57,628 research outputs found
Reduced complexity on-line estimation of hidden Markov model parameters
In this paper we propose and study low complexity algorithms for on-line estimation of hidden Markov model (HMM) parameters. The estimates approach the true model parameters as the measurement noise approaches zero, but otherwise give improved estimates, albeit with bias. On a nite data set in the high noise case, the bias may not be signi cantly more severe than for a higher complexity asymptotically optimal scheme. Our algorithms require O(N3) calculations per time instant, where N is the number of states. Previous algorithms based on earlier hidden Markov model signal processing methods, including the expectation-maximumisation (EM) algorithm require O(N4) calculations per time instant
Isolated Word Recognition by Recursive HMM Parameter Estimation Algorithm
Automatic speech recognition (ASR) technologies enable humans to communicate with computers. Isolated word recognition (IWR) is an important part of many known ASR systems. Minimizing the word error rate in cases of incremental learning is a unique challenge for developing an on-line ASR system. This paper focuses on on-line IWR using a recursive hidden Markov model (HMM) multivariate parameter estimation algorithm. The maximum likelihood method was used to estimate the unknown parameters of the model, and an algorithm for the adapted recursive EM algorithm for HMMs parameter estimation was derived. The resulting recursive EM algorithm is unique among its counterparts because of state transition probabilities calculation. It obtains more accurate parameter estimates compared to other algorithms of this type. In our experiment, the algorithm was implemented and adapted to several datasets for IWR. Thus, the recognition rate and algorithm convergence results are discussed in this work
Statistical Physics Analysis of Maximum a Posteriori Estimation for Multi-channel Hidden Markov Models
The performance of Maximum a posteriori (MAP) estimation is studied
analytically for binary symmetric multi-channel Hidden Markov processes. We
reduce the estimation problem to a 1D Ising spin model and define order
parameters that correspond to different characteristics of the MAP-estimated
sequence. The solution to the MAP estimation problem has different operational
regimes separated by first order phase transitions. The transition points for
-channel system with identical noise levels, are uniquely determined by
being odd or even, irrespective of the actual number of channels. We
demonstrate that for lower noise intensities, the number of solutions is
uniquely determined for odd , whereas for even there are exponentially
many solutions. We also develop a semi analytical approach to calculate the
estimation error without resorting to brute force simulations. Finally, we
examine the tradeoff between a system with single low-noise channel and one
with multiple noisy channels.Comment: The paper has been submitted to Journal of Statistical Physics with
submission number JOSS-S-12-0039
Sequential Bayesian inference for implicit hidden Markov models and current limitations
Hidden Markov models can describe time series arising in various fields of
science, by treating the data as noisy measurements of an arbitrarily complex
Markov process. Sequential Monte Carlo (SMC) methods have become standard tools
to estimate the hidden Markov process given the observations and a fixed
parameter value. We review some of the recent developments allowing the
inclusion of parameter uncertainty as well as model uncertainty. The
shortcomings of the currently available methodology are emphasised from an
algorithmic complexity perspective. The statistical objects of interest for
time series analysis are illustrated on a toy "Lotka-Volterra" model used in
population ecology. Some open challenges are discussed regarding the
scalability of the reviewed methodology to longer time series,
higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages,
10 figure
Detection of recombination in DNA multiple alignments with hidden markov models
CConventional phylogenetic tree estimation methods assume that all sites in a DNA multiple alignment have the same evolutionary history. This assumption is violated in data sets from certain bacteria and viruses due to recombination, a process that leads to the creation of mosaic sequences from different strains and, if undetected, causes systematic errors in phylogenetic tree estimation. In the current work, a hidden Markov model (HMM) is employed to detect recombination events in multiple alignments of DNA sequences. The emission probabilities in a given state are determined by the branching order (topology) and the branch lengths of the respective phylogenetic tree, while the transition probabilities depend on the global recombination probability. The present study improves on an earlier heuristic parameter optimization scheme and shows how the branch lengths and the recombination probability can be optimized in a maximum likelihood sense by applying the expectation maximization (EM) algorithm. The novel algorithm is tested on a synthetic benchmark problem and is found to clearly outperform the earlier heuristic approach. The paper concludes with an application of this scheme to a DNA sequence alignment of the argF gene from four Neisseria strains, where a likely recombination event is clearly detected
Nonparametric inference in hidden Markov models using P-splines
Hidden Markov models (HMMs) are flexible time series models in which the
distributions of the observations depend on unobserved serially correlated
states. The state-dependent distributions in HMMs are usually taken from some
class of parametrically specified distributions. The choice of this class can
be difficult, and an unfortunate choice can have serious consequences for
example on state estimates, on forecasts and generally on the resulting model
complexity and interpretation, in particular with respect to the number of
states. We develop a novel approach for estimating the state-dependent
distributions of an HMM in a nonparametric way, which is based on the idea of
representing the corresponding densities as linear combinations of a large
number of standardized B-spline basis functions, imposing a penalty term on
non-smoothness in order to maintain a good balance between goodness-of-fit and
smoothness. We illustrate the nonparametric modeling approach in a real data
application concerned with vertical speeds of a diving beaked whale,
demonstrating that compared to parametric counterparts it can lead to models
that are more parsimonious in terms of the number of states yet fit the data
equally well
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