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A Bayesian Approach to Recurrence in Neural Networks

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2021年第8期43卷 2527-2537页

作者： Garner, Philip N. Tong, Sibo Idiap Res Inst CH-1920 Martigny Switzerland

We begin by reiterating that common neural network activation functions have simple Bayesian origins. In this spirit, we go on to show that Bayes's theorem also implies a simple recurrence relation;this leads to a Bayesian recurrent unit with a prescribed feedback formulation. We show that introduction of a context indicator leads to a variable feedback that is similar to the forget mechanism in conventional recurrent units. A similar approach leads to a probabilistic input gate. The Bayesian formulation leads naturally to the two pass algorithm of the Kalman smoother or forward-backward algorithm, meaning that inference naturally depends upon future inputs as well as past ones. Experiments on speech recognition confirm that the resulting architecture can perform as well as a bidirectional recurrent network with the same number of parameters as a unidirectional one. Further, when configured explicitly bidirectionally, the architecture can exceed the performance of a conventional bidirectional recurrence.

关键词： Logic gates Probabilistic logic Bayes methods Signal processing algorithms Hidden Markov models Training Computer architecture Neural networks bayesian statistics recurrence forward-backward algorithm speech recognition bidirectional LSTM

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Measuring the Influence of Observations in HMMs Through the Kullback-Leibler Distance

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IEEE SIGNAL PROCESSING LETTERS 2013年第2期20卷 145-148页

作者： Perduca, Vittorio Nuel, Gregory Univ Paris 05 Lab MAP5 Sorbonne Paris Cite France CNRS Sorbonne Paris Cite France

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.

关键词： forward-backward algorithm Hidden Markov Models local outlier factor outlier detection relative entropy

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Quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration

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OPTIMIZATION METHODS & SOFTWARE 2022年第6期37卷 2225-2240页

作者： Cheval, Horaiu Leustean, Laureniu Univ Bucharest Fac Math & Comp Sci Res Ctr Log Optimizat & Secur LOS Dept Comp Sci Acad 14 Bucharest 010014 Romania Romanian Acad Simion Stoilow Inst Math Calea Grivitei 21 Bucharest 010702 Romania

In this paper, we compute quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration in W-hyperbolic spaces. This iteration is an extension to a nonlinear setting of the modified Mann iteration defined recently by Bo, Csetnek and Meier in Hilbert spaces. Furthermore, we show that the Douglas-Rachford and forward-backward algorithms with Tikhonov regularization terms are special cases, in Hilbert spaces, of our Tikhonov-Mann iteration.

关键词： Mann iteration Tikhonov regularization rates of asymptotic regularity Douglas-Rachford algorithm forward-backward algorithm proof mining

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Turbo Segmentation of Textured Images

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2011年第1期33卷 16-29页

作者： Lehmann, Frederic TELECOM SudParis Inst TELECOM Dept CITI F-91011 Evry France

We consider the problem of semi-supervised segmentation of textured images. Existing model-based approaches model the intensity field of textured images as a Gauss-Markov random field to take into account the local spatial dependencies between the pixels. Classical Bayesian segmentation consists of also modeling the label field as a Markov random field to ensure that neighboring pixels correspond to the same texture class with high probability. Well-known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion. But, these techniques are usually computationally intensive because they require a large number of iterations to converge. In this paper, we propose a new Bayesian framework by modeling two-dimensional textured images as the concatenation of two one-dimensional hidden Markov autoregressive models for the lines and the columns, respectively. A segmentation algorithm, which is similar to turbo decoding in the context of error-correcting codes, is obtained based on a factor graph approach. The proposed method estimates the unknown parameters using the Expectation-Maximization algorithm.

关键词： Texture segmentation Markov random field hidden Markov autoregressive model factor graph forward-backward algorithm turbo processing

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Path partitions and forward-only trellis algorithms

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IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第1期49卷 38-52页

作者： Ma, X Kavcic, A Harvard Univ Div Engn & Appl Sci Cambridge MA 02138 USA

This is a semitutorial paper on trellis-based algorithms. We argue that most decoding/detection algorithms described on trellises can be formulated as path-partitioning algorithms, with proper definitions of mappings from subsets of paths to metrics of subsets. Thereby, the only two operations needed are path-concatenation and path-collection, which play the roles of multiplication and addition, respectively. Furthermore, we show that the trellis structure permits the path-partitioning algorithms to be formulated as forward-only algorithms (with structures resembling the Viterbi algorithm), thus eliminating the need for backward computations regardless of what task needs to be performed on the trellis. While all of the actual decoding/detection algorithms presented here are rederivations of variations of previously known methods, we believe that the exposition of the algorithms in a unified manner as forward-only path-partitioning algorithms is the most intuitive manner in which to generalize the Viterbi algorithm. We also believe that this approach may, in fact, influence the practical implementation of the algorithms as well as influence the construction of other forward-only algorithms (e.g., byte-wise forward-only detection algorithms).

关键词： Babl-Cocke-Jelinek-Raviv (BCJR) algorithm forward-backward algorithm forward-only algorithm Markov processes sum-product algorithm trellis graph Viterbi algorithm

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A Proximal Interior Point algorithm with Applications to Image Processing

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2020年第6-7期62卷 919-940页

作者： Chouzenoux, Emilie Corbineau, Marie-Caroline Pesquet, Jean-Christophe Univ Paris Saclay Inria Saclay Cent Supelec CVN 9 Rue Joliot Curie F-91190 Gif Sur Yvette France

In this article, we introduce a new proximal interior point algorithm (PIPA). This algorithm is able to handle convex optimization problems involving various constraints where the objective function is the sum of a Lipschitz differentiable term and a possibly nonsmooth one. Each iteration of PIPA involves the minimization of a merit function evaluated for decaying values of a logarithmic barrier parameter. This inner minimization is performed thanks to a finite number of subiterations of a variable metric forward-backward method employing a line search strategy. The convergence of this latter step as well as the convergence the global method itself is analyzed. The numerical efficiency of the proposed approach is demonstrated in two image processing applications.

关键词： Interior point methods Proximity operator Constrained optimization forward-backward algorithm Variable metric Line search Armijo strategy Hyperspectral unmixing Geometry-texture decomposition

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A PARALLEL SPLITTING METHOD FOR COUPLED MONOTONE INCLUSIONS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2010年第5期48卷 3246-3270页

作者： Attouch, Hedy Briceno-Arias, Luis M. Combettes, Patrick L. Univ Paris 06 UPMC Lab Jacques Louis Lions UMR CNRS 7598 F-75005 Paris France Equipe Combinatoire & Optimisat UMR CNRS 7090 F-75005 Paris France Univ Montpellier 2 Inst Math & Modelisat Montpellier UMR CNRS 5149 F-34095 Montpellier 5 France

A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist. Unlike existing alternating algorithms, which are limited to two variables and linear coupling, our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes. The breadth and flexibility of the proposed framework is illustrated through applications in the areas of evolution inclusions, variational problems, best approximation, and network flows.

关键词： coupled systems demiregular operator evolution inclusion forward-backward algorithm maximal monotone operator operator splitting parallel algorithm weak convergence

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Sequencing barcode construction and identification methods based on block error-correction codes

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Science China(Life Sciences) 2020年第10期63卷 1580-1592页

作者： Weigang Chen Lixia Wang Mingzhe Han Changcai Han Bingzhi Li School of Microelectronics Tianjin UniversityTianjin 300072China School of Chemical Engineering and Technology Tianjin UniversityTianjin 300072China

Multiplexed sequencing relies on specific sample labels,the barcodes,to tag DNA fragments belonging to different samples and to separate the output of the ***,the barcodes are often corrupted by insertion,deletion and substitution errors introduced during sequencing,which may lead to sample *** this paper,we propose a barcode construction method,which combines a block error-correction code with a predetermined pseudorandom sequence to generate a base sequence for labeling different ***,to identify the corrupted barcodes for assigning reads to their respective samples,we present a soft decision identification method that consists of inner decoding and outer *** inner decoder establishes the hidden Markov model(HMM)for base insertion/deletion estimation with the pseudorandom sequence,and adapts the forward-backward(FB)algorithm to output the soft information of each bit in the block *** outer decoder performs soft decision decoding using the soft information to effectively correct multiple errors in the *** results show that the proposed methods are highly robust to high error rates of insertions,deletions and substitutions in the *** addition,compared with the inner decoding algorithm of the barcodes based on watermarks,the proposed inner decoding algorithm can greatly reduce the decoding complexity.

关键词： DNA sequencing barcode insertion/deletion errors hidden Markov model(HMM) forward-backward algorithm

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Irregular Marker Codes for Insertion/Deletion-AWGN Channels

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IEEE ACCESS 2020年 8卷 50733-50739页

作者： Liu, Yuan He, Yashuo Zhao, Xiaonan Xie, Meng Hong, Yi Zhang, Cuiping Tianjin Normal Univ Tianjin Key Lab Wireless Mobile Commun & Power Tr Tianjin 300387 Peoples R China Tianjin Normal Univ Coll Elect & Commun Engn Tianjin 300387 Peoples R China

A concatenated coding scheme employing an irregular marker code as the inner code is designed to improve the ability of correcting insertions/deletions. In this scheme, bits associated with each marker symbol are allocated to the symbol of the LDPC code non-uniformly. Since the non-binary marker symbol at the irregular position provides reliable forward/backward quantities, significant amount of insertions and deletions can be detected and corrected by the presented method. Simulation results show that the proposed scheme has an improved performance with only a very small penalty in coding rate compared with the traditional regular marker code.

关键词： Decoding Parity check codes Encoding Channel models Synchronization Concatenated codes Indexes Concatenated coding scheme marker codes insertions deletions forward-backward algorithm

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Correcting Insertions/Deletions in DPPM Using Hidden Markov Model

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IEEE ACCESS 2020年 8卷 46417-46426页

作者： Chen, Weigang Wang, Lixia Han, Changcai Tianjin Univ Sch Microelect Tianjin 300072 Peoples R China

Differential pulse-position modulation (DPPM) shows significant power and bandwidth efficiency, but suffers from serious insertion/deletion and substitution errors if the DPPM soft-decision symbol-by-symbol detection method is used. In this paper, based on the DPPM transmission scheme combining the watermark with the low-density parity-check (LDPC) code, and the equivalent source and channel models, we propose an efficient decoding scheme using hidden Markov model (HMM). Specifically, with the known watermark and the equivalent source and channel models, a hidden markov model is first established to estimate the insertion/deletion errors of the received symbols. Then, a hard-decision forward-backward algorithm is used to recover synchronization and output the estimate of the codeword. Finally, Belief-Propagation (BP) decoding algorithm in the logarithmic domain is performed to correct the residual substitution errors. Simulation results reveal that compared with the decoding scheme using the dynamic programming (DP) and Viterbi algorithms, the proposed decoding scheme has superior performance in correcting insertion, deletion and substitution errors in DPPM transmission.

关键词： DPPM insertion/deletion hidden Markov model (HMM) forward-backward algorithm

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