Types Of Hidden Markov Models Research Articles

Increasing the accuracy of single-molecule data analysis using tMAVEN

Time-dependent single-molecule experiments contain rich kinetic information about the functional dynamics of biomolecules. A key step in extracting this information is the application of kinetic models, such as hidden Markov models (HMMs), which characterize the molecular mechanism governing the experimental system. Unfortunately, researchers rarely know the physicochemical details of this molecular mechanism a priori, which raises questions about how to select the most appropriate kinetic model for a given single-molecule data set and what consequences arise if the wrong model is chosen. To address these questions, we have developed and used time-series modeling, analysis, and visualization environment (tMAVEN), a comprehensive, open-source, and extensible software platform. tMAVEN can perform each step of the single-molecule analysis pipeline, from preprocessing to kinetic modeling to plotting, and has been designed to enable the analysis of a single-molecule data set with multiple types of kinetic models. Using tMAVEN, we have systematically investigated mismatches between kinetic models and molecular mechanisms by analyzing simulated examples of prototypical single-molecule data sets exhibiting common experimental complications, such as molecular heterogeneity, with a series of different types of HMMs. Our results show that no single kinetic modeling strategy is mathematically appropriate for all experimental contexts. Indeed, HMMs only correctly capture the underlying molecular mechanism in the simplest of cases. As such, researchers must modify HMMs using physicochemical principles to avoid the risk of missing the significant biological and biophysical insights into molecular heterogeneity that their experiments provide. By enabling the facile, side-by-side application of multiple types of kinetic models to individual single-molecule data sets, tMAVEN allows researchers to carefully tailor their modeling approach to match the complexity of the underlying biomolecular dynamics and increase the accuracy of their single-molecule data analyses.

Seismic activity analysis of five major earthquake source segments in the Sumatra megathrust zone

The Sumatra megathrust zone has five major earthquake sources, namely the Aceh-Andaman, Nias-Simeulue, Mentawai-Siberut, Mentawai-Pagai, and Enggano segments. This paper provides seismic activity analysis in these five segments via an unobserved process study of tectonic plate movements, which is conducted in two cases: each of the five segments independently (Case 1), and a pair of two adjacent segments (Case 2). To do this, two specific types of Hidden Markov Models (HMMs), i.e., Poisson-HMMs and Copula-HMMs, dealing with unobserved process issues, are applied. In practice, the data used is the annual frequency of mainshock earthquakes with a magnitude of >4.6 that occurred from 1971 to 2018. This data is obtained by working out the declustering process and estimating the magnitude of completeness from a particular earthquake catalogue. Due to the incompleteness of the data sets, the parameters of the two HMMs are estimated using the Expectation-Maximization algorithm. Results show that for Case 1, the model that fits the data for each of the five segments is the 3-state Poisson-HMM. The three states, in this instance, stand for the rates of seismic activity that correspond to the dynamic level of tectonic plate movements. Furthermore, in Case 2, the selected model for the Aceh-Andaman with Nias-Simeulue is the 2-state Gumbel Copula-HMM. Meanwhile, for the three groups remaining, namely Nias-Simeulue with Mentawai-Siberut, Mentawai-Siberut with Mentawai-Pagai, and Mentawai-Pagai with Enggano, the appropriate models are Gaussian, Gumbel, and Frank Copulas, respectively. In this case, the number of states represents the seismic activity association of two adjacent segments that corresponds to the association level of two adjacent tectonic plate dynamics.

Hidden Markov models with binary dependence

Hidden Markov models are widely used to model the probabilistic structures with latent variables. The main assumption of hidden Markov models is that; observation symbols are conditionally independent and identically distributed random variables. There exist some cases where this assumption may not be valid in practice. That is, an observation symbol that occurs in the current state may depend on the previous observation symbol that occurred in the previous state. In this study, a new type of hidden Markov model is introduced in which the current pair of hidden state-emitted observation symbol and the previous pair of those have a first-order Markov dependency. The proposed model is capable of capturing a possible first-order Markov dependency between the last and the previous steps of the system. In addition, it provides a better representation for the appropriate real-life problems where, if the observation symbols have conditional dependence. It is an alternative model to the classical hidden Markov model for revealing the Markov dependency between the current and the previous binary information of the system. An experimental study is conducted to show the performance of the proposed model compared to the classical hidden Markov model. Besides, two different case studies are conducted namely the occurrences of strong earthquakes and daily stock prices are modeled with both the classical hidden Markov model and the proposed model, and the results are compared.

Statistical learning and estimation of piano fingering

Automatic estimation of piano fingering is important for understanding the computational process of music performance and applicable to performance assistance and education systems. While a natural way to formulate the quality of fingerings is to construct models of the constraints/costs of performance, it is generally difficult to find appropriate parameter values for these models. Here we study an alternative data-driven approach based on statistical modeling in which the appropriateness of a given fingering is described by probabilities. Specifically, we construct two types of hidden Markov models (HMMs) and their higher-order extensions. We also study deep neural network (DNN)-based methods for comparison. Using a newly released dataset of fingering annotations, we conduct systematic evaluations of these models as well as a representative constraint-based method. We find that the methods based on high-order HMMs outperform the other methods in terms of estimation accuracies. We also quantitatively study individual difference of fingering and propose evaluation measures that can be used with multiple ground truth data. We conclude that the HMM-based methods are currently state of the art and generate acceptable fingerings in most parts and that they have certain limitations such as ignorance of phrase boundaries and interdependence of the two hands.

Testing Applicability of Virtual Stochastic Sensors for Non-Intrusive Appliance Load Monitoring

Non-intrusive appliance load monitoring (NIALM) aims at reconstructing the electricity consumption of household appliances based only on the cumulative consumption data collected via a smart meter. Various approaches have been proposed to perform NIALM including various types of Hidden Markov Model (HMM) offspring. Most do not consider the explicit duration of an appliance activation. Virtual stochastic sensors (VSS) and their underlying Hidden non-Markovian Models (HnMM) can include explicit process durations. This paper tests whether VSS can solve the NIALM task, and analyzes the methods reconstruction accuracy on the publicly available SMART* data set. Models of the household appliances with different inherent states are automatically extracted from the appliance data. The combined model, including a subset of the appliances, is then used to disaggregate the cumulative energy consumption data. Experiments show a reconstruction accuracy of up to 90% with appropriate method parameters, showing that VSS can compete with existing NIALM approaches.

On Quitting: Performance and Practice in Online Game Play

We study the relationship between performance and practice by analyzing the activity of many players of a casual online game. We find significant heterogeneity in the improvement of player performance, given by score, and address this by dividing players into similar skill levels and segmenting each player's activity into sessions, that is, sequence of game rounds without an extended break. After disaggregating data, we find that performance improves with practice across all skill levels. More interestingly, players are more likely to end their session after an especially large improvement, leading to a peak score in their very last game of a session. In addition, success is strongly correlated with a lower quitting rate when the score drops, and only weakly correlated with skill, in line with psychological findings about the value of persistence and “grit:” successful players are those who persist in their practice despite lower scores. Finally, we train an ε-machine, a type of hidden Markov model, and find a plausible mechanism of game play that can predict player performance and quitting the game. Our work raises the possibility of real-time assessment and behavior prediction that can be used to optimize human performance.

Hidden Markov Modelling of Sparse Time Series from Non-Volcanic Tremor Observations

SummaryTremor activity has been recently detected in various tectonic areas world wide and is spatially segmented and temporally recurrent. We design a type of hidden Markov models to investigate this phenomenon, where each state represents a distinct segment of tremor sources. A mixture distribution of a Bernoulli variable and a continuous variable is introduced into the hidden Markov model to solve the problem that tremor clusters are very sparse in time. We applied our model to the tremor data from the Tokai region in Japan to identify distinct segments of tremor source regions and the results reveal the spatiotemporal migration pattern among these segments.

Bayesian Identification of Hidden Markov Models and Their Use for Condition-Based Monitoring

In this paper, we propose a Bayesian estimation scheme for hidden Markov model (HMM) parameters, as well as a method for monitoring systems whose degradation processes are modeled using HMMs identified using this novel estimation approach. The Bayesian estimation naturally yields information about model parametric uncertainties via posterior distributions of HMM parameters emanating from the estimation procedure. Numerous simulations implementing the newly proposed method for estimation of HMM parameters were conducted demonstrating its capability to identify several types of HMMs, including the commonly encountered ergodic and homogeneous HMM, as well as less commonly studied nonergodic or/and nonhomogeneous HMM. In addition, a novel condition monitoring scheme based on uncertain HMMs of the degradation process is proposed and demonstrated on a large dataset obtained from a semiconductor-manufacturing facility. A small portion of the data was used to build operating mode specific HMMs of machine degradation via the newly proposed Bayesian estimation, while the remainder of the data was used for condition monitoring based on the uncertain degradation HMMs yielded by the novel Bayesian estimation method. Comparison with a traditional sensory signature-based statistical monitoring method showed that the newly proposed approach significantly outperforms the traditional method in terms of its detection capabilities and false alarm ratios.

Outer-Product Hidden Markov Model and Polyphonic MIDI Score Following

We present a polyphonic MIDI score-following algorithm capable of following performances with arbitrary repeats and skips, based on a probabilistic model of musical performances. It is attractive in practical applications of score following to handle repeats and skips which may be made arbitrarily present during performances, but the algorithms previously described in the literature cannot be applied to scores of practical length due to problems with large computational complexity. We propose a new type of hidden Markov model (HMM) as a performance model which can describe arbitrary repeats and skips including performer tendencies on distributed score positions before and after them, and derive an efficient score-following algorithm that reduces computational complexity without pruning. A theoretical discussion on how much such information on performer tendencies improves the score-following results is given. The proposed score-following algorithm also admits performance mistakes and is demonstrated to be effective in practical situations by carrying out evaluations with human performances. The proposed HMM is potentially valuable for other topics in information processing and we also provide a detailed description of inference algorithms.

Non-Markovian properties and multiscale hidden Markovian network buried in single molecule time series

We present a novel scheme to extract a multiscale state space network (SSN) from single-molecule time series. The multiscale SSN is a type of hidden Markov model that takes into account both multiple states buried in the measurement and memory effects in the process of the observable whenever they exist. Most biological systems function in a nonstationary manner across multiple timescales. Combined with a recently established nonlinear time series analysis based on information theory, a simple scheme is proposed to deal with the properties of multiscale and nonstationarity for a discrete time series. We derived an explicit analytical expression of the autocorrelation function in terms of the SSN. To demonstrate the potential of our scheme, we investigated single-molecule time series of dissociation and association kinetics between epidermal growth factor receptor (EGFR) on the plasma membrane and its adaptor protein Ash/Grb2 (Grb2) in an in vitro reconstituted system. We found that our formula successfully reproduces their autocorrelation function for a wide range of timescales (up to 3 s), and the underlying SSNs change their topographical structure as a function of the timescale; while the corresponding SSN is simple at the short timescale (0.033-0.1 s), the SSN at the longer timescales (0.1 s to ~3 s) becomes rather complex in order to capture multiscale nonstationary kinetics emerging at longer timescales. It is also found that visiting the unbound form of the EGFR-Grb2 system approximately resets all information of history or memory of the process.

A Model-Based Sequence Similarity with Application to Handwritten Word Spotting

This paper proposes a novel similarity measure between vector sequences. We work in the framework of model-based approaches, where each sequence is first mapped to a Hidden Markov Model (HMM) and then a measure of similarity is computed between the HMMs. We propose to model sequences with semicontinuous HMMs (SC-HMMs). This is a particular type of HMM whose emission probabilities in each state are mixtures of shared Gaussians. This crucial constraint provides two major benefits. First, the a priori information contained in the common set of Gaussians leads to a more accurate estimate of the HMM parameters. Second, the computation of a similarity between two SC-HMMs can be simplified to a Dynamic Time Warping (DTW) between their mixture weight vectors, which significantly reduces the computational cost. Experiments are carried out on a handwritten word retrieval task in three different datasets-an in-house dataset of real handwritten letters, the George Washington dataset, and the IFN/ENIT dataset of Arabic handwritten words. These experiments show that the proposed similarity outperforms the traditional DTW between the original sequences, and the model-based approach which uses ordinary continuous HMMs. We also show that this increase in accuracy can be traded against a significant reduction of the computational cost.

Visual Speech Recognition based on Improved type of Hidden Markov Model

Visual Speech Recognition based on Improved type of Hidden Markov Model

Speech command recognition using a system based on the digital signal processor TMS320F2812 of Texas Instruments.

This paper describes the hardware design of a multi‐purpose electronic system for speech command recognition based on the digital signal processor TMS320F2812 of Texas Instruments. In the paper, we utilize this system for speech command recognition. Specifically, we design and build an electronic system capable of recognizing speech commands. The main blocks are a power source, oscillator, adc, amplifier, jtag, reset boot mode, and monitor LED. The technique used for recognition is a multi section vector quantization, which is a well known technique in the field. This was selected over techniques such as discrete hidden Markov models (HMMs), Gaussian mixture models, or dynamic time warping. It is faster and equally precise compared to these techniques for the purpose of a very limited vocabulary, although we are aware that several types of HMMs are the techniques more widely used until now for continuous speech recognition systems. Preliminary tests for five words give us a rate of 96% in recognition accuracy for 10 repetitions for training and 10 for testing (one subject, under a 20 dB of signal‐to‐noise ratio). In these months, the system will be tested for more words and subjects. Also, it will be tested in real situations.

Hidden Markov Models and their Applications in Biological Sequence Analysis

Hidden Markov models (HMMs) have been extensively used in biological sequence analysis. In this paper, we give a tutorial review of HMMs and their applications in a variety of problems in molecular biology. We especially focus on three types of HMMs: the profile-HMMs, pair-HMMs, and context-sensitive HMMs. We show how these HMMs can be used to solve various sequence analysis problems, such as pairwise and multiple sequence alignments, gene annotation, classification, similarity search, and many others.

A Bound on Modeling Error in Observable Operator Models and an Associated Learning Algorithm

Observable operator models (OOMs) generalize hidden Markov models (HMMs) and can be represented in a structurally similar matrix formalism. The mathematical theory of OOMs gives rise to a family of constructive, fast, and asymptotically correct learning algorithms, whose statistical efficiency, however, depends crucially on the optimization of two auxiliary transformation matrices. This optimization task is nontrivial; indeed, even formulating computationally accessible optimality criteria is not easy. Here we derive how a bound on the modeling error of an OOM can be expressed in terms of these auxiliary matrices, which in turn yields an optimization procedure for them and finally affords us with a complete learning algorithm: the error-controlling algorithm. Models learned by this algorithm have an assured error bound on their parameters. The performance of this algorithm is illuminated by comparisons with two types of HMMs trained by the expectation-maximization algorithm, with the efficiency-sharpening algorithm, another recently found learning algorithm for OOMs, and with predictive state representations (Littman & Sutton, 2001 ) trained by methods representing the state of the art in that field.

Beyond Output Voting: Detecting Compromised Replicas Using HMM-Based Behavioral Distance

Many host-based anomaly detection techniques have been proposed to detect code-injection attacks on servers. The vast majority, however, are susceptible to attacks in which the injected code masquerades as the original server software, including returning the correct service responses, while conducting its attack. Behavioral distance, by which two diverse replicas processing the same inputs are continually monitored to detect divergence in their low-level (system-call) behaviors and hence potentially the compromise of one of them, has been proposed for detecting mimicry attacks. In this paper, we present a novel approach to behavioral distance measurement using a new type of hidden Markov model, and present an architecture realizing this new approach. We evaluate the detection capability of this approach using synthetic workloads and recorded workloads of production Web and game servers, and show that it detects intrusions with substantially greater accuracy than a prior proposal on measuring behavioral distance. We also detail the design and implementation of a new architecture, which takes advantage of virtualization to measure behavioral distance. We apply our architecture to implement intrusion-tolerant Web and game servers, and through trace-driven simulations demonstrate that it experiences moderate performance costs even when thresholds are set to detect stealthy mimicry attacks.

Markov and Semi-Markov Switching of Source Appearances for Nonstationary Independent Component Analysis

Independent component analysis (ICA) is currently the most popularly used approach to blind source separation (BSS), the problem of recovering unknown source signals when their mixtures are observed but the actual mixing process is unknown. Many ICA algorithms assume that a fixed set of source signals consistently exists in mixtures throughout the time-series to be examined. However, real-world signals often have such difficult nonstationarity that each source signal abruptly appears or disappears, thus the set of active sources dynamically changes with time. In this paper, we propose switching ICA (SwICA), which focuses on such situations. The proposed approach is based on the noisy ICA formulated as a generative model. We employ a special type of hidden Markov model (HMM) to represent such prior knowledge that the source may abruptly appear or disappear with time. The special HMM setting t hen provides an effect ofvariable selection in a dynamic way. We use the variational Bayes (VB) method to derive an effective approximation of Bayesian inference for this model. In simulation experiments using artificial and realistic source signals, the proposed method exhibited performance superior to existing methods, especially in the presence of noise. The compared methods include the natural-gradient ICA with a nonholonomic constraint, and the existing ICA method incorporating an HMM source model, which aims to deal with general nonstationarities that may exist in source signals. In addition, the proposed method could successfully recover the source signals even when the total number of true sources was overestimated or was larger than that of mixtures. We also propose a modification of the basic Markov model into a semi-Markov model, and show that the semi-Markov one is more effective for robust estimation of the source appearance.

On some stochastic models for replication of character strings

In this note, some probabilistic models for replication of character strings are considered. These replication processes involve random mutations, deletions and insertions of characters. We investigate invariance of certain probabilistic properties of replicating character strings under the proposed stochastic models for the replication process. It is shown that some well-known types of hidden Markov models with finite state spaces arise as special cases of our stochastic replication models. We also introduce the notion of a hidden mixed Markov model for a character string that arises in a situation where the replication process satisfies exchangeability conditions.

Hidden Markov models with states depending on observations

In the standard hidden Markov model, the current state depends only on the immediately preceding state, but has nothing to do with the immediately preceding observation. This paper presents a new type of hidden Markov models in which the current state depends both on the immediately preceding state and the immediately preceding observation, and the state sequence is still a Markov chain. Several new algorithms are given and simulated for the three basic problems of interest, including probability evaluation, optimal state sequence and parameter estimation. One example of its initial applications shows that the new model may outperform the standard model in some circumstance.

SPRT and CUSUM in hidden Markov models

In this paper, we study the problems of sequential probability ratio tests for parameterized hidden Markov models. We investigate in some detail the performance of the tests and derive corrected Brownian approximations for error probabilities and expected sample sizes. Asymptotic optimality of the sequential probability ratio test for testing simple hypotheses based on hidden Markov chain data is established. Next, we consider the cumulative sum (CUSUM) procedure for change point detection in this model. Based on the renewal property of the stopping rule, CUSUM can be regarded as a repeated one-sided sequential probability ratio test. Asymptotic optimality of the CUSUM procedure is proved in the sense of Lorden (1971). Motivated by the sequential analysis in hidden Markov models, Wald's likelihood ratio identity and Wald's equation for products of Markov random matrices are also given. We apply these results to several types of hidden Markov models: i.i.d. hidden Markov models, switch Gaussian regression and switch Gaussian autoregression, which are commonly used in digital communications, speech recognition, bioinformatics and economics.