Capacity and Complexity of HMM Duration Modeling Techniques

The ability of a standard hidden Markov model (HMM) or expanded state HMM (ESHMM) to accurately model duration distributions of phonemes is compared with specific duration-focused approaches such as semi-Markov models or variable transition probabilities. It is demonstrated that either a three-state ESHMM or a standard HMM with an increased number of states is capable of closely matching both Gamma distributions and duration distributions of phonemes from the TIMIT corpus, as measured by Bhattacharyya distance to the true distributions. Standard HMMs are easily implemented with off-the-shelf tools, whereas duration models require substantial algorithmic development and have higher computational costs when implemented, suggesting that a simple adjustment to HMM topologies is perhaps a more efficient solution to the problem of duration than more complex approaches

Semi-Markov Arnason-Schwarz models

We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process assumes that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using for example a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis

Hidden Markov Model with Binned Duration and Its Application

Hidden Markov models (HMM) have been widely used in various applications such as speech processing and bioinformatics. However, the standard hidden Markov model requires state occupancy durations to be geometrically distributed, which can be inappropriate in some real-world applications where the distributions on state intervals deviate signi cantly from the geometric distribution, such as multi-modal distributions and heavy-tailed distributions. The hidden Markov model with duration (HMMD) avoids this limitation by explicitly incor- porating the appropriate state duration distribution, at the price of signi cant computational expense. As a result, the applications of HMMD are still quited limited. In this work, we present a new algorithm - Hidden Markov Model with Binned Duration (HMMBD), whose result shows no loss of accuracy compared to the HMMD decoding performance and a com- putational expense that only diers from the much simpler and faster HMM decoding by a constant factor. More precisely, we further improve the computational complexity of HMMD from (TNN +TND) to (TNN +TND ), where TNN stands for the computational com- plexity of the HMM, D is the max duration value allowed and can be very large and D generally could be a small constant value

A Coupled Duration-Focused Architecture for Real-Time Music-to-Score Alignment

International audienceThe capacity for realtime synchronization and coordination is a common ability among trained musicians performing a music score that presents an interesting challenge for machine intelligence. Compared to speech recognition, which has influenced many music information retrieval systems, music's temporal dynamics and complexity pose challenging problems to common approximations regarding time modeling of data streams. In this paper, we propose a design for a realtime music to score alignment system. Given a live recording of a musician playing a music score, the system is capable of following the musician in realtime within the score and decoding the tempo (or pace) of its performance. The proposed design features two coupled audio and tempo agents within a unique probabilistic inference framework that adaptively updates its parameters based on the realtime context. Online decoding is achieved through the collaboration of the coupled agents in a Hidden Hybrid Markov/semi-Markov framework where prediction feedback of one agent affects the behavior of the other. We perform evaluations for both realtime alignment and the proposed temporal model. An implementation of the presented system has been widely used in real concert situations worldwide and the readers are encouraged to access the actual system and experiment the results

Hidden Semi-Markov Models for Predictive Maintenance

Realistic predictive maintenance approaches are essential for condition monitoring and predictive maintenance of industrial machines. In this work, we propose Hidden Semi-Markov Models (HSMMs) with (i) no constraints on the state duration density function and (ii) being applied to continuous or discrete observation. To deal with such a type of HSMM, we also propose modifications to the learning, inference, and prediction algorithms. Finally, automatic model selection has been made possible using the Akaike Information Criterion. This paper describes the theoretical formalization of the model as well as several experiments performed on simulated and real data with the aim of methodology validation. In all performed experiments, the model is able to correctly estimate the current state and to effectively predict the time to a predefined event with a low overall average absolute error. As a consequence, its applicability to real world settings can be beneficial, especially where in real time the Remaining Useful Lifetime (RUL) of the machine is calculated

Activity, context, and plan recognition with computational causal behavior models

Objective of this thesis is to answer the question "how to achieve efficient sensor-based reconstruction of causal structures of human behaviour in order to provide assistance?". To answer this question, the concept of Computational Causal Behaviour Models (CCBMs) is introduced. CCBM allows the specification of human behaviour by means of preconditions and effects and employs Bayesian filtering techniques to reconstruct action sequences from noisy and ambiguous sensor data. Furthermore, a novel approximative inference algorithm – the Marginal Filter – is introduced

Threat assessment for safe navigation in environments with uncertainty in predictability

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 213-224).This thesis develops threat assessment algorithms to improve the safety of the decision making of autonomous and human-operated vehicles navigating in dynamic and uncertain environments, where the source of uncertainty is in the predictability of the nearby vehicles' future trajectories. The first part of the thesis introduces two classes of algorithms to classify drivers behaviors at roads intersections based on Support Vector Machines (SVM) and Hidden Markov Models (HMM). These algorithms are successfully validated using a large real-world intersection dataset, and can be used as part of future driver assistance systems. They are also compared to three popular traditional methods, and the results show significant and consistent improvements with the developed algorithms. The second part of the thesis presents an efficient trajectory prediction algorithm that has been developed to improve the performance of future collision avoidance and detection systems. The proposed approach, RR-GP, combines the Rapidly-exploring Random Trees (RRT) based algorithm, RRT-Reach, with mixtures of Gaussian Processes (GP) to compute dynamically feasible paths, in real-time, while embedding the flexibility of GP's nonparametric Bayesian model. RR-GP efficiently approximates the reachability sets of surrounding vehicles, and is shown in simulation and on naturalistic data to improve the performance over two standard GP-based algorithms. The third part introduces new path planning algorithms that build upon the tools that have been previously introduced in this thesis. The focus is on safe autonomous navigation in the presence of other vehicles with uncertain motion patterns. First, it presents a new threat assessment module (TAM) that combines the RRT-Reach algorithm with an SVM-based intention predictor, to develop a threat-aware path planner. The strengths of this approach are demonstrated through simulation and experiments performed in the MIT RAVEN testbed. Second, another novel path planning technique is developed by integrating the RR-GP trajectory prediction algorithm with a state-of-the-art chance-constrained RRT planner. This framework provides several theoretical guarantees on the probabilistic satisfaction of collision avoidance constraints. Extensive simulation results show that the resulting approach can be used in real-time to efficiently and accurately execute safe paths. The last part of the thesis considers the decision-making problem for a human-driven vehicle crossing a road intersection in the presence of other, potentially errant, drivers. The proposed approach uses the TAM framework to compute the threat level in real-time, and provides the driver with a warning signal and the best escape maneuver through the intersection. Experimental results with small autonomous and human-driven vehicles in the RAVEN testbed demonstrate that this approach can be successfully used in real-time to minimize the risk of collision in urban-like environments.by Georges Salim Aoudé.Ph.D