2,850 research outputs found
Accuracy of MAP segmentation with hidden Potts and Markov mesh prior models via Path Constrained Viterbi Training, Iterated Conditional Modes and Graph Cut based algorithms
In this paper, we study statistical classification accuracy of two different
Markov field environments for pixelwise image segmentation, considering the
labels of the image as hidden states and solving the estimation of such labels
as a solution of the MAP equation. The emission distribution is assumed the
same in all models, and the difference lays in the Markovian prior hypothesis
made over the labeling random field. The a priori labeling knowledge will be
modeled with a) a second order anisotropic Markov Mesh and b) a classical
isotropic Potts model. Under such models, we will consider three different
segmentation procedures, 2D Path Constrained Viterbi training for the Hidden
Markov Mesh, a Graph Cut based segmentation for the first order isotropic Potts
model, and ICM (Iterated Conditional Modes) for the second order isotropic
Potts model.
We provide a unified view of all three methods, and investigate goodness of
fit for classification, studying the influence of parameter estimation,
computational gain, and extent of automation in the statistical measures
Overall Accuracy, Relative Improvement and Kappa coefficient, allowing robust
and accurate statistical analysis on synthetic and real-life experimental data
coming from the field of Dental Diagnostic Radiography. All algorithms, using
the learned parameters, generate good segmentations with little interaction
when the images have a clear multimodal histogram. Suboptimal learning proves
to be frail in the case of non-distinctive modes, which limits the complexity
of usable models, and hence the achievable error rate as well.
All Matlab code written is provided in a toolbox available for download from
our website, following the Reproducible Research Paradigm
Parameter estimation in pair hidden Markov models
This paper deals with parameter estimation in pair hidden Markov models
(pair-HMMs). We first provide a rigorous formalism for these models and discuss
possible definitions of likelihoods. The model being biologically motivated,
some restrictions with respect to the full parameter space naturally occur.
Existence of two different Information divergence rates is established and
divergence property (namely positivity at values different from the true one)
is shown under additional assumptions. This yields consistency for the
parameter in parametrization schemes for which the divergence property holds.
Simulations illustrate different cases which are not covered by our results.Comment: corrected typo
A mixed MAP/MLSE receiver for convolutional coded signals transmitted over a fading channel
Copyright © 2002 IEEEThis paper addresses the problem of estimating a rapidly fading convolutionally coded signal such as might be found in a wireless telephony or data network. We model both the channel gain and the convolutionally coded signal as Markov processes and, thus, the noisy received signal as a hidden Markov process (HMP). Two now-classical methods for estimating finite-state hidden Markov processes are the Viterbi (1967) algorithm and the a posteriori probability (APP) filter. A hybrid recursive estimation procedure is derived whereby one hidden process (the encoder state in our application) is estimated using a Viterbi-type (i.e., sequence based) cost and the other (the fading process) using an APP-based cost such as maximum a posteriori probability. The paper presents the new algorithm as applied specifically to this problem but also formulates the problem in a more general setting. The algorithm is derived in this general setting using reference probability methods. Using simulations, performance of the optimal scheme is compared with a number of suboptimal techniques-decision-directed Kalman and HMP predictors and Kalman filter and HMP filter per-survivor processing techniquesLangford B. White and Robert J. Elliot
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
Bayesian Structural Inference for Hidden Processes
We introduce a Bayesian approach to discovering patterns in structurally
complex processes. The proposed method of Bayesian Structural Inference (BSI)
relies on a set of candidate unifilar HMM (uHMM) topologies for inference of
process structure from a data series. We employ a recently developed exact
enumeration of topological epsilon-machines. (A sequel then removes the
topological restriction.) This subset of the uHMM topologies has the added
benefit that inferred models are guaranteed to be epsilon-machines,
irrespective of estimated transition probabilities. Properties of
epsilon-machines and uHMMs allow for the derivation of analytic expressions for
estimating transition probabilities, inferring start states, and comparing the
posterior probability of candidate model topologies, despite process internal
structure being only indirectly present in data. We demonstrate BSI's
effectiveness in estimating a process's randomness, as reflected by the Shannon
entropy rate, and its structure, as quantified by the statistical complexity.
We also compare using the posterior distribution over candidate models and the
single, maximum a posteriori model for point estimation and show that the
former more accurately reflects uncertainty in estimated values. We apply BSI
to in-class examples of finite- and infinite-order Markov processes, as well to
an out-of-class, infinite-state hidden process.Comment: 20 pages, 11 figures, 1 table; supplementary materials, 15 pages, 11
figures, 6 tables; http://csc.ucdavis.edu/~cmg/compmech/pubs/bsihp.ht
On the Viterbi process with continuous state space
This paper deals with convergence of the maximum a posterior probability path
estimator in hidden Markov models. We show that when the state space of the
hidden process is continuous, the optimal path may stabilize in a way which is
essentially different from the previously considered finite-state setting.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ294 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
- …