Hierarchical Hidden Markov Models (HHMMs) are sophisticated stochastic models that enable us to capture a hierarchical context characterization of sequence data.

The hierarchical hidden Markov model (HHMM) is a generalization of the hidden Markov model (HMM) that models sequences with structure at many length/time scales [FST98]. Unfortunately, the original infer- is ence algorithm is rather complicated, and takes the length of the sequence, making it impractical for many domains. In this paper, we show how HHMMs are a special kind of dynamic Bayesian network (DBN), and thereby derive a much simpler inference algorithm, which only takes time. Furthermore, by drawing the connection between HHMMs and DBNs, we enable the application of many stan- dard approximation techniques to further speed up inference.

Hierarchical Hidden Markov Models (HHMMs) are sophisticated stochastic models that enable us to capture a hierarchical context characterization of sequence data. However, existing HHMM parameter estimation methods require large computations of time complexity O(TN {2D}) at least for model inference, where D is the depth of the hierarchy, N is the number of states in each level, and T is the sequence length. In this paper, we propose a new inference method of HHMMs for which the time complexity is O(TN {D 1}). A key idea of our algorithm is application of the forward-backward algorithm to ''state activation probabilities''. The notion of a state activation, which offers a simple formalization of the hierarchical transition behavior of HHMMs, enables us to conduct model inference efficiently. We present some experiments to demonstrate that our proposed method works more efficiently to estimate HHMM parameters than do some existing methods such as the flattening method and Gibbs sampling method.

Sleep constitutes a key indicator of human health, performance, and quality of life. Sleep deprivation has long been related to the onset, development, and worsening of several mental and metabolic disorders, constituting an essential marker for preventing, evaluating, and treating different health conditions. Sleep Activity Recognition methods can provide indicators to assess, monitor, and characterize subjects' sleep-wake cycles and detect behavioral changes. In this work, we propose a general method that continuously operates on passively sensed data from smartphones to characterize sleep and identify significant sleep episodes. Thanks to their ubiquity, these devices constitute an excellent alternative data source to profile subjects' biorhythms in a continuous, objective, and non-invasive manner, in contrast to traditional sleep assessment methods that usually rely on intrusive and subjective procedures. A Heterogeneous Hidden Markov Model is used to model a discrete latent variable process associated with the Sleep Activity Recognition task in a self-supervised way. We validate our results against sleep metrics reported by tested wearables, proving the effectiveness of the proposed approach and advocating its use to assess sleep without more reliable sources.

Psychiatric patients' passive activity monitoring is crucial to detect behavioural shifts in real-time, comprising a tool that helps clinicians supervise patients' evolution over time and enhance the associated treatments' outcomes. Frequently, sleep disturbances and mental health deterioration are closely related, as mental health condition worsening regularly entails shifts in the patients' circadian rhythms. Therefore, Sleep Activity Recognition constitutes a behavioural marker to portray patients' activity cycles and to detect behavioural changes among them. Moreover, mobile passively sensed data captured from smartphones, thanks to these devices' ubiquity, constitute an excellent alternative to profile patients' biorhythm. In this work, we aim to identify major sleep episodes based on passively sensed data. To do so, a Heterogeneous Hidden Markov Model is proposed to model a discrete latent variable process associated with the Sleep Activity Recognition task in a self-supervised way. We validate our results against sleep metrics reported by clinically tested wearables, proving the effectiveness of the proposed approach.

Hierarchical Hidden Markov Models (HHMMs) are sophisticated stochastic models that enable us to capture a hierarchical context characterization of sequence data. However, existing HHMM parameter estimation methods require large computations of time complexity O(TN {2D}) at least for model inference, where D is the depth of the hierarchy, N is the number of states in each level, and T is the sequence length. In this paper, we propose a new inference method of HHMMs for which the time complexity is O(TN {D 1}). A key idea of our algorithm is application of the forward-backward algorithm to ''state activation probabilities''. The notion of a state activation, which offers a simple formalization of the hierarchical transition behavior of HHMMs, enables us to conduct model inference efficiently.

We propose a hierarchical extension to hidden Markov model (HMM) under the Bayesian framework to overcome its limited model capacity. The model parameters are treated as random variables whose distributions are governed by hyperparameters. Therefore the variation in data can be modeled at both instance level and distribution level. We derive a novel learning method for estimating the parameters and hyperparameters of our model based on adversarial learning framework, which has shown promising results in generating photorealistic images and videos. We demonstrate the benefit of the proposed method on human motion capture data through comparison with both state-of-the-art methods and the same model that is learned by maximizing likelihood. The first experiment on reconstruction shows the model's capability of generalizing to novel testing data. The second experiment on synthesis shows the model's capability of generating realistic and diverse data.

We propose a Bayesian nonparametric mixture model for prediction- and information extraction tasks with an efficient inference scheme. It models categorical-valued time series that exhibit dynamics from multiple underlying patterns (e.g. user behavior traces). We simplify the idea of capturing these patterns by hierarchical hidden Markov models (HHMMs) - and extend the existing approaches by the additional representation of structural information. Our empirical results are based on both synthetic- and real world data. They indicate that the results are easily interpretable, and that the model excels at segmentation and prediction performance: it successfully identifies the generating patterns and can be used for effective prediction of future observations.

Hierarchical Hidden Markov Models (HHMMs) are sophisticated stochastic models that enable us to capture a hierarchical context characterization of sequence data. However, existing HHMM parameter estimation methods require large computations of time complexity O(TN^{2D}) at least for model inference, where D is the depth of the hierarchy, N is the number of states in each level, and T is the sequence length. In this paper, we propose a new inference method of HHMMs for which the time complexity is O(TN^{D+1}). A key idea of our algorithm is application of the forward-backward algorithm to ''state activation probabilities''. The notion of a state activation, which offers a simple formalization of the hierarchical transition behavior of HHMMs, enables us to conduct model inference efficiently. We present some experiments to demonstrate that our proposed method works more efficiently to estimate HHMM parameters than do some existing methods such as the flattening method and Gibbs sampling method.

The hierarchical hidden Markov model (HHMM) is a generalization of the hidden Markov model (HMM) that models sequences with structure at many length/time scales [FST98].