Second-order hidden Markov models(HMM2) have been used for a long time in pattern recognition,especially in speech *** main advantages are their capabilities to model noisy temporal signals of variable length. In this...
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Second-order hidden Markov models(HMM2) have been used for a long time in pattern recognition,especially in speech *** main advantages are their capabilities to model noisy temporal signals of variable length. In this paper a new HMM2 for modeling state duration is *** order to describe the state duration of HMM2,the probability of state duration is defined,and the structure of state duration HMM2 is *** using Bayes statistics methods,a new forward-backward algorithm are given based on traditional *** addition,the reestimation formulae of the parameters about new models are brought forward using new forward-backward algorithm.
This paper is devoted to a stochastic differential game (SDG) of decoupled functional forward-backward stochastic differential equation (FBSDE). For our SDG, the associated upper and lower value functions of the SDG a...
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This paper is devoted to a stochastic differential game (SDG) of decoupled functional forward-backward stochastic differential equation (FBSDE). For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs). Applying the Girsanov transformation method introduced by Buckdahn and Li (2008), the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations to the path-dependent ones. By establishing the dynamic programming principal (DPP), we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.
In this paper we study the relationship between functional forward-backward stochastic systems and path-dependent PDEs. In the framework of functional Ito calculus, we introduce a path-dependent PDE and prove that its...
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In this paper we study the relationship between functional forward-backward stochastic systems and path-dependent PDEs. In the framework of functional Ito calculus, we introduce a path-dependent PDE and prove that its solution is uniquely determined by a functional forward-backward stochastic system.
This paper introduces a generalized forward-backward splitting algorithm for finding a zero of a sum of maximal monotone operators B + Sigma(n)(i=1) A(i), where B is cocoercive. It involves the computation of B in an ...
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This paper introduces a generalized forward-backward splitting algorithm for finding a zero of a sum of maximal monotone operators B + Sigma(n)(i=1) A(i), where B is cocoercive. It involves the computation of B in an explicit (forward) step and the parallel computation of the resolvents of the A(i)'s in a subsequent implicit (backward) step. We prove the algorithm's convergence in infinite dimension and its robustness to summable errors on the computed operators in the explicit and implicit steps. In particular, this allows efficient minimization of the sum of convex functions f + Sigma(n)(i=1) g(i), where f has a Lipschitz-continuous gradient and each g(i) is simple in the sense that its proximity operator is easy to compute. The resulting method makes use of the regularity of f in the forward step, and the proximity operators of the g(i) is are applied in parallel in the backward step. While the forward-backward algorithm cannot deal with more than n = 1 nonsmooth function, we generalize it to the case of arbitrary n. Examples on inverse problems in imaging demonstrate the advantage of the proposed methods in comparison to other splitting algorithms.
We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the condit...
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We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting meaningful observations} in HMM data series.
Bayesian modeling requires the specification of prior and likelihood models. In reservoir characterization, it is common practice to estimate the prior from a training image. This paper considers a multi-grid approach...
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Bayesian modeling requires the specification of prior and likelihood models. In reservoir characterization, it is common practice to estimate the prior from a training image. This paper considers a multi-grid approach for the construction of prior models for binary variables. On each grid level we adopt a Markov random field (MRF) conditioned on values in previous levels. Parameter estimation in MRFs is complicated by a computationally intractable normalizing constant. To cope with this problem, we generate a partially ordered Markov model (POMM) approximation to the MRF and use this in the model fitting procedure. Approximate unconditional simulation from the fitted model can easily be done by again adopting the POMM approximation to the fitted MRF. Approximate conditional simulation, for a given and easy to compute likelihood function, can also be performed either by the Metropolis-Hastings algorithm based on an approximation to the fitted MRF or by constructing a new POMM approximation to this approximate conditional distribution. The proposed methods are illustrated using three frequently used binary training images.
A convolutional two-level hidden Markov model is defined and evaluated. The bottom level contains an unobserved categorical Markov chain, and given the variables in this level the middle level contains unobserved cond...
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A convolutional two-level hidden Markov model is defined and evaluated. The bottom level contains an unobserved categorical Markov chain, and given the variables in this level the middle level contains unobserved conditionally independent Gaussian variables. The top level contains observable variables that are a convolution of the variables in the middle level plus additive Gaussian errors. The objective is to assess the categorical variables in the bottom level given the convolved observations in the top level. The inversion is cast in a Bayesian setting with a Markov chain prior model and convolved Gaussian likelihood model. The associated posterior model cannot be assessed since the normalizing constant is too computer demanding to calculate for realistic problems. Three approximate posterior models based on approximations of the likelihood model on generalized factorial form are defined. These approximations can be exactly assessed by the forward-backward algorithm. Both a synthetic case and a real seismic inversion case are used in an empirical evaluation. It is concluded that reliable and computationally efficient approximate posterior models for convolutional two-level hidden Markov models can be defined. (C) 2012 Elsevier B.V. All rights reserved.
We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the properties of the cocoercive operators appearing...
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We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the properties of the cocoercive operators appearing in the model. Several splitting algorithms recently proposed in the literature are recovered as special cases.
To investigate interactions between parasite species in a host, a population of field voles was studied longitudinally, with presence or absence of six different parasites measured repeatedly. Although trapping sessio...
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To investigate interactions between parasite species in a host, a population of field voles was studied longitudinally, with presence or absence of six different parasites measured repeatedly. Although trapping sessions were regular, a different set of voles was caught at each session, leading to incomplete profiles for all subjects. We use a discrete time hidden Markov model for each disease with transition probabilities dependent on covariates via a set of logistic regressions. For each disease the hidden states for each of the other diseases at a given time point form part of the covariate set for the Markov transition probabilities from that time point. This allows us to gauge the influence of each parasite species on the transition probabilities for each of the other parasite species. Inference is performed via a Gibbs sampler, which cycles through each of the diseases, first using an adaptive Metropolis-Hastings step to sample from the conditional posterior of the covariate parameters for that particular disease given the hidden states for all other diseases and then sampling from the hidden states for that disease given the parameters. We find evidence for interactions between several pairs of parasites and of an acquired immune response for two of the parasites.
In this paper we present a parallel implementation of a MAP decoder for synchronization error correcting codes. For a modest implementation effort, we demonstrate a considerable decoding speedup, up to two orders of m...
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In this paper we present a parallel implementation of a MAP decoder for synchronization error correcting codes. For a modest implementation effort, we demonstrate a considerable decoding speedup, up to two orders of magnitude even on consumer GPUs. This enables the analysis of much larger codes and worse channel conditions than previously possible, and makes applications of such codes feasible for software implementations.
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