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generative PCFG

A generative probabilistic context-free grammar, often abbreviated as a generative PCFG, is a statistical grammar model that defines a joint probability distribution over sentences and their corresponding syntactic parse trees. It extends standard context-free grammars by assigning a conditional probability to each production rule, such that the probabilities of all expansion options for any given nonterminal symbol sum to one. Under this model, the joint probability of generating a sentence and its derivation tree is calculated as the product of the probabilities of all the grammar rules applied from the root start symbol down to the surface words. Unlike discriminative parsing models that predict the conditional distribution of a structure given an observed sentence, a generative PCFG models the complete stochastic generation of both the grammatical structure and the terminal words, facilitating tasks such as computing sentence likelihoods, training via the inside-outside algorithm, and decoding the most probable parse tree using probabilistic dynamic programming algorithms.

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Support vector machine learning for interdependent and structured output spaces

Support vector machine learning for interdependent and structured output spaces

Ioannis Tsochantaridis, Thomas Hofmann, Thorsten Joachims, Yasemin Altun

OrganizationsBrown UniversityCornell University

Why you should read this

Presents a maximum-margin framework that extends Support Vector Machines to complex, structured prediction tasks and solves the resulting exponential-sized optimization problem via an efficient cutting-plane algorithm.

Learning general functional dependencies is one of the main goals in machine learning. Recent progress in kernel-based methods has focused on designing flexible and powerful input representations. This paper addresses the complementary issue of problems involving complex outputs such as multiple dependent output variables and structured output spaces. We propose to generalize multiclass Support Vector Machine learning in a formulation that involves features extracted jointly from inputs and outputs. The resulting optimization problem is solved efficiently by a cutting plane algorithm that exploits the sparseness and structural decomposition of the problem. We demonstrate the versatility and effectiveness of our method on problems ranging from supervised grammar learning and named-entity recognition, to taxonomic text classification and sequence alignment.

Added

2026-09-25