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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Marion Foare Nelly Pustelnik Laurent Condat ENS de Lyon Univ. Lyon 1 CNRS Laboratoire de Physique Univ. Lyon Lyon F-69342 France CNRS Grenoble INP GIPSA-lab Univ. Grenoble Alpes Grenoble 38000 France

ISBN: (纸本)9781538646595

In this paper, we propose an adaptation of the PAM algorithm to the minimization of a nonconvex functional designed for joint image denoising and contour detection. This new functional is based on the Ambrosio-Tortorelli approximation of the well-known Mumford-Shah functional. We motivate the proposed approximation, offering flexibility in the choice of the possibly non-smooth penalization, and we derive closed form expression for the proximal steps involved in the algorithm. We focus our attention on two types of penalization: l_1-norm and a proposed quadratic-f. function. Numerical experiments show that the proposed method is able to detect sharp contours and to reconstruct piecewise smooth approximations with low computational cost and convergence guarantees. We also compare the results with state-of-the-art relaxations of the Mumford-Shah functional and a recent discrete formulation of the Ambrosio-Tortorelli functional.

关键词： Segmentation restoration Ambrosio-Tortorelli non-smooth optimization proximal algorithm

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Moderní restaurace audiosignálu s chybějícími úseky

Moderní restaurace audiosignálu s chybějícími úseky

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作者： Skyva, Pavel Brno University of Technology

Tato bakalářská práce se zabývá moderní metodou restaurace audiosignálů s chybějícími úseky. Rekonstrukce je založena především na řídkých reprezentac&... 详细信息

Tato bakalářská práce se zabývá moderní metodou restaurace audiosignálů s chybějícími úseky. Rekonstrukce je založena především na řídkých reprezentací signálů. V práci je popsán způsob hledání řídkého řešení pomocí proximálního Douglas-Rachfordova algoritmu a jeho následné užití pro výpočet zrekonstruovaného signálu. Výpočetní program je implementován v prostředí MATLAB a k výpočtům využívá toolbox LTFAT. Výsledky rekonstrukce jsou hodnoceny objektivní metodou odstupu signálu od šumu (SNR).

关键词： Autoregrese Douglas-Rachfordův algoritmus LTFAT MATLAB proximální algoritmus restaurace audiosignálu řídké reprezentace. Audio restoration autoregression Douglas-Rachford algorithm LTFAT MATLAB proximal algorithm sparse represenations. Text

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Elaborated-Structure Awareness SAR Imagery Using Hessian-Enhanced TV Regularization

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2023年 61卷 1页

作者： Yang, Lei Gai, Minghui Wang, Tengteng Xing, Mengdao Civil Aviat Univ China Tianjin Key Lab Adv Signal Proc Tianjin 300300 Peoples R China Xidian Univ Natl Key Lab Radar Signal Proc Xian 710071 Peoples R China

Due to the sparse feature enhancement only concentrating on strong scatterers of target of interest, the conventional sparsity-driven synthetic aperture radar (SAR) imagery often encounters the loss of elaborated-structure features, where weak scatterers would be overlapped by the sidelobes of strong scatterers. In this article, an elaborated-structure awareness SAR (ESA-SAR) imaging algorithm is proposed based on Hessian-enhanced total variation (HETV) regularization and cooperation. By encoding the Hessian operator onto the prior of the interested target, the high-order information connected with elaborated-structure features of interests can be captured. Different from the conventional high-order formulation that is projected onto Euclidean norm balls, the proposed algorithm uses the Schatten norm balls as the projection space, where the high-order structure tensor is established, and the elaborated-structure feature can be extracted under the intended convex regularizer. More specifically, the HETV regularizer is analytically solved under the proximal algorithm considering its nondifferentiability. An eigen-soft-thresholding (E-ST) operator is derived, so that a closed-form solution for the elaborated-structure feature can be obtained. Moreover, a synergistic multitask learning framework embedded with the sparse feature enhancement is introduced, in which the elaborated-structure feature can be solved in a cooperative manner. The cooperative learning is guaranteed in terms of both theoretical and practical aspects. Finally, both simulated and raw SAR data are processed to validate the effectiveness of the ESA-SAR algorithm. Comparisons with conventional algorithms examine the superiority of the proposed algorithm.

关键词： Hessian matrix proximal algorithm Schatten norm synthetic aperture radar (SAR) total variation (TV)

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Communication-efficient and Byzantine-robust distributed learning with statistical guarantee

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PATTERN RECOGNITION 2023年第1期137卷

作者： Zhou, Xingcai Chang, Le Xu, Pengfei Lv, Shaogao Nanjing Audit Univ Sch Stat & Data Sci Nanjing 211815 Jiangsu Peoples R China

Communication efficiency and robustness are two major issues in modern distributed learning frame-works. This is due to the practical situations where some computing nodes may have limited commu-nication power or may behave adversarial behaviors. To address the two issues simultaneously, this pa-per develops two communication-efficient and robust distributed learning algorithms for convex prob-lems. Our motivation is based on surrogate likelihood framework and the median and trimmed mean operations. Particularly, the proposed algorithms are provably robust against Byzantine failures, and also achieve optimal statistical rates for strong convex losses and convex (non-smooth) penalties. For typical statistical models such as generalized linear models, our results show that statistical errors dominate op-timization errors in finite iterations. Simulated and real data experiments are conducted to demonstrate the numerical performance of our algorithms.(c) 2023 Elsevier Ltd. All rights reserved.

关键词： Distributed learning Byzantine failure Communication efficiency Surrogate likelihood proximal algorithm

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Augmented Lagrangian Tracking for distributed optimization with equality and inequality coupling constraints

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AUTOMATICA 2023年第1期157卷

作者： Falsone, Alessandro Prandini, Maria Politecn Milan Dipartimento Elettron Informaz & Bioingn Via Ponzio 34-5 I-20133 Milan Italy

In this paper we propose a novel Augmented Lagrangian Tracking distributed optimization algorithm for solving multi-agent optimization problems where each agent has its own decision variables, cost function and constraint set, and the goal is to minimize the sum of the agents' cost functions subject to local constraints plus some additional coupling constraint involving the decision variables of all the agents. In contrast to alternative approaches available in the literature, the proposed algorithm jointly features a constant penalty parameter, the ability to cope with unbounded local constraint sets, and the ability to handle both affine equality and nonlinear inequality coupling constraints, while requiring convexity only. The effectiveness of the approach is shown first on an artificial example with complexity features that make other state-of-the-art algorithms not applicable and then on a realistic example involving the optimization of the charging schedule of a fleet of electric vehicles.& COPY;2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Distributed optimization Constraint-coupled optimization proximal algorithm Augmented Lagrangian ADMM

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Improving POI Recommendation via Non-Convex Regularized Tensor Completion

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Journal of Information Hiding and Privacy Protection 2020年第3期2卷 125-134页

作者： Ming Zhao Tao Liu School of Computer Science and Engineering Central South UniversityChangsha410000China

The problem of low accuracy of POI(Points of Interest)recommendation in LBSN(Location-Based Social Networks)has not been effectively *** this paper,a POI recommendation algorithm based on non-convex regularized tensor completion is *** fourth-order tensor is constructed by using the current location category,the next location category,time and season,the regularizer is added to the objective function of tensor completion to prevent over-fitting and reduce the error of the *** proximal algorithm is used to solve the objective function,and the adaptive momentum is introduced to improve the efficiency of the *** experimental results show that the algorithm can improve recommendation accuracy while reducing the time cost.

关键词： POI recommendation tensor completion proximal algorithm adaptive momentum

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Sparse graphical linear dynamical systems

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2024年第1期25卷 10882-10934页

作者： Emilie Chouzenoux Víctor Elvira Center for Visual Computing Inria University Paris Saclay Gif-sur-Yvette France School of Mathematics University of Edinburgh Edinburgh UK

Time-series datasets are central in machine learning with applications in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs), which are powerful mathematical tools that allow for probabilistic and interpretable learning on time series. Learning the model parameters in SSMs is arguably one of the most complicated tasks, and the inclusion of prior knowledge is known to both ease the interpretation but also to complicate the inferential tasks. Very recent works have attempted to incorporate a graphical perspective on some of those model parameters, but they present notable limitations that this work addresses. More generally, existing graphical modeling tools are designed to incorporate either static information, focusing on statistical dependencies among independent random variables (e.g., graphical Lasso approach), or dynamic information, emphasizing causal relationships among time series samples (e.g., graphical Granger approaches). However, there are no joint approaches combining static and dynamic graphical modeling within the context of SSMs. This work proposes a novel approach to fill this gap by introducing a joint graphical modeling framework that bridges the graphical Lasso model and a causal-based graphical approach for the linear-Gaussian SSM. We present DGLASSO (Dynamic Graphical Lasso), a new inference method within this framework that implements an efficient block alternating majorization-minimization algorithm. The algorithm's convergence is established by departing from modern tools from nonlinear analysis. Experimental validation on various synthetic data showcases the effectiveness of the proposed model and inference algorithm. This work will significantly contribute to the understanding and utilization of time-series data in diverse scientific and engineering applications where incorporating a graphical approach is essential to perform the i

关键词： state-space models graph inference sparsity graphical lasso majorization-minimization proximal algorithm

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Factorization machines with regularization for sparse feature interactions

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2021年第1期22卷 6783-6832页

作者： Kyohei Atarashi Satoshi Oyama Masahito Kurihara Graduate School of Information Science and Technology Hokkaido University Kita-ku Sapporo Hokkaido Japan Faculty of Information Science and Technology Hokkaido University Kita-ku Sapporo Hokkaido Japan

Factorization machines (FMs) are machine learning predictive models based on second-order feature interactions and FMs with sparse regularization are called sparse FMs. Such regularizations enable feature selection, which selects the most relevant features for accurate prediction, and therefore they can contribute to the improvement of the model accuracy and interpretability. However, because FMs use second-order feature interactions, the selection of features often causes the loss of many relevant feature interactions in the resultant models. In such cases, FMs with regularization specially designed for feature interaction selection trying to achieve interaction-level sparsity may be preferred instead of those just for feature selection trying to achieve feature-level sparsity. In this paper, we present a new regularization scheme for feature interaction selection in FMs. For feature interaction selection, our proposed regularizer makes the feature interaction matrix sparse without a restriction on sparsity patterns imposed by the existing methods. We also describe efficient proximal algorithms for the proposed FMs and how our ideas can be applied or extended to feature selection and other related models such as higher-order FMs and the all-subsets model. The analysis and experimental results on synthetic and real-world datasets show the effectiveness of the proposed methods.

关键词： factorization machines sparse regularization feature interaction selection feature selection proximal algorithm

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Low-rank tensor learning with nonconvex overlapped nuclear norm regularization

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 6083-6142页

作者： Quanming Yao Yaqing Wang Bo Han James T. Kwok Department of Electronic Engineering Tsinghua University Baidu Research Baidu Inc. Department of Computer Science Hong Kong Baptist University Department of Computer Science and Engineering Hong Kong University of Science and Technology

Nonconvex regularization has been popularly used in low-rank matrix learning. However, extending it for low-rank tensor learning is still computationally expensive. To address this problem, we develop an efficient solver for use with a nonconvex extension of the overlapped nuclear norm regularizer. Based on the proximal average algorithm, the proposed algorithm can avoid expensive tensor folding/unfolding operations. A special "sparse plus low-rank" structure is maintained throughout the iterations, and allows fast computation of the individual proximal steps. Empirical convergence is further improved with the use of adaptive momentum. We provide convergence guarantees to critical points on smooth losses and also on objectives satisfying the Kurdyka-Łojasiewicz condition. While the optimization problem is nonconvex and nonsmooth, we show that its critical points still have good statistical performance on the tensor completion problem. Experiments on various synthetic and real-world data sets show that the proposed algorithm is efficient in both time and space and more accurate than the existing state-of-the-art.

关键词： low-rank tensor proximal algorithm proximal average algorithm nonconvex regularization overlapped nuclear norm

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A cubic spline penalty for sparse approximation under tight frame balanced model

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2020年第2期46卷 36-36页

作者： Pang, Tongyao Wu, Chunlin Liu, Zhifang Natl Univ Singapore Dept Math Singapore 119076 Singapore Nankai Univ Sch Math Sci Tianjin 300071 Peoples R China Tianjin Normal Univ Sch Math Sci Tianjin 300387 Peoples R China

The study of non-convex penalties has recently received considerable attentions in sparse approximation. The existing non-convex penalties are proposed on the principle of seeking for a continuous alternative to the l(0)-norm penalty. In this paper, we come up with a cubic spline penalty (CSP) which is also continuous but closer to l(0)-norm penalty compared to the existing ones. As a result, it produces the weakest bias among them. Wavelet tight frames are efficient for sparse approximation due to its redundancy and fast implementation algorithm. We adopt a tight frame balanced model with our proposed cubic spline penalty since the balanced model takes the advantages of both analysis and synthesis model. To solve the non-convex CSP penalized problem, we employ a proximal local linear approximation (PLLA) algorithm and prove the generated sequence converges to a stationary point of the model if it is bounded. Under additional conditions, we find that the limit point behaves as well as the oracle solution, which is obtained by using the exact support of the ground truth signal. The efficiency of our cubic spline penalty are further demonstrated in applications of variable selection and image deblurring.

关键词： Sparse approximation Thresholding rule Concave penalty proximal algorithm Oracle property Wavelet tight frame

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