A decision-theoretic approach for segmental classification

This paper is concerned with statistical methods for the segmental classification of linear sequence data where the task is to segment and classify the data according to an underlying hidden discrete state sequence. Such analysis is commonplace in the empirical sciences including genomics, finance and speech processing. In particular, we are interested in answering the following question: given data $y$ and a statistical model $\pi(x,y)$ of the hidden states $x$, what should we report as the prediction $\hat{x}$ under the posterior distribution $\pi (x|y)$? That is, how should you make a prediction of the underlying states? We demonstrate that traditional approaches such as reporting the most probable state sequence or most probable set of marginal predictions can give undesirable classification artefacts and offer limited control over the properties of the prediction. We propose a decision theoretic approach using a novel class of Markov loss functions and report $\hat{x}$ via the principle of minimum expected loss (maximum expected utility). We demonstrate that the sequence of minimum expected loss under the Markov loss function can be enumerated exactly using dynamic programming methods and that it offers flexibility and performance improvements over existing techniques. The result is generic and applicable to any probabilistic model on a sequence, such as Hidden Markov models, change point or product partition models.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS657 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R

This paper describes the R package mhsmm which implements estimation and prediction methods for hidden Markov and semi-Markov models for multiple observation sequences. Such techniques are of interest when observed data is thought to be dependent on some unobserved (or hidden) state. Hidden Markov models only allow a geometrically distributed sojourn time in a given state, while hidden semi-Markov models extend this by allowing an arbitrary sojourn distribution. We demonstrate the software with simulation examples and an application involving the modelling of the ovarian cycle of dairy cows.

Hidden hybrid Markov/semi-Markov chains.

http://www.sciencedirect.com/science?ₒb=IssueURL&_tockey=%23TOC%235880%232005%23999509996%23596026%23FLA%23&ₐuth=y&view=c&ₐcct=C000056834&_version=1&_urlVersion=0&_userid=2292769&md5=87e7f8be94f92a8574da566c600ce631International audienceModels that combine Markovian states with implicit geometric state occupancy distributions and semi-Markovian states with explicit state occupancy distributions, are investigated. This type of model retains the flexibility of hidden semi-Markov chains for the modeling of short or medium size homogeneous zones along sequences but also enables the modeling of long zones with Markovian states. The forward-backward algorithm, which in particular enables to implement efficiently the E-step of the EM algorithm, and the Viterbi algorithm for the restoration of the most likely state sequence are derived. It is also shown that macro-states, i.e. series-parallel networks of states with common observation distribution, are not a valid alternative to semi-Markovian states but may be useful at a more macroscopic level to combine Markovian states with semi-Markovian states. This statistical modeling approach is illustrated by the analysis of branching and flowering patterns in plants

Hidden Markov Model with Binned Duration and Its Application

Hidden Markov models (HMM) have been widely used in various applications such as speech processing and bioinformatics. However, the standard hidden Markov model requires state occupancy durations to be geometrically distributed, which can be inappropriate in some real-world applications where the distributions on state intervals deviate signi cantly from the geometric distribution, such as multi-modal distributions and heavy-tailed distributions. The hidden Markov model with duration (HMMD) avoids this limitation by explicitly incor- porating the appropriate state duration distribution, at the price of signi cant computational expense. As a result, the applications of HMMD are still quited limited. In this work, we present a new algorithm - Hidden Markov Model with Binned Duration (HMMBD), whose result shows no loss of accuracy compared to the HMMD decoding performance and a com- putational expense that only diers from the much simpler and faster HMM decoding by a constant factor. More precisely, we further improve the computational complexity of HMMD from (TNN +TND) to (TNN +TND ), where TNN stands for the computational com- plexity of the HMM, D is the max duration value allowed and can be very large and D generally could be a small constant value

Duration and Interval Hidden Markov Model for Sequential Data Analysis

Analysis of sequential event data has been recognized as one of the essential tools in data modeling and analysis field. In this paper, after the examination of its technical requirements and issues to model complex but practical situation, we propose a new sequential data model, dubbed Duration and Interval Hidden Markov Model (DI-HMM), that efficiently represents "state duration" and "state interval" of data events. This has significant implications to play an important role in representing practical time-series sequential data. This eventually provides an efficient and flexible sequential data retrieval. Numerical experiments on synthetic and real data demonstrate the efficiency and accuracy of the proposed DI-HMM

Estimating hidden semi-Markov chains from discrete sequences.

International audienceThis article addresses the estimation of hidden semi-Markov chains from nonstationary discrete sequences. Hidden semi-Markov chains are particularly useful to model the succession of homogeneous zones or segments along sequences. A discrete hidden semi-Markov chain is composed of a nonobservable state process, which is a semi-Markov chain, and a discrete output process. Hidden semi-Markov chains generalize hidden Markov chains and enable the modeling of various durational structures. From an algorithmic point of view, a new forward-backward algorithm is proposed whose complexity is similar to that of the Viterbi algorithm in terms of sequence length (quadratic in the worst case in time and linear in space). This opens the way to the maximum likelihood estimation of hidden semi-Markov chains from long sequences. This statistical modeling approach is illustrated by the analysis of branching and flowering patterns in plants

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