A generalized risk approach to path inference based on hidden Markov models

Motivated by the unceasing interest in hidden Markov models (HMMs), this paper re-examines hidden path inference in these models, using primarily a risk-based framework. While the most common maximum a posteriori (MAP), or Viterbi, path estimator and the minimum error, or Posterior Decoder (PD), have long been around, other path estimators, or decoders, have been either only hinted at or applied more recently and in dedicated applications generally unfamiliar to the statistical learning community. Over a decade ago, however, a family of algorithmically defined decoders aiming to hybridize the two standard ones was proposed (Brushe et al., 1998). The present paper gives a careful analysis of this hybridization approach, identifies several problems and issues with it and other previously proposed approaches, and proposes practical resolutions of those. Furthermore, simple modifications of the classical criteria for hidden path recognition are shown to lead to a new class of decoders. Dynamic programming algorithms to compute these decoders in the usual forward-backward manner are presented. A particularly interesting subclass of such estimators can be also viewed as hybrids of the MAP and PD estimators. Similar to previously proposed MAP-PD hybrids, the new class is parameterized by a small number of tunable parameters. Unlike their algorithmic predecessors, the new risk-based decoders are more clearly interpretable, and, most importantly, work "out of the box" in practice, which is demonstrated on some real bioinformatics tasks and data. Some further generalizations and applications are discussed in conclusion.Comment: Section 5: corrected denominators of the scaled beta variables (pp. 27-30), => corrections in claims 1, 3, Prop. 12, bottom of Table 1. Decoder (49), Corol. 14 are generalized to handle 0 probabilities. Notation is more closely aligned with (Bishop, 2006). Details are inserted in eqn-s (43); the positivity assumption in Prop. 11 is explicit. Fixed typing errors in equation (41), Example

Public procurement as an industrial policy tool an option for developing countries?

So far, only 40 countries have joined WTOÿs Government Procurement Agreement (GPA), from the developing world only some East Asian (Hong Kong [China], South Korea, Singapore) economies and ten Eastern European countries are parties to the agreement. This article sets out to answer two interrelated questions: is it advisable for developing countries to use public procurement efforts for development, and should more developing countries join the GPA? We survey key arguments for and against joining the GPA, and by adopting the framework of public procurement for innovation, we argue that government procurement should not be seen only as an indirect support measure for development, but also as a direct vehicle for promoting innovation and industries and, thus, growth and development. We also show that using public procurement for development assumes high levels of policy capacity, which most developing countries lack. In addition, we show how the GPA as well as other WTO agreements make it complicated for the developing countries to benefit from public procurement for innovation. As a result, the article suggests that the developing countries could apply a mix of direct and indirect (so-called soft) publicprocurement- for-innovation measures. In order to do this, developing countries need to develop the policy capacity to take advantage of the complex and multi-layered industrial policy space still available under WTO rules.

On the accuracy of the Viterbi alignment

In a hidden Markov model, the underlying Markov chain is usually hidden. Often, the maximum likelihood alignment (Viterbi alignment) is used as its estimate. Although having the biggest likelihood, the Viterbi alignment can behave very untypically by passing states that are at most unexpected. To avoid such situations, the Viterbi alignment can be modified by forcing it not to pass these states. In this article, an iterative procedure for improving the Viterbi alignment is proposed and studied. The iterative approach is compared with a simple bunch approach where a number of states with low probability are all replaced at the same time. It can be seen that the iterative way of adjusting the Viterbi alignment is more efficient and it has several advantages over the bunch approach. The same iterative algorithm for improving the Viterbi alignment can be used in the case of peeping, that is when it is possible to reveal hidden states. In addition, lower bounds for classification probabilities of the Viterbi alignment under different conditions on the model parameters are studied

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