Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Approximate Bayesian computation (ABC) is a popular technique for analysing data for complex models where the likelihood function is intractable. It involves using simulation from the model to approximate the likelihood, with this approximate likelihood then being used to construct an approximate posterior. In this paper, we consider methods that estimate the parameters by maximizing the approximate likelihood used in ABC. We give a theoretical analysis of the asymptotic properties of the resulting estimator. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how sequential Monte Carlo methods provide a natural method for implementing our likelihood-based ABC procedures.

Segmentação de nome e endereço por meio de modelos escondidos de Markov e sua aplicação em processos de vinculação de registros

A segmentação dos nomes nas suas partes constitutivas é uma etapa fundamental no processo de integração de bases de dados por meio das técnicas de vinculação de registros. Esta separação dos nomes pode ser realizada de diferentes maneiras. Este estudo teve como objetivo avaliar a utilização do Modelo Escondido de Markov (HMM) na segmentação nomes e endereços de pessoas e a eficiência desta segmentação no processo de vinculação de registros. Foram utilizadas as bases do Sistema de Informações sobre Mortalidade (SIM) e do Subsistema de Informação de Procedimentos de Alta Complexidade (APAC) do estado do Rio de Janeiro no período entre 1999 a 2004. Uma metodologia foi proposta para a segmentação de nome e endereço sendo composta por oito fases, utilizando rotinas implementadas em PL/SQL e a biblioteca JAHMM, implementação na linguagem Java de algoritmos de HMM. Uma amostra aleatória de 100 registros de cada base foi utilizada para verificar a correção do processo de segmentação por meio do modelo HMM.Para verificar o efeito da segmentação do nome por meio do HMM, três processos de vinculação foram aplicados sobre uma amostra das duas bases citadas acima, cada um deles utilizando diferentes estratégias de segmentação, a saber: 1) divisão dos nomes pela primeira parte, última parte e iniciais do nome do meio; 2) divisão do nome em cinco partes; (3) segmentação segundo o HMM. A aplicação do modelo HMM como mecanismo de segmentação obteve boa concordância quando comparado com o observador humano. As diferentes estratégias de segmentação geraram resultados bastante similares na vinculação de registros, tendo a estratégia 1 obtido um desempenho pouco melhor que as demais. Este estudo sugere que a segmentação de nomes brasileiros por meio do modelo escondido de Markov não é mais eficaz do que métodos tradicionais de segmentação.

Recurrent input transformations for Hidden Markov models

This paper presents a new architecture which integrates recurrent input transformations (RIT) and continuous density HMMs. The basic HMM structure is extended to accommodate recurrent neural networks which transform the input observations before they enter the Gaussian output distributions associated with the states of the HMM. During training the parameters of both HMM and RIT are simultaneously optimized according to the Maximum Mutual Information (MMI) criterion. Results are presented for the E-set recognition task which demonstrate the ability of recurrent input transformations to exploit longer term correlations in the speech signal and to give improved discrimination.

Equivalence and Reduction of Hidden Markov Models

This report studies when and why two Hidden Markov Models (HMMs) may represent the same stochastic process. HMMs are characterized in terms of equivalence classes whose elements represent identical stochastic processes. This characterization yields polynomial time algorithms to detect equivalent HMMs. We also find fast algorithms to reduce HMMs to essentially unique and minimal canonical representations. The reduction to a canonical form leads to the definition of 'Generalized Markov Models' which are essentially HMMs without the positivity constraint on their parameters. We discuss how this generalization can yield more parsimonious representations of stochastic processes at the cost of the probabilistic interpretation of the model parameters.

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.

A Comparative study of HMM and SVM in Malayalam Digit Recognition

A primary medium for the human beings to communicate through language is Speech. Automatic Speech Recognition is wide spread today. Recognizing single digits is vital to a number of applications such as voice dialling of telephone numbers, automatic data entry, credit card entry, PIN (personal identification number) entry, entry of access codes for transactions, etc. In this paper we present a comparative study of SVM (Support Vector Machine) and HMM (Hidden Markov Model) to recognize and identify the digits used in Malayalam speech.

Estimation of Hidden Markov Models parameters using differential evolution

Hidden Markov Models (HMMs) have been successfully applied to different modelling and classification problems from different areas over the recent years. An important step in using HMMs is the initialisation of the parameters of the model as the subsequent learning of HMM’s parameters will be dependent on these values. This initialisation should take into account the knowledge about the addressed problem and also optimisation techniques to estimate the best initial parameters given a cost function, and consequently, to estimate the best log-likelihood. This paper proposes the initialisation of Hidden Markov Models parameters using the optimisation algorithm Differential Evolution with the aim to obtain the best log-likelihood.

USE OF HIDDEN MARKOV MODELS FOR QTL MAPPING

An important aspect of the QTL mapping problem is the treatment of missing genotype data. If complete genotype data were available, QTL mapping would reduce to the problem of model selection in linear regression. However, in the consideration of loci in the intervals between the available genetic markers, genotype data is inherently missing. Even at the typed genetic markers, genotype data is seldom complete, as a result of failures in the genotyping assays or for the sake of economy (for example, in the case of selective genotyping, where only individuals with extreme phenotypes are genotyped). We discuss the use of algorithms developed for hidden Markov models (HMMs) to deal with the missing genotype data problem.

Time delay estimation with hidden Markov models

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models to identify the lag (or delay) between different variables for such data. Adopting an information-theoretic approach, we develop a procedure for training HMMs to maximise the mutual information (MMI) between delayed time series. The method is used to model the oil drilling process. We show that cross-correlation gives no information and that the MMI approach outperforms maximum likelihood.

Bayesian online algorithms for learning in discrete Hidden Markov Models

We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.

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.