Constrained Conditional Model

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A Constrained Conditional Model (CCM) is a machine learning and inference framework that refers to augmenting 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.

Models of this kind have recently attracted much attention within the 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.


Motivation

Making decisions in many learning domains (such as natural language processing and computer vision problems) often involve 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 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 is 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. In most applications of this framework in NLP, following <ref>Dan Roth and Wen-tau Yih, "A Linear Programming Formulation for Global Inference in Natural Language Tasks." CoNLL, (2004).</ref>, Integer Linear Programming (ILP) was used as the inference framework, although other algorithms can be used for that purpose.


Training Paradigms

Learning Local VS. Global Models

The objective function used by CCMs can be decomposed and learned in several ways, ranging from a complete joint training of the model along with the constraints to completely decoupling between the learning and the inference stage. In the latter case, several local models are learned independently and the dependency between these models is considered only at decision time via a global decision process. The advantages of each approach are discussed in <ref>Vasin Punyakanok and Dan Roth and Wen-Tau Yih and Dav Zimak, "Learning and Inference over Constrained Output." IJCAI, (2005).</ref>, which studies the two training paradigms: (1) local models: L+I (learning+inference) and (2) global model: IBT (Inference based training), and shows both theoretically and experimentally that while IBT (joint training) is best in the limit, under some conditions (basically, ”good” components”) L+I can generalize better.

Minimally Supervised CCM

CCM can help reduce supervision by using domain knowledge (expressed as constraints) to drive learning. These setting were studied in <ref>Ming-Wei Chang and Lev Ratinov and Dan Roth, "Guiding Semi-Supervision with Constraint-Driven Learning." ACL, (2007).</ref> and <ref>Ming-Wei Chang and Lev Ratinov and Dan Roth, "Constraints as Prior Knowledge." ICML Workshop on Prior Knowledge for Text and Language Processing}, (2008).</ref>. These works introduce semi-supervised Constraints Driven Learning (CODL) and show that by incorporating domain knowledge the performance of the learned model improves significantly.

Learning over Latent Representations

CCMs were also applied to latent learning frameworks, where the learning problem is defined over a latent representation layer. Since the notion of a correct representation is inherently ill-defined no gold-labeled data regarding the representation decision is available to the learner. Identifying the correct (or optimal) learning representation is viewed as a structured prediction process and therefore modeled as a CCM. This problem was studied by several papers, in both supervised <ref>Ming-Wei Chang and Dan Goldwasser and Dan Roth and Vivek Srikumar, " Discriminative Learning over Constrained Latent Representations." NAACL, (2010).</ref> and unsupervised <ref>Ming-Wei Chang Dan Goldwasser Dan Roth and Yuancheng Tu, "Unsupervised Constraint Driven Learning For Transliteration Discovery." NAACL, (2009).</ref> settings and in all cases showed that explicitly modeling the interdependencies between representation decisions via constraints results in an improved performance.

CCM for Natural Language Processing Applications

The advantages of the CCM declarative formulation and the availability of off-the-shelf solvers have led to a large variety of natural language processing tasks being formulated within framework, including semantic role labeling <ref>Vasin Punyakanok, Dan Roth, Wen-tau Yih and Dav Zimak, "Semantic Role Labeling via Integer Linear Programming Inference." COLING, (2004).</ref>, syntactic parsing <ref>Sagae, K. and Miyao, Y. and Tsujii, J., "HPSG Parsing with Shallow Dependency Constraints." ACL, (2007).</ref>, coreference resolution <ref>P. Denis and J. Baldridge, "Joint Determination of Anaphoricity and Coreference Resolution using Integer Programming." NAACL-HLT, (2007).</ref>, summarization <ref>J. Clarke and M. Lapata, "Global Inference for Sentence Compression: An Integer Linear Programming Approach." Journal of Artificial Intelligence Research (JAIR), (2008).</ref>, transliteration <ref>D. Goldwasser and D. Roth, "Transliteration as Constrained Optimization." EMNLP, (2008).</ref> and joint information extraction <ref>D. Roth and W. Yih}, [http://l2r.cs.uiuc.edu/~danr/Papers/RothYi07.pdf "Global Inference for Entity and Relation Identification via a Linear Programming Formulation."] Introduction to Statistical Relational Learning,MIT Press, (2007).</ref>.

Most of these works use an Integer Linear Programming solver to solve the decision problem. Although theoretically solving an Integer Linear Program is exponential in the size of the decision problem in practice using state-of-the-art solvers and sophisticated formulations <ref>André F. T. Martins, Noah A. Smith, and Eric P. Xing , "Concise Integer Linear Programming Formulations for Dependency Parsing ." ACL, (2009).</ref> large scale problems can be solved efficiently.

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References

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