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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Repetti, Audrey Chouzenoux, Emilie Pesquet, Jean-Christophe Univ Paris Est Lab Informat Gaspard Monge CNRS UMR 8049 F-77454 Champs Sur Marne Marne La Vallee France

ISBN: (纸本)9781479928934

Many inverse problems require to minimize a criterion being the sum of a non necessarily smooth function and a Lipschitz differentiable function. Such an optimization problem can be solved with the forward-backward algorithm which can be accelerated thanks to the use of variable metrics derived from the Majorize-Minimize principle. The convergence of this approach is guaranteed provided that the criterion satisfies some additional technical conditions. Combining this method with an alternating minimization strategy will be shown to allow us to address a broad class of optimization problems involving large-size signals. An application example to a nonconvex spectral unmixing problem will be presented.

关键词： Block coordinate algorithm forward-backward algorithm Nonconvex optimization Nonsmooth optimization Large-scale problems

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forward-backward Splitting with Bregman Distances

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VIETNAM JOURNAL OF MATHEMATICS 2017年第3期45卷 519-539页

作者： Quang Van Nguyen Hanoi Natl Univ Educ Dept Math 136 Xuan Thuy St Hanoi Vietnam Ecole Polytech Fed Lausanne Lab Informat Theory & Inference Syst LIONS Lausanne Switzerland

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone sequences. Various examples are discussed, including some in Euclidean spaces, where new algorithms are obtained.

关键词： Banach space Bregman distance forward-backward algorithm Legendre function Multivariate minimization Variable quasi-Bregman monotonicity

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An Efficient Phone N-gram forward-backward Computation Using Dense Matrix Multiplication 18

An Efficient Phone <i>N</i>-gram Forward-backward Computatio...

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18th Annual Conference of the International-Speech-Communication-Association (INTERSPEECH 2017)

作者： Sim, Khe Chai Narayanan, Arun Google Inc Mountain View CA 94043 USA

ISBN: (纸本)9781510848764

The forward-backward algorithm is commonly used to train neural network acoustic models when optimizing a sequence objective like MMI and sMBR. Recent work on lattice-free MMI training of neural network acoustic models shows that the forward-backward algorithm can be computed efficiently in the probability domain as a series of sparse matrix multiplications using GPUs. In this paper. we present a more efficient way of computing forward-backward using a dense matrix multiplication approach. We do this by exploiting the block-diagonal structure of the n-gram state transition matrix;instead of multiplying large sparse matrices, the proposed method involves a series of smaller dense matrix multiplications, which can be computed in parallel. Efficient implementation can be easily achieved by leveraging on the optimized matrix multiplication routines provided by standard libraries, such as NumPy and TensorFlow. Runtime benchmarks show that the dense multiplication method is consistently faster than the sparse multiplication method (on both CPUs and GPUs), when applied to a 4-gram phone language model. This is still the case even when the sparse multiplication method uses a more compact finite state model representation by excluding unseen n-grams.

关键词： forward-backward algorithm sequence training

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The Viscosity Approximation forward-backward Splitting Method for Zeros of the Sum of Monotone Operators

Abstract and Applied Analysis

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Abstract and Applied Analysis 2016年第none期2016卷 1-10页

作者： Boikanyo, Oganeditse Aaron Department of Mathematics and Statistical Sciences Botswana International University of Science and Technology Private Bag Box 16 Palapye Botswana

We investigate the convergence analysis of the following general inexact algorithm for approximating a zero of the sum of a cocoercive operator A and maximal monotone operators B with D(B)⊂H: xn+1=αnf(xn)+γnxn+δn(I+rnB)-1(I-rnA)xn+en, for n=1,2,., for given x1 in a real Hilbert space H, where (αn), (γn), and (δn) are sequences in (0,1) with αn+γn+δn=1 for all n≥1, (en) denotes the error sequence, and f:H→H is a contraction. The algorithm is known to converge under the following assumptions on δn and en: (i) (δn) is bounded below away from 0 and above away from 1 and (ii) (en) is summable in norm. In this paper, we show that these conditions can further be relaxed to, respectively, the following: (i) (δn) is bounded below away from 0 and above away from 3/2 and (ii) (en) is square summable in norm;and we still obtain strong convergence results. © 2016 Oganeditse Aaron Boikanyo.

关键词： VISCOSITY APPROXIMATION theory forward-backward algorithm ZERO (The number) ADDITION (Mathematics) MONOTONE operators

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A forward-backward Strategy for Handling Non-linearity in Electrical Impedance Tomography 21st

A Forward-Backward Strategy for Handling Non-linearity in El...

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21st International Conference on Computational Science and Its Applications (ICCSA)

作者： Huska, Martin Lazzaro, Damiana Morigi, Serena Univ Bologna Dept Math Bologna Italy

ISBN: (纸本)9783030869700;9783030869694

Electrical Impedance Tomography (EIT) is known to be a nonlinear and ill-posed inverse problem. Conventional penalty-based regularization methods rely on the linearized model of the nonlinear forward operator. However, the linearized problem is only a rough approximation of the real situation, where the measurements can further contain unavoidable noise. The proposed reconstruction variational framework allows to turn the complete nonlinear ill-posed EIT problem into a sequence of regularized linear least squares optimization problems via a forward-backward splitting strategy, thus converting the ill-posed problem to a well-posed one. The framework can easily integrate suitable penalties to enforce smooth or piecewise-constant conductivity reconstructions depending on prior information. Numerical experiments validate the effectiveness and feasibility of the proposed approach.

关键词： EIT inverse problem forward-backward algorithm Nonlinear optimization Regularization

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forward-backward Stochastic Equations Associated with Systems of Quasilinear Parabolic Equations and Comparison Theorems

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Journal of Mathematical Sciences (United States) 2015年第1期204卷 7-27页

作者： Belopolskaya, Ya I. St.Petersburg State University for Architecture and Civil Engineering St. Petersburg Russian Federation

We develop a probabilistic approach to construction of a viscosity solution of the Cauchy problem for a system of quasilinear parabolic equations with respect to a vector function u(t, x) ∈ R^d1, x ∈ R^d. Our approach is based on the possibility to reduce the original quasilinear parabolic system to a quasilinear parabolic equation in an alternative phase space and derive forward-backward stochastic differential equations associated with it. This reduction allows us to prove some comparison theorems for BSDEs, and, as a result, to construct a probabilistic representation of a viscosity solution of the original Cauchy problem. Bibliography: 16 titles. © 2014, Springer Science+Business Media New York.

关键词： STOCHASTIC processes forward-backward algorithm QUASILINEARIZATION CAUCHY problem COMPARATIVE studies

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Channel Modeling and Signal Processing for Probe Storage Channels

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2010年第2期28卷 143-157页

作者： Pozidis, Haralampos Cherubini, Giovanni Pantazi, Angeliki Sebastian, Abu Eleftheriou, Evangelos IBM Res Zurich Storage Technol Dept CH-8803 Ruschlikon Switzerland

Probe-storage devices employ large arrays of probes to write/read data in parallel in some storage medium, and combine ultra-high density, low access times, and low power consumption. A particular probe-storage technique utilizes thermomechanical means to store and retrieve information in thin polymer films. In this paper, a system-level channel model for the thermomechanical probe-storage channel is presented. Each of the components of the proposed model is derived by extensive characterization of experimentally obtained readback signals from probe recording tests. Moreover, detection techniques that are actually utilized in a probe-storage prototype implementation are described, followed by coding techniques for added reliability in the presence of particles or other impurities of the storage medium. In addition to low-complexity coding constructs, a concatenated coding scheme with an outer LDPC and inner modulation code is considered, in order to establish a benchmark for overall system performance. A novel methodology for joint decoding of outer LDPC and inner (d,k) modulation codes is developed. Furthermore, an optimal soft decoder for the modulation code is proposed, based on a modification of the decoder metrics to accurately account for the probe storage channel output statistics. Experimental results are used throughout the paper to validate the channel model and identify its relevant parameters, as well as to verify the system performance obtained by simulations.

关键词： Channel modeling probe storage intersymbol interference jitter electronics noise medium noise noise shaping run-length-limited (RLL) codes low-density parity-check (LDPC) codes concatenated coding soft-decision decoding forward-backward algorithm

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Confidence measures for large vocabulary continuous speech recognition

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IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING 2001年第3期9卷 288-298页

作者： Wessel, F Schlüter, R Macherey, K Ney, H Rhein Westfal TH Aachen Lehrstuhl Informat 6 D-52056 Aachen Germany

In this paper, we present several confidence measures for large vocabulary continuous speech recognition. We propose to estimate the confidence of a hypothesized word directly as its posterior probability, given all acoustic observations of the utterance. These probabilities are computed on word graphs using a forward-backward algorithm. We also study the estimation of posterior probabilities on N-best lists instead of word graphs and compare both algorithms in detail. In addition, we compare the posterior probabilities with two alternative confidence measures, i.e., the acoustic stability and the hypothesis density. We present experimental results on five different corpora: the Dutch ARISE 1k evaluation corpus, the German Verbmobil '98 7k evaluation corpus, the English North American Business '94 20k and 64k development corpora, and the English Broadcast News '96 65k evaluation corpus, We show that the posterior probabilities computed on word graphs outperform all other confidence measures. The relative reduction in confidence error rate ranges between 19% and 35% compared to the baseline confidence error rate.

关键词： confidence measures forward-backward algorithm N-best lists posterior probabilities speech recognition word graphs

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Hidden hybrid Markov/semi-Markov chains

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2005年第3期49卷 663-688页

作者： Guédon, Y Univ Montpellier 2 INRA CNRS UMRCIRAD F-34398 Montpellier France

Models 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. (c) 2004 Elsevier B.V. All rights reserved.

关键词： forward-backward algorithm hidden Markov chain hidden semi-Markov chain macro-state plant structure analysis smoothing algorithm viterbi algorithm

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QUASI-NONEXPANSIVE ITERATIONS ON THE AFFINE HULL OF ORBITS: FROM MANN'S MEAN VALUE algorithm TO INERTIAL METHODS

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SIAM JOURNAL ON OPTIMIZATION 2017年第4期27卷 2356-2380页

作者： Combettes, Patrick L. Glaudin, Lilian E. North Carolina State Univ Dept Math Raleigh NC 27695 USA UPMC Univ Paris 06 Sorbonne Univ UMR 7598 Lab Jacques Louis Lions F-75005 Paris France

Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasi-nonexpansive operators to a point in the affine hull of the orbit generated up to the current iterate. This investigation unifies several algorithmic constructs, including Mann's mean value method, inertial methods, and multilayer memoryless methods. It also provides a framework for the development of new algorithms, such as those we propose for solving monotone inclusion and minimization problems.

关键词： averaged operator fixed point iteration forward-backward algorithm inertial algorithm mean value iterations monotone operator splitting nonsmooth minimization Peaceman-Rachford algorithm proximal algorithm

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