Adjusted Viterbi training for hidden Markov models

To estimate the emission parameters in hidden Markov models one commonly uses the EM algorithm or its variation. Our primary motivation, however, is the Philips speech recognition system wherein the EM algorithm is replaced by the Viterbi training algorithm. Viterbi training is faster and computationally less involved than EM, but it is also biased and need not even be consistent. We propose an alternative to the Viterbi training -- adjusted Viterbi training -- that has the same order of computational complexity as Viterbi training but gives more accurate estimators. Elsewhere, we studied the adjusted Viterbi training for a special case of mixtures, supporting the theory by simulations. This paper proves the adjusted Viterbi training to be also possible for more general hidden Markov models.Comment: 45 pages, 2 figure

A constructive proof of the existence of Viterbi processes

Since the early days of digital communication, hidden Markov models (HMMs) have now been also routinely used in speech recognition, processing of natural languages, images, and in bioinformatics. In an HMM $(X_i,Y_i)_{i\ge 1}$, observations $X_1,X_2,...$ are assumed to be conditionally independent given an ``explanatory'' Markov process $Y_1,Y_2,...$, which itself is not observed; moreover, the conditional distribution of $X_i$ depends solely on $Y_i$. Central to the theory and applications of HMM is the Viterbi algorithm to find {\em a maximum a posteriori} (MAP) estimate $q_{1:n}=(q_1,q_2,...,q_n)$ of $Y_{1:n}$ given observed data $x_{1:n}$. Maximum {\em a posteriori} paths are also known as Viterbi paths or alignments. Recently, attempts have been made to study the behavior of Viterbi alignments when $n\to \infty$. Thus, it has been shown that in some special cases a well-defined limiting Viterbi alignment exists. While innovative, these attempts have relied on rather strong assumptions and involved proofs which are existential. This work proves the existence of infinite Viterbi alignments in a more constructive manner and for a very general class of HMMs.Comment: Submitted to the IEEE Transactions on Information Theory, focuses on the proofs of the results presented in arXiv:0709.2317, and arXiv:0803.239

Infinite Viterbi alignments in the two state hidden Markov models

Since the early days of digital communication, Hidden Markov Models (HMMs) have now been routinely used in speech recognition, processing of natural languages, images, and in bioinformatics. An HMM $(X_i,Y_i)_{i\ge 1}$ assumes observations $X_1,X_2,...$ to be conditionally independent given an "explanotary" Markov process $Y_1,Y_2,...$, which itself is not observed; moreover, the conditional distribution of $X_i$ depends solely on $Y_i$. Central to the theory and applications of HMM is the Viterbi algorithm to find {\em a maximum a posteriori} estimate $q_{1:n}=(q_1,q_2,...,q_n)$ of $Y_{1:n}$ given the observed data $x_{1:n}$. Maximum {\em a posteriori} paths are also called Viterbi paths or alignments. Recently, attempts have been made to study the behavior of Viterbi alignments of HMMs with two hidden states when $n$ tends to infinity. It has indeed been shown that in some special cases a well-defined limiting Viterbi alignment exists. While innovative, these attempts have relied on rather strong assumptions. This work proves the existence of infinite Viterbi alignments for virtually any HMM with two hidden states.Comment: Several minor changes and corrections have been made in the arguments as suggested by anonymous reviewers, which should hopefully improve readability. Abstract has been adde

Family doctors' knowledge and self-reported care of type 2 diabetes patients in comparison to the clinical practice guideline: cross-sectional study

BACKGROUND: It is widely believed that providing doctors with guidelines will lead to more effective clinical practice and better patient care. However, different studies have shown contradictory results in quality improvement as a result of guideline implementation. The aim of this study was to compare family doctors' knowledge and self-reported care of type 2 diabetes patients with recommendation standards of the clinical practice guideline. METHODS: In April 2003 a survey was conducted among family doctors in Estonia. The structured questionnaire focused on the knowledge and self-reported behavior of doctors regarding the guideline of type 2 diabetes. The demographic and professional data of the respondents was also provided. RESULTS: Of the 354 questionnaires distributed, 163 were returned for a response rate of 46%. Seventy-six percent of the responded doctors stated that they had a copy of the guideline available while 24% reported that they did not. Eighty-three percent of the doctors considered it applicable and 79% reported using it in daily practice. The doctors tended to start treatment with medications and were satisfied with treatment outcomes at higher fasting blood glucose levels than the levels recommended in the guideline. Doctors' self-reported performance of the tests and examinations named in the guideline, which should be performed within a certain time limit, varied from overuse to underuse. Blood pressure, serum creatinine, eye examination and checking patients' ability to manage their diabetes were the best-followed items while glycosylated hemoglobin and weight reduction were the most poorly followed. Doctors' behavior was not related to the fact of whether they had the guideline available, whether they considered it applicable, or whether they actually used it. CONCLUSION: Doctors' knowledge and self-reported behavior in patient follow-up of type 2 diabetes is very variable and is not related to the reported availability or usage of the guideline. Practice guidelines may be a useful source of information but they should not be overestimated