Variational Hidden Conditional Random Fields with Coupled Dirichlet Process Mixtures

Abstract

Abstract. Hidden Conditional Random Fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An infinite HCRF is an HCRF with a countably infinite number of hidden states, which rids us not only of the necessity to specify a priori a fixed number of hidden states available but also of the problem of overfitting. Markov chain Monte Carlo (MCMC) sampling algorithms are often employed for inference in such models. However, convergence of such algorithms is rather difficult to verify, and as the complexity of the task at hand increases, the computational cost of such algorithms often becomes prohibitive. These limitations can be overcome by variational techniques. In this paper, we present a generalized framework for infinite HCRF models, and a novel variational inference approach on a model based on coupled Dirichlet Process Mixtures, the HCRF-DPM. We show that the variational HCRF-DPM is able to converge to a correct number of represented hidden states, and performs as well as the best parametric HCRFs -chosen via cross-validation-for the difficult tasks of recognizing instances of agreement, disagreement, and pain in audiovisual sequences.

Multivariate Time-Series Classification Using the Hidden-Unit Logistic Model

“…An alternative approach to expanding the number of hidden states of the HCRF is the infinite HCRF (iHCRF), which employs a Dirichlet process to determine the number of hidden states. Inference in the iHCRF can be performed via collapsed Gibbs sampling [2] or variational inference [3]. Whilst theoretically facilitating infinitely many states, the modeling power of the iHCRF is, however, limited to the number of "represented" hidden states.…”

Non-parametric Hidden Conditional Random Fields for action classification

“…We do not enforce any such constraints on the features or parameters. Further, unlike the point estimates produced for HCRF parameters using gradient descent in [20], the work here estimates posterior distribution for the parameters.…”

“…The works in [19,20] extend HCRF to be non-parametric with a DP prior. The MCMC based approach in [19] is not applicable for continuous observation features and excludes the HCRF normalization term.…”

“…In contrast, our procedure handles continuous observations and takes into full account the normalization term. The variational inference based approach in [20] has non-negative constraints on the observation features. We do not enforce any such constraints on the features or parameters.…”

Abnormal Crowd Motion Detection with Hidden Conditional Random Fields Model

“…CRF can choose contextual features to solve the problem of the tag bias, and can get the global optimal value through globally normalizing all the characteristics. Because of these good characteristics, CRF has been widely used in the vision community [7][8].…”