On the relationship between hidden Markov Models and convex functional transforms for simulating scanning probe Microscopy

Models for simulating Scanning Probe Microscopy (SPM) may serve as a reference point for validating experimental data and practice. Generally, simulations use a microscopic model of the sample-probe interaction based on a first-principles approach, or a geometric model of macroscopic distortions due to the probe geometry. Examples of the latter include use of neural networks, the Legendre Transform, and dilation/erosion transforms from mathematical morphology. Dilation and the Legendre Transform fall within a general family of functional transforms, which distort a function by imposing a convex solution.In earlier work, the authors proposed a generalized approach to modeling SPM using a hidden Markov model, wherein both the sample-probe interaction and probe geometry may be taken into account. We present a discussion of the hidden Markov model and its relationship to these convex functional transforms for simulating and restoring SPM images.©2009 SPIE.

State estimation schemes for independent component coupled hidden Markov models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13, 17]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6]. In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large. The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results. © Taylor & Francis Group, LLC.

Predicting market direction with hidden Markov models

This paper develops the model of Bicego, Grosso, and Otranto (2008) and applies Hidden Markov Models to predict market direction. The paper draws an analogy between financial markets and speech recognition, seeking inspiration from the latter to solve common issues in quantitative investing. Whereas previous works focus mostly on very complex modifications of the original hidden markov model algorithm, the current paper provides an innovative methodology by drawing inspiration from thoroughly tested, yet simple, speech recognition methodologies. By grouping returns into sequences, Hidden Markov Models can then predict market direction the same way they are used to identify phonemes in speech recognition. The model proves highly successful in identifying market direction but fails to consistently identify whether a trend is in place. All in all, the current paper seeks to bridge the gap between speech recognition and quantitative finance and, even though the model is not fully successful, several refinements are suggested and the room for improvement is significant.

Modeling sequencing errors by combining Hidden Markov models.

Among the largest resources for biological sequence data is the large amount of expressed sequence tags (ESTs) available in public and proprietary databases. ESTs provide information on transcripts but for technical reasons they often contain sequencing errors. Therefore, when analyzing EST sequences computationally, such errors must be taken into account. Earlier attempts to model error prone coding regions have shown good performance in detecting and predicting these while correcting sequencing errors using codon usage frequencies. In the research presented here, we improve the detection of translation start and stop sites by integrating a more complex mRNA model with codon usage bias based error correction into one hidden Markov model (HMM), thus generalizing this error correction approach to more complex HMMs. We show that our method maintains the performance in detecting coding sequences.

Detecting recombination in 4-taxa DNA sequence alignments with Bayesian hidden Markov models and Markov chain Monte Carlo

This article presents a statistical method for detecting recombination in DNA sequence alignments, which is based on combining two probabilistic graphical models: (1) a taxon graph (phylogenetic tree) representing the relationship between the taxa, and (2) a site graph (hidden Markov model) representing interactions between different sites in the DNA sequence alignments. We adopt a Bayesian approach and sample the parameters of the model from the posterior distribution with Markov chain Monte Carlo, using a Metropolis-Hastings and Gibbs-within-Gibbs scheme. The proposed method is tested on various synthetic and real-world DNA sequence alignments, and we compare its performance with the established detection methods RECPARS, PLATO, and TOPAL, as well as with two alternative parameter estimation schemes.

Hierarchical hidden Markov models with general state hierarchy

The hierarchical hidden Markov model (HHMM) is an extension of the hidden Markov model to include a hierarchy of the hidden states. This form of hierarchical modeling has been found useful in applications such as handwritten character recognition, behavior recognition, video indexing, and text retrieval. Nevertheless, the state hierarchy in the original HHMM is restricted to a tree structure. This prohibits two different states from having the same child, and thus does not allow for sharing of common substructures in the model. In this paper, we present a general HHMM in which the state hierarchy can be a lattice allowing arbitrary sharing of substructures. Furthermore, we provide a method for numerical scaling to avoid underflow, an important issue in dealing with long observation sequences. We demonstrate the working of our method in a simulated environment where a hierarchical behavioral model is automatically learned and later used for recognition.

Human activity learning and segmentation using partially hidden discriminative models

Learning and understanding the typical patterns in the daily activities and routines of people from low-level sensory data is an important problem in many application domains such as building smart environments, or providing intelligent assistance. Traditional approaches to this problem typically rely on supervised learning and generative models such as the hidden Markov models and its extensions. While activity data can be readily acquired from pervasive sensors, e.g. in smart environments, providing manual labels to support supervised training is often extremely expensive. In this paper, we propose a new approach based on semi-supervised training of partially hidden discriminative models such as the conditional random field (CRF) and the maximum entropy Markov model (MEMM). We show that these models allow us to incorporate both labeled and unlabeled data for learning, and at the same time, provide us with the flexibility and accuracy of the discriminative framework. Our experimental results in the video surveillance domain illustrate that these models can perform better than their generative counterpart, the partially hidden Markov model, even when a substantial amount of labels are unavailable.

Neuron’s spikes noise level classification using hidden markov models

Considering that the uncertainty noise produced the decline in the quality of collected neural signal, this paper proposes a signal quality assessment method for neural signal. The method makes an automated measure to detect the noise levels in neural signal. Hidden Markov Models were used to build a classification model that classifies the neural spikes based on the noise level associated with the signal. This neural quality assessment measure will help doctors and researchers to focus on the patterns in the signal that have high signal to noise ratio and carry more information.

Hidden Markov models for cancer classification using gene expression profiles

This paper introduces an approach to cancer classification through gene expression profiles by designing supervised learning hidden Markov models (HMMs). Gene expression of each tumor type is modelled by an HMM, which maximizes the likelihood of the data. Prominent discriminant genes are selected by a novel method based on a modification of the analytic hierarchy process (AHP). Unlike conventional AHP, the modified AHP allows to process quantitative factors that are ranking outcomes of individual gene selection methods including t-test, entropy, receiver operating characteristic curve, Wilcoxon test and signal to noise ratio. The modified AHP aggregates ranking results of individual gene selection methods to form stable and robust gene subsets. Experimental results demonstrate the performance dominance of the HMM approach against six comparable classifiers. Results also show that gene subsets generated by modified AHP lead to greater accuracy and stability compared to competing gene selection methods, i.e. information gain, symmetrical uncertainty, Bhattacharyya distance, and ReliefF. The modified AHP improves the classification performance not only of the HMM but also of all other classifiers. Accordingly, the proposed combination between the modified AHP and HMM is a powerful tool for cancer classification and useful as a real clinical decision support system for medical practitioners.

Bayesian Hidden Markov Modeling of Array CGH Data

Genomic alterations have been linked to the development and progression of cancer. The technique of Comparative Genomic Hybridization (CGH) yields data consisting of fluorescence intensity ratios of test and reference DNA samples. The intensity ratios provide information about the number of copies in DNA. Practical issues such as the contamination of tumor cells in tissue specimens and normalization errors necessitate the use of statistics for learning about the genomic alterations from array-CGH data. As increasing amounts of array CGH data become available, there is a growing need for automated algorithms for characterizing genomic profiles. Specifically, there is a need for algorithms that can identify gains and losses in the number of copies based on statistical considerations, rather than merely detect trends in the data. We adopt a Bayesian approach, relying on the hidden Markov model to account for the inherent dependence in the intensity ratios. Posterior inferences are made about gains and losses in copy number. Localized amplifications (associated with oncogene mutations) and deletions (associated with mutations of tumor suppressors) are identified using posterior probabilities. Global trends such as extended regions of altered copy number are detected. Since the posterior distribution is analytically intractable, we implement a Metropolis-within-Gibbs algorithm for efficient simulation-based inference. Publicly available data on pancreatic adenocarcinoma, glioblastoma multiforme and breast cancer are analyzed, and comparisons are made with some widely-used algorithms to illustrate the reliability and success of the technique.

A novel framework of training hidden Markov support vector machines from lightly-annotated data

Natural language understanding (NLU) aims to map sentences to their semantic mean representations. Statistical approaches to NLU normally require fully-annotated training data where each sentence is paired with its word-level semantic annotations. In this paper, we propose a novel learning framework which trains the Hidden Markov Support Vector Machines (HM-SVMs) without the use of expensive fully-annotated data. In particular, our learning approach takes as input a training set of sentences labeled with abstract semantic annotations encoding underlying embedded structural relations and automatically induces derivation rules that map sentences to their semantic meaning representations. The proposed approach has been tested on the DARPA Communicator Data and achieved 93.18% in F-measure, which outperforms the previously proposed approaches of training the hidden vector state model or conditional random fields from unaligned data, with a relative error reduction rate of 43.3% and 10.6% being achieved.

A model to predict hypovigilance during a monotonous task

The driving task requires sustained attention during prolonged periods, and can be performed in highly predictable or repetitive environments. Such conditions could create drowsiness or hypovigilance and impair the ability to react to critical events. Identifying vigilance decrement in monotonous conditions has been a major subject of research, but no research to date has attempted to predict this vigilance decrement. This pilot study aims to show that vigilance decrements due to monotonous tasks can be predicted through mathematical modelling. A short vigilance task sensitive to short periods of lapses of vigilance called Sustained Attention to Response Task is used to assess participants’ performance. This task models the driver’s ability to cope with unpredicted events by performing the expected action. A Hidden Markov Model (HMM) is proposed to predict participants’ hypovigilance. Driver’s vigilance evolution is modelled as a hidden state and is correlated to an observable variable: the participant’s reactions time. This experiment shows that the monotony of the task can lead to an important vigilance decline in less than five minutes. This impairment can be predicted four minutes in advance with an 86% accuracy using HMMs. This experiment showed that mathematical models such as HMM can efficiently predict hypovigilance through surrogate measures. The presented model could result in the development of an in-vehicle device that detects driver hypovigilance in advance and warn the driver accordingly, thus offering the potential to enhance road safety and prevent road crashes.

Using accelerometer, high sample rate GPS and magnetometer data to develop a cattle movement and behaviour model

The study described in this paper developed a model of animal movement, which explicitly recognised each individual as the central unit of measure. The model was developed by learning from a real dataset that measured and calculated, for individual cows in a herd, their linear and angular positions and directional and angular speeds. Two learning algorithms were implemented: a Hidden Markov model (HMM) and a long-term prediction algorithm. It is shown that a HMM can be used to describe the animal's movement and state transition behaviour within several “stay” areas where cows remained for long periods. Model parameters were estimated for hidden behaviour states such as relocating, foraging and bedding. For cows’ movement between the “stay” areas a long-term prediction algorithm was implemented. By combining these two algorithms it was possible to develop a successful model, which achieved similar results to the animal behaviour data collected. This modelling methodology could easily be applied to interactions of other animal species.

Multivariate Markov Process Models for the transmission of methicillin-resistant Staphylococcus Aureus in a hospital ward

Methicillin-resistant Staphylococcus Aureus (MRSA) is a pathogen that continues to be of major concern in hospitals. We develop models and computational schemes based on observed weekly incidence data to estimate MRSA transmission parameters. We extend the deterministic model of McBryde, Pettitt, and McElwain (2007, Journal of Theoretical Biology 245, 470–481) involving an underlying population of MRSA colonized patients and health-care workers that describes, among other processes, transmission between uncolonized patients and colonized health-care workers and vice versa. We develop new bivariate and trivariate Markov models to include incidence so that estimated transmission rates can be based directly on new colonizations rather than indirectly on prevalence. Imperfect sensitivity of pathogen detection is modeled using a hidden Markov process. The advantages of our approach include (i) a discrete valued assumption for the number of colonized health-care workers, (ii) two transmission parameters can be incorporated into the likelihood, (iii) the likelihood depends on the number of new cases to improve precision of inference, (iv) individual patient records are not required, and (v) the possibility of imperfect detection of colonization is incorporated. We compare our approach with that used by McBryde et al. (2007) based on an approximation that eliminates the health-care workers from the model, uses Markov chain Monte Carlo and individual patient data. We apply these models to MRSA colonization data collected in a small intensive care unit at the Princess Alexandra Hospital, Brisbane, Australia.