Hidden Markov Model Identifiability via Tensors

The prevalence of hidden Markov models (HMMs) in various applications of statistical signal processing and communications is a testament to the power and flexibility of the model. In this paper, we link the identifiability problem with tensor decomposition, in particular, the Canonical Polyadic decomposition. Using recent results in deriving uniqueness conditions for tensor decomposition, we are able to provide a necessary and sufficient condition for the identification of the parameters of discrete time finite alphabet HMMs. This result resolves a long standing open problem regarding the derivation of a necessary and sufficient condition for uniquely identifying an HMM. We then further extend recent preliminary work on the identification of HMMs with multiple observers by deriving necessary and sufficient conditions for identifiability in this setting.Comment: Accepted to ISIT 2013. 5 pages, no figure

Making Sense of the Mental Universe

In 2005, an essay was published in Nature asserting that the universe is mental and that we must abandon our tendency to conceptualize observations as things. Since then, experiments have confirmed that — as predicted by quantum mechanics — reality is contextual, which contradicts at least intuitive formulations of realism and corroborates the hypothesis of a mental universe. Yet, to give this hypothesis a coherent rendering, one must explain how a mental universe can — at least in principle — accommodate (a) our experience of ourselves as distinct individual minds sharing a world beyond the control of our volition; and (b) the empirical fact that this world is contextual despite being seemingly shared. By combining a modern formulation of the ontology of idealism with the relational interpretation of quantum mechanics, the present paper attempts to provide a viable explanatory framework for both points. In the process of doing so, the paper also addresses key philosophical qualms of the relational interpretation

Naturalistic Affective Expression Classification by a Multi-Stage Approach Based on Hidden Markov Models

In naturalistic behaviour, the affective states of a person change at a rate much slower than the typical rate at which video or audio is recorded (e.g. 25fps for video). Hence, there is a high probability that consecutive recorded instants of expressions represent a same affective content. In this paper, a multi-stage automatic affective expression recognition system is proposed which uses Hidden Markov Models (HMMs) to take into account this temporal relationship and finalize the classification process. The hidden states of the HMMs are associated with the levels of affective dimensions to convert the classification problem into a best path finding problem in HMM. The system was tested on the audio data of the Audio/Visual Emotion Challenge (AVEC) datasets showing performance significantly above that of a one-stage classification system that does not take into account the temporal relationship, as well as above the baseline set provided by this Challenge. Due to the generality of the approach, this system could be applied to other types of affective modalities

Multiscale Discriminant Saliency for Visual Attention

The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between center and surround classes. Discriminant power of features for the classification is measured as mutual information between features and two classes distribution. The estimated discrepancy of two feature classes very much depends on considered scale levels; then, multi-scale structure and discriminant power are integrated by employing discrete wavelet features and Hidden markov tree (HMT). With wavelet coefficients and Hidden Markov Tree parameters, quad-tree like label structures are constructed and utilized in maximum a posterior probability (MAP) of hidden class variables at corresponding dyadic sub-squares. Then, saliency value for each dyadic square at each scale level is computed with discriminant power principle and the MAP. Finally, across multiple scales is integrated the final saliency map by an information maximization rule. Both standard quantitative tools such as NSS, LCC, AUC and qualitative assessments are used for evaluating the proposed multiscale discriminant saliency method (MDIS) against the well-know information-based saliency method AIM on its Bruce Database wity eye-tracking data. Simulation results are presented and analyzed to verify the validity of MDIS as well as point out its disadvantages for further research direction.Comment: 16 pages, ICCSA 2013 - BIOCA sessio