Algorithms for Hidden Markov Models With Imprecisely Specified Parameters

Hidden Markov models (HMMs) are widely used models for sequential data. As with other probabilistic graphical models, they require the specification of precise probability values, which can be too restrictive for some domains, especially when data are scarce or costly to acquire. We present a generalized version of HMMs, whose quantification can be done by sets of, instead of single, probability distributions. Our models have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. Efficient inference algorithms are developed to address standard HMM usage such as the computation of likelihoods and most probable explanations. Experiments with real data show that the use of imprecise probabilities leads to more reliable inferences without compromising efficiency.

Hidden Markov Models With Set-Valued Parameters

Hidden Markov models (HMMs) are widely used probabilistic models of sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, whose assessment can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we consider iHMMs under the strong independence interpretation, for which we develop efficient inference algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations, as well as performing filtering and predictive inference. Experiments with real data show that iHMMs produce more reliable inferences without compromising the computational efficiency.

Inter-Frame Contextual Modelling For Visual Speech Recognition

In this paper, we present a new approach to visual speech recognition which improves contextual modelling by combining Inter-Frame Dependent and Hidden Markov Models. This approach captures contextual information in visual speech that may be lost using a Hidden Markov Model alone. We apply contextual modelling to a large speaker independent isolated digit recognition task, and compare our approach to two commonly adopted feature based techniques for incorporating speech dynamics. Results are presented from baseline feature based systems and the combined modelling technique. We illustrate that both of these techniques achieve similar levels of performance when used independently. However significant improvements in performance can be achieved through a combination of the two. In particular we report an improvement in excess of 17% relative Word Error Rate in comparison to our best baseline system.

FPGA Implementation of a Pipelined Gaussian Calculation for HMM-Based Large Vocabulary Speech Recognition

A scalable large vocabulary, speaker independent speech recognition system is being developed using Hidden Markov Models (HMMs) for acoustic modeling and a Weighted Finite State Transducer (WFST) to compile sentence, word, and phoneme models. The system comprises a software backend search and an FPGA-based Gaussian calculation which are covered here. In this paper, we present an efficient pipelined design implemented both as an embedded peripheral and as a scalable, parallel hardware accelerator. Both architectures have been implemented on an Alpha Data XRC-5T1, reconfigurable computer housing a Virtex 5 SX95T FPGA. The core has been tested and is capable of calculating a full set of Gaussian results from 3825 acoustic models in 9.03 ms which coupled with a backend search of 5000 words has provided an accuracy of over 80%. Parallel implementations have been designed with up to 32 cores and have been successfully implemented with a clock frequency of 133?MHz.

Combining missing-feature theory, speech enhancement, and speaker-dependent/-independent modeling for speech separation

This paper considers the separation and recognition of overlapped speech sentences assuming single-channel observation. A system based on a combination of several different techniques is proposed. The system uses a missing-feature approach for improving crosstalk/noise robustness, a Wiener filter for speech enhancement, hidden Markov models for speech reconstruction, and speaker-dependent/-independent modeling for speaker and speech recognition. We develop the system on the Speech Separation Challenge database, involving a task of separating and recognizing two mixing sentences without assuming advanced knowledge about the identity of the speakers nor about the signal-to-noise ratio. The paper is an extended version of a previous conference paper submitted for the challenge.

Probabilistic Inference in Credal Networks: New Complexity Results

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove an analogous result for inference in Naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and Naive Bayes networks are used in real applications of imprecise probability.

Effect of major lifestyle risk factors, independent and jointly, on life expectancy with and without cardiovascular disease: results from the Consortium on Health and Ageing Network of Cohorts in Europe and the United States (CHANCES)

Seldom have studies taken account of changes in lifestyle habits in the elderly, or investigated their impact on disease-free life expectancy (LE) and LE with cardiovascular disease (CVD). Using data on subjects aged 50+ years from three European cohorts (RCPH, ESTHER and Tromsø), we used multi-state Markov models to calculate the independent and joint effects of smoking, physical activity, obesity and alcohol consumption on LE with and without CVD. Men and women aged 50 years who have a favourable lifestyle (overweight but not obese, light/moderate drinker, non-smoker and participates in vigorous physical activity) lived between 7.4 (in Tromsø men) and 15.7 (in ESTHER women) years longer than those with an unfavourable lifestyle (overweight but not obese, light/moderate drinker, smoker and does not participate in physical activity). The greater part of the extra life years was in terms of "disease-free" years, though a healthy lifestyle was also associated with extra years lived after a CVD event. There are sizeable benefits to LE without CVD and also for survival after CVD onset when people favour a lifestyle characterized by salutary behaviours. Remaining a non-smoker yielded the greatest extra years in overall LE, when compared to the effects of routinely taking physical activity, being overweight but not obese, and drinking in moderation. The majority of the overall LE benefit is in disease free years. Therefore, it is important for policy makers and the public to know that prevention through maintaining a favourable lifestyle is "never too late".

Discrete Conditional Phase-type models utilising classification trees: Application to modelling health service capacities

Discrete Conditional Phase-type (DC-Ph) models consist of a process component (survival distribution) preceded by a set of related conditional discrete variables. This paper introduces a DC-Ph model where the conditional component is a classification tree. The approach is utilised for modelling health service capacities by better predicting service times, as captured by Coxian Phase-type distributions, interfaced with results from a classification tree algorithm. To illustrate the approach, a case-study within the healthcare delivery domain is given, namely that of maternity services. The classification analysis is shown to give good predictors for complications during childbirth. Based on the classification tree predictions, the duration of childbirth on the labour ward is then modelled as either a two or three-phase Coxian distribution. The resulting DC-Ph model is used to calculate the number of patients and associated bed occupancies, patient turnover, and to model the consequences of changes to risk status.

Dynamic pricing models for used products in remanufacturing with lost-sales and uncertain quality

In this paper, we investigate the remanufacturing problem of pricing single-class used products (cores) in the face of random price-dependent returns and random demand. Specifically, we propose a dynamic pricing policy for the cores and then model the problem as a continuous-time Markov decision process. Our models are designed to address three objectives: finite horizon total cost minimization, infinite horizon discounted cost, and average cost minimization. Besides proving optimal policy uniqueness and establishing monotonicity results for the infinite horizon problem, we also characterize the structures of the optimal policies, which can greatly simplify the computational procedure. Finally, we use computational examples to assess the impacts of specific parameters on optimal price and reveal the benefits of a dynamic pricing policy. © 2013 Elsevier B.V. All rights reserved.

Multilinear and Integer Programming for Markov Decision Processes with Imprecise Probabilities

Markov Decision Processes (MDPs) are extensively used to encode sequences of decisions with probabilistic effects. Markov Decision Processes with Imprecise Probabilities (MDPIPs) encode sequences of decisions whose effects are modeled using sets of probability distributions. In this paper we examine the computation of Γ-maximin policies for MDPIPs using multilinear and integer programming. We discuss the application of our algorithms to “factored” models and to a recent proposal, Markov Decision Processes with Set-valued Transitions (MDPSTs), that unifies the fields of probabilistic and “nondeterministic” planning in artificial intelligence research.