# Tutorial on Conditional Random Fields for Sequence Prediction. Ariadna Quattoni

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1 Tutorial on Conditional Random Fields for Sequence Prediction Ariadna Quattoni

2 RoadMap Sequence Prediction Problem CRFs for Sequence Prediction Generalizations of CRFs Hidden Conditional Random Fields (HCRFs) HCRFs for Object Recognition

3 RoadMap Sequence Prediction Problem CRFs for Sequence Prediction Generalizations of CRFs Hidden Conditional Random Fields (HCRFs) HCRFs for Object Recognition

4 Sequence Prediction Problem Example: Part-of-Speech Tagging He reckons the current account deficit will narrow significantly [PRP] [VB] [DT] [JJ] [NN] [NN] [MD] [VB] [RB]

5 Gesture Recognition [HTF] [HTF] [HTF] [HOF] [HOF] [HOS]

6 RoadMap Sequence Prediction Problem CRFs for Sequence Prediction Generalizations of CRFs Hidden Conditional Random Fields (HCRFs) HCRFs for Object Recognition

7 Conditional Random Fields: Modelling the Conditional Distribution Model the Conditional Distribution: To predict a sequence compute: Must be able to compute it efficiently.

8 Conditional Random Fields: Feature Functions Feature Functions:

9 Feature Functions Express some characteristic of the empirical distribution that we wish to hold in the model distribution

10 Conditional Random Fields:: Distribution Label sequence modelled as a normalized product of feature functions: The model is log-linear on the Feature Functions

11 Parameter Estimation:Maximum Likelihood IID training samples: (negative) Conditional Log-Likelihood:

12 Parameter Estimation: Maximum Likelihood Maximum Likelihood Estimation Set optimal parameters to be: This function is convex, i.e. no local minimums

13 Parameter Estimation:Optimization Let: Differentiating the log-likelihood with respect to parameter Observed Mean Feature Value Expected Feature Value Under The Model

14 Parameter Estimation: Optimization Generally, it is not possible to find and analytic solution to the previous objective. Iterative techniques, i.e. gradient based methods.

15 Maximum Entropy Interpretation Notice that at the optimal solution of: We must have that: Maximizing log-likelihood Finding max-entropy distribution that satisfies the set of constraints defined by the feature functions

16 CRF s Inference Given a model, i.e. parameter values Can we compute the following efficiently? Best Label Sequence Expected Values Both can be computed using dynamic programming.

17 RoadMap Sequence Prediction Problem CRFs for Sequence Prediction Generalizations of CRFs Hidden Conditional Random Fields (HCRFs) HCRFs for Object Recognition

18 Generalization I: CRFs Beyond Sequences Predicting Trees: Application Constituent Parsing S NP VP PP NP D N V P D N The boy smiled at the girl

19 Generalization II: Factorized Linear Models To predict a sequence compute: Linear Model Objective: making accurate predictions on unseen data The parameters of the linear model can be optimized using other loss functions

20 Generalization II: Factorized Linear Models Structured Hinge Loss Let be the correct label sequence: Structured SVM

21 RoadMap Sequence Prediction Problem CRFs for Sequence Prediction Generalizations of CRFs Hidden Conditional Random Fields (HCRFs) HCRFs for Object Recognition

22 Hidden Conditional Random Fields Sentiment Detection This movie greatly appealed to me for many reasons - I loved it +1 Positive Review As dumb as history gets -1 Negative Review

23 Hidden Conditional Random Fields Object Recognition A training sample +1 Car

24 Hidden Conditional Random Fields Model the conditional probability: We introduce hidden variables: Analogus to the standard CRF we define: Maps a configuration to the reals.

25 Hidden Conditional Random Fields Feature Functions

26 Parameter Estimation Maximum Likelihood: Find optimal parameters: Iterative techniques, i.e. gradient based methods. But now the function is not convex!!! At test time make prediction:

27 Parameter Estimation The derivative of the loss function is given by: The derivative can be expressed in terms of components: that can be calculated using dynamic programming. Similarly the argmax can also be computed efficiently.

28 RoadMap Sequence Prediction Problem CRFs for Sequence Prediction Generalizations of CRFs Hidden Conditional Random Fields (HCRFs) HCRFs for Object Recognition

29 Application :: Object Recognition SemiSupervised Part-based Models

30 Motivation Use a discriminative model. Spatial dependencies between parts. It is convenient to use an intermediate discrete hidden variable. Potential of learning semantically-meaningful parts. Framework for investigating which part structures emerge.

31 Graph Structure

32 Feature Functions is a minimum spanning tree. Weight (i, j)= distance between patches x i and x j obtained with Lowe s detector (textured regions) SIFT features (describes the texture of the image region). Patch description also includes relative location.

33 Viterbi Configuration

34 Learning Shape

35 Conclusions Factorized Linear Models generalize linear prediction models to the setting of structure prediction. In standard linear prediction, finding the argmax and computing gradients is trivial. In structure prediction it involves inference. Factored representations allow for efficient inference algorithms (most times based on dynamic programming) Conditional Random Fields are an instance of this framework Future Work Better Algorithms for training HCRFs

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