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An Introduction to Conditional Random Fields

Foundations and Trends R. in Machine Learning Vol. 4, No. 4 (2011) 267 373.. c 2012 C. Sutton and A. McCallum DOI: An Introduction to Conditional Random Fields By Charles Sutton and Andrew McCallum Contents 1 Introduction 268. Implementation Details 271. 2 Modeling 272. Graphical Modeling 272. Generative versus Discriminative Models 278. Linear-chain CRFs 286. General CRFs 290. Feature Engineering 293. Examples 298. Applications of CRFs 306. Notes on Terminology 308. 3 Overview of Algorithms 310. 4 Inference 313. Linear-Chain CRFs 314. Inference in Graphical Models 318. Implementation Concerns 328. 5 Parameter Estimation 331. Maximum Likelihood 332. Stochastic Gradient Methods 341. Parallelism 343. Approximate Training 343. Implementation Concerns 350. 6 Related Work and Future Directions 352. Related Work 352. Frontier Areas 359. Acknowledgments 362. References 363. Foundations and Trends R. in Machine Learning Vol.

classification. This is the approach taken by conditional random fields (CRFs). CRFs are essentially a way of combining the advantages of dis-criminative classification and graphical modeling, combining the ability to compactly model multivariate outputs y with the ability to leverage a large number of input features x for prediction.

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  Multivariate, Random, Conditional, Conditional random

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