Non-parametric hidden conditional random fields for action classification

Conditional Random Fields (CRF), a structured prediction method, combines probabilistic graphical models and discriminative classification techniques in order to predict class labels in sequence recognition problems. Its extension the Hidden Conditional Random Fields (HCRF) uses hidden state variables in order to capture intermediate structures. The number of hidden states in an HCRF must be specified a priori. This number is often not known in advance. A non-parametric extension to the HCRF, with the number of hidden states automatically inferred from data, is proposed here. This is a significant advantage over the classical HCRF since it avoids ad hoc model selection procedures. Further, the training and inference procedure is fully Bayesian eliminating the over fitting problem associated with frequentist methods. In particular, our construction is based on scale mixtures of Gaussians as priors over the HCRF parameters and makes use of Hierarchical Dirichlet Process (HDP) and Laplace distribution. The proposed inference procedure uses elliptical slice sampling, a Markov Chain Monte Carlo (MCMC) method, in order to sample optimal and sparse posterior HCRF parameters. The above technique is applied for classifying human actions that occur in depth image sequences – a challenging computer vision problem. Experiments with real world video datasets confirm the efficacy of our classification approach

Geometry and Expressive Power of Conditional Restricted Boltzmann Machines

Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability distributions on the states of the output units given the states of the input units, parametrized by interaction weights and biases. We address the representational power of these models, proving results their ability to represent conditional Markov random fields and conditional distributions with restricted supports, the minimal size of universal approximators, the maximal model approximation errors, and on the dimension of the set of representable conditional distributions. We contribute new tools for investigating conditional probability models, which allow us to improve the results that can be derived from existing work on restricted Boltzmann machine probability models.Comment: 30 pages, 5 figures, 1 algorith

Grammatical-Restrained Hidden Conditional Random Fields for Bioinformatics applications

<p>Abstract</p> <p>Background</p> <p>Discriminative models are designed to naturally address classification tasks. However, some applications require the inclusion of grammar rules, and in these cases generative models, such as Hidden Markov Models (HMMs) and Stochastic Grammars, are routinely applied.</p> <p>Results</p> <p>We introduce Grammatical-Restrained Hidden Conditional Random Fields (GRHCRFs) as an extension of Hidden Conditional Random Fields (HCRFs). GRHCRFs while preserving the discriminative character of HCRFs, can assign labels in agreement with the production rules of a defined grammar. The main GRHCRF novelty is the possibility of including in HCRFs prior knowledge of the problem by means of a defined grammar. Our current implementation allows <it>regular grammar </it>rules. We test our GRHCRF on a typical biosequence labeling problem: the prediction of the topology of Prokaryotic outer-membrane proteins.</p> <p>Conclusion</p> <p>We show that in a typical biosequence labeling problem the GRHCRF performs better than CRF models of the same complexity, indicating that GRHCRFs can be useful tools for biosequence analysis applications.</p> <p>Availability</p> <p>GRHCRF software is available under GPLv3 licence at the website</p> <p><url>http://www.biocomp.unibo.it/~savojard/biocrf-0.9.tar.gz.</url></p

Hidden conditional random fields for classification of imaginary motor tasks from EEG data

Brain-computer interfaces (BCIs) are systems that allow the control of external devices using information extracted from brain signals. Such systems find application in rehabilitation of patients with limited or no muscular control. One mechanism used in BCIs is the imagination of motor activity, which produces variations on the power of the electroencephalography (EEG) signals recorded over the motor cortex. In this paper, we propose a new approach for classification of imaginary motor tasks based on hidden conditional random fields (HCRFs). HCRFs are discriminative graphical models that are attractive for this problem because they involve learned statistical models matched to the classification problem; they do not suffer from some of the limitations of generative models; and they include latent variables that can be used to model different brain states in the signal. Our approach involves auto-regressive modeling of the EEG signals, followed by the computation of the power spectrum. Frequency band selection is performed on the resulting time-frequency representation through feature selection methods. These selected features constitute the data that are fed to the HCRF, parameters of which are learned from training data. Inference algorithms on the HCRFs are used for classification of motor tasks. We experimentally compare this approach to the best performing methods in BCI competition IV and the results show that our approach overperforms all methods proposed in the competition. In addition, we present a comparison with an HMM-based method, and observe that the proposed method produces better classification accuracy

Efficient Structured Prediction with Latent Variables for General Graphical Models

In this paper we propose a unified framework for structured prediction with latent variables which includes hidden conditional random fields and latent structured support vector machines as special cases. We describe a local entropy approximation for this general formulation using duality, and derive an efficient message passing algorithm that is guaranteed to converge. We demonstrate its effectiveness in the tasks of image segmentation as well as 3D indoor scene understanding from single images, showing that our approach is superior to latent structured support vector machines and hidden conditional random fields.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Multi-signal gesture recognition using temporal smoothing hidden conditional random fields

We present a new approach to multi-signal gesture recognition that attends to simultaneous body and hand movements. The system examines temporal sequences of dual-channel input signals obtained via statistical inference that indicate 3D body pose and hand pose. Learning gesture patterns from these signals can be quite challenging due to the existence of long-range temporal-dependencies and low signal-to-noise ratio (SNR). We incorporate a Gaussian temporal-smoothing kernel into the inference framework, capturing long-range temporal-dependencies and increasing the SNR efficiently. An extensive set of experiments was performed, allowing us to (1) show that combining body and hand signals significantly improves the recognition accuracy; (2) report on which features of body and hands are most informative; and (3) show that using a Gaussian temporal-smoothing significantly improves gesture recognition accuracy.United States. Office of Naval Research (Science of Autonomy program, Contract #N000140910625)National Science Foundation (U.S.) (NSF grant #IIS-1018055

The stability of conditional Markov processes and Markov chains in random environments

We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this conditional signal is weakly ergodic when the signal is ergodic and the observations are nondegenerate. This permits a delicate exchange of the intersection and supremum of $\sigma$-fields, which is key for the stability of the nonlinear filter and partially resolves a long-standing gap in the proof of a result of Kunita [J. Multivariate Anal. 1 (1971) 365--393]. A similar result is obtained also in the continuous time setting. The proofs are based on an ergodic theorem for Markov chains in random environments in a general state space.Comment: Published in at http://dx.doi.org/10.1214/08-AOP448 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Aneuploidy prediction and tumor classification with heterogeneous hidden conditional random fields

Motivation: The heterogeneity of cancer cannot always be recognized by tumor morphology, but may be reflected by the underlying genetic aberrations. Array comparative genome hybridization (array-CGH) methods provide high-throughput data on genetic copy numbers, but determining the clinically relevant copy number changes remains a challenge. Conventional classification methods for linking recurrent alterations to clinical outcome ignore sequential correlations in selecting relevant features. Conversely, existing sequence classification methods can only model overall copy number instability, without regard to any particular position in the genome

Tagging Complex Non-Verbal German Chunks with Conditional Random Fields

We report on chunk tagging methods for German that recognize complex non-verbal phrases using structural chunk tags with Conditional Random Fields (CRFs). This state-of-the-art method for sequence classification achieves 93.5% accuracy on newspaper text. For the same task, a classical trigram tagger approach based on Hidden Markov Models reaches a baseline of 88.1%. CRFs allow for a clean and principled integration of linguistic knowledge such as part-of-speech tags, morphological constraints and lemmas. The structural chunk tags encode phrase structures up to a depth of 3 syntactic nodes. They include complex prenominal and postnominal modifiers that occur frequently in German noun phrases