents a set of tests and an algorithm for agnostic, data-driven selection among macroeconomic DSGE models inspired by structure learning methods for DAGs. As the log-linear state-space solution to any DSGE model is also a DAG…
Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables.…