Constrained conditional model

A constrained conditional model (CCM) is a machine learning and inference framework that augments the learning of conditional (probabilistic or discriminative) models with declarative constraints. The constraint can be used as a way to incorporate expressive prior knowledge into the model and bias the assignments made by the learned model to satisfy these constraints. The framework can be used to support decisions in an expressive output space while maintaining modularity and tractability of training and inference. Models of this kind have recently attracted much attention within the natural language processing (NLP) community. Formulating problems as constrained optimization problems over the output of learned models has several advantages. It allows one to focus on the modeling of problems by providing the opportunity to incorporate domain-specific knowledge as global constraints using a first order language. Using this declarative framework frees the developer from low level feature engineering while capturing the problem's domain-specific properties and guarantying exact inference. From a machine learning perspective it allows decoupling the stage of model generation (learning) from that of the constrained inference stage, thus helping to simplify the learning stage while improving the quality of the solutions.…

A constrained conditional model (CCM) is a machine learning and inference framework that augments the learning of conditional (probabilistic or discriminative) models with declarative constraints. The constraint can be used as a way to incorporate expressive prior knowledge into the model and bias the assignments made by the learned model to satisfy these constraints. The framework can be used to support decisions in an expressive output space while maintaining modularity and tractability of training and inference. Models of this kind have recently attracted much attention within the natural language processing (NLP) community. Formulating problems as constrained optimization problems over the output of learned models has several advantages. It allows one to focus on the modeling of problems by providing the opportunity to incorporate domain-specific knowledge as global constraints using a first order language. Using this declarative framework frees the developer from low level feature engineering while capturing the problem's domain-specific properties and guarantying exact inference. From a machine learning perspective it allows decoupling the stage of model generation (learning) from that of the constrained inference stage, thus helping to simplify the learning stage while improving the quality of the solutions. For example, in the case of generating compressed sentences, rather than simply relying on a language model to retain the most commonly used n-grams in the sentence, constraints can be used to ensure that if a modifier is kept in the compressed sentence, its subject will also be kept.

Motivation

Making decisions in many domains (such as natural language processing and computer vision problems) often involves assigning values to sets of interdependent variables where the expressive dependency structure can influence, or even dictate, what assignments are possible. These settings are applicable not only to Structured Learning problems such as semantic role labeling, but also for cases that require making use of multiple pre-learned components, such as summarization, textual entailment and question answering. In all these cases, it is natural to formulate the decision problem as a constrained optimization problem, with an objective function that is composed of learned models, subject to domain- or problem-specific constraints. Constrained conditional models form a learning and inference framework that augments the learning of conditional (probabilistic or discriminative) models with declarative constraints (written, for example, using a first-order representation) as a way to support decisions in an expressive output space while maintaining modularity and tractability of training and inference. These constraints can express either hard restrictions, completely prohibiting some assignments, or soft restrictions, penalizing unlikely assignments. In most applications of this framework in NLP, following, Integer Linear Programming (ILP) was used as the inference framework, although other algorithms can be used for that purpose.

Formal Definition

Given a set of feature functions \{ \phi_i(x,y) \} and a set of constraints \{ C_i (x,y)\} , defined over an input structure x \in X and an output structure y \in Y , a constraint conditional model is characterized by two weight vectors, w and \rho , and is defined as the solution to the following optimization problem: argmax_{y} \sum_i w_i \phi_i (x,y) - \sum \rho_i C_i (x,y) . Each constraint C_i \in C is a boolean mapping indicating if the joint assignment (x,y) violates a constraint, and \rho is the penalty incurred for violating the constraints. Constraints assigned an infinite penalty are known as hard constraints, and represent unfeasible assignments to the optimization problem.

Training paradigms

External links

University of Illinois Cognitive Computation Group Workshop on Integer Linear Programming for Natural Language Processing, NAACL-2009

References

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