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Probabilistic Models for Segmenting and Labeling Sequence Data Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data John Lafferty†∗ [email protected] Andrew McCallum∗† [email protected] Fernando Pereira∗‡ [email protected] ∗WhizBang! Labs–Research, 4616 Henry Street, Pittsburgh, PA 15213 USA †School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 USA ‡Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA 19104 USA Abstract mize the joint likelihood of training examples. To define a joint probability over observation and label sequences, We present conditional random fields, a frame- a generative model needs to enumerate all possible ob- work for building probabilistic models to seg- servation sequences, typically requiring a representation ment and label sequence data. Conditional ran- in which observations are task-appropriate atomic entities, dom fields offer several advantages over hid- such as words or nucleotides. In particular, it is not practi- den Markov models and stochastic grammars cal to represent multiple interacting features or long-range for such tasks, including the ability to relax dependencies of the observations, since the inference prob- strong independence assumptions made in those lem for such models is intractable. models. Conditional random fields also avoid a fundamental limitation of maximum entropy This difficulty is one of the main motivations for looking at Markov models (MEMMs) and other discrimi- conditional models as an alternative. A conditional model native Markov models based on directed graph- specifies the probabilities of possible label sequences given ical models, which can be biased towards states an observation sequence. Therefore, it does not expend with few successor states. We present iterative modeling effort on the observations, which at test time parameter estimation algorithms for conditional are fixed anyway. Furthermore, the conditional probabil- random fields and compare the performance of ity of the label sequence can depend on arbitrary, non- the resulting models to HMMs and MEMMs on independent features of the observation sequence without synthetic and natural-language data. forcing the model to account for the distribution of those dependencies. The chosen features may represent attributes at different levels of granularity of the same observations 1. Introduction (for example, words and characters in English text), or aggregate properties of the observation sequence (for in- The need to segment and label sequences arises in many stance, text layout). The probability of a transition between different problems in several scientific fields. Hidden labels may depend not only on the current observation, Markov models (HMMs) and stochastic grammars are well but also on past and future observations, if available. In understood and widely used probabilistic models for such contrast, generative models must make very strict indepen- problems. In computational biology, HMMs and stochas- dence assumptions on the observations, for instance condi- tic grammars have been successfully used to align bio- tional independence given the labels, to achieve tractability. logical sequences, find sequences homologous to a known evolutionary family, and analyze RNA secondary structure Maximum entropy Markov models (MEMMs) are condi- (Durbin et al., 1998). In computational linguistics and tional probabilistic sequence models that attain all of the computer science, HMMs and stochastic grammars have above advantages (McCallum et al., 2000). In MEMMs, 1 been applied to a wide variety of problems in text and each source state has a exponential model that takes the speech processing, including topic segmentation, part-of- observation features as input, and outputs a distribution speech (POS) tagging, information extraction, and syntac- over possible next states. These exponential models are tic disambiguation (Manning & Schutze,¨ 1999). trained by an appropriate iterative scaling method in the HMMs and stochastic grammars are generative models, as- 1Output labels are associated with states; it is possible for sev- signing a joint probability to paired observation and label eral states to have the same label, but for simplicity in the rest of this paper we assume a one-to-one correspondence. sequences; the parameters are typically trained to maxi- maximum entropy framework. Previously published exper- i:_ r:_ 1 2 b:rib imental results show MEMMs increasing recall and dou- 0 3 bling precision relative to HMMs in a FAQ segmentation r:_ b:rob o:_ task. 4 5 MEMMs and other non-generative finite-state models based on next-state classifiers, such as discriminative Label bias example, after (Bottou, 1991). For concise- Markov models (Bottou, 1991), share a weakness we call Figure 1. ness, we place observation-label pairs o : l on transitions rather here the label bias problem: the transitions leaving a given than states; the symbol ‘ ’ represents the null output label. state compete only against each other, rather than against all other transitions in the model. In probabilistic terms, We present the model, describe two training procedures and transition scores are the conditional probabilities of pos- sketch a proof of convergence. We also give experimental sible next states given the current state and the observa- results on synthetic data showing that CRFs solve the clas- tion sequence. This per-state normalization of transition sical version of the label bias problem, and, more signifi- scores implies a “conservation of score mass” (Bottou, cantly, that CRFs perform better than HMMs and MEMMs 1991) whereby all the mass that arrives at a state must be when the true data distribution has higher-order dependen- distributed among the possible successor states. An obser- cies than the model, as is often the case in practice. Finally, vation can affect which destination states get the mass, but we confirm these results as well as the claimed advantages not how much total mass to pass on. This causes a bias to- of conditional models by evaluating HMMs, MEMMs and ward states with fewer outgoing transitions. In the extreme CRFs with identical state structure on a part-of-speech tag- case, a state with a single outgoing transition effectively ging task. ignores the observation. In those cases, unlike in HMMs, Viterbi decoding cannot downgrade a branch based on ob- servations after the branch point, and models with state- 2. The Label Bias Problem transition structures that have sparsely connected chains of Classical probabilistic automata (Paz, 1971), discrimina- states are not properly handled. The Markovian assump- tive Markov models (Bottou, 1991), maximum entropy tions in MEMMs and similar state-conditional models in- taggers (Ratnaparkhi, 1996), and MEMMs, as well as sulate decisions at one state from future decisions in a way non-probabilistic sequence tagging and segmentation mod- that does not match the actual dependencies between con- els with independently trained next-state classifiers (Pun- secutive states. yakanok & Roth, 2001) are all potential victims of the label This paper introduces conditional random fields (CRFs), a bias problem. sequence modeling framework that has all the advantages For example, Figure 1 represents a simple finite-state of MEMMs but also solves the label bias problem in a model designed to distinguish between the two words rib principled way. The critical difference between CRFs and and rob. Suppose that the observation sequence is rib. MEMMs is that a MEMM uses per-state exponential mod- In the first time step, r matches both transitions from the els for the conditional probabilities of next states given the start state, so the probability mass gets distributed roughly current state, while a CRF has a single exponential model equally among those two transitions. Next we observe i. for the joint probability of the entire sequence of labels Both states 1 and 4 have only one outgoing transition. State given the observation sequence. Therefore, the weights of 1 has seen this observation often in training, state 4 has al- different features at different states can be traded off against most never seen this observation; but like state 1, state 4 each other. has no choice but to pass all its mass to its single outgoing We can also think of a CRF as a finite state model with un- transition, since it is not generating the observation, only normalized transition probabilities. However, unlike some conditioning on it. Thus, states with a single outgoing tran- other weighted finite-state approaches (LeCun et al., 1998), sition effectively ignore their observations. More generally, CRFs assign a well-defined probability distribution over states with low-entropy next state distributions will take lit- possible labelings, trained by maximum likelihood or MAP tle notice of observations. Returning to the example, the estimation. Furthermore, the loss function is convex,2 guar- top path and the bottom path will be about equally likely, anteeing convergence to the global optimum. CRFs also independently of the observation sequence. If one of the generalize easily to analogues of stochastic context-free two words is slightly more common in the training set, the grammars that would be useful in such problems as RNA transitions out of the start state will slightly prefer its cor- secondary structure prediction and natural language pro- responding transition, and that word’s state sequence will cessing. always win. This behavior is demonstrated experimentally in Section
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