Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

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Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

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Convex Analysisの二,三の進展について

Summary Background Since December, 2019, Wuhan, China, has experienced an outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epidemiological and clinical characteristics of patients with COVID-19 have been reported but risk factors for mortality and a detailed clinical course of illness, including viral shedding, have not been well described. Methods In this retrospective, multicentre cohort study, we included all adult inpatients (≥18 years old) with laboratory-confirmed COVID-19 from Jinyintan Hospital and Wuhan Pulmonary Hospital (Wuhan, China) who had been discharged or had died by Jan 31, 2020. Demographic, clinical, treatment, and laboratory data, including serial samples for viral RNA detection, were extracted from electronic medical records and compared between survivors and non-survivors. We used univariable and multivariable logistic regression methods to explore the risk factors associated with in-hospital death. Findings 191 patients (135 from Jinyintan Hospital and 56 from Wuhan Pulmonary Hospital) were included in this study, of whom 137 were discharged and 54 died in hospital. 91 (48%) patients had a comorbidity, with hypertension being the most common (58 [30%] patients), followed by diabetes (36 [19%] patients) and coronary heart disease (15 [8%] patients). Multivariable regression showed increasing odds of in-hospital death associated with older age (odds ratio 1·10, 95% CI 1·03–1·17, per year increase; p=0·0043), higher Sequential Organ Failure Assessment (SOFA) score (5·65, 2·61–12·23; p Interpretation The potential risk factors of older age, high SOFA score, and d-dimer greater than 1 μg/mL could help clinicians to identify patients with poor prognosis at an early stage. Prolonged viral shedding provides the rationale for a strategy of isolation of infected patients and optimal antiviral interventions in the future. Funding Chinese Academy of Medical Sciences Innovation Fund for Medical Sciences; National Science Grant for Distinguished Young Scholars; National Key Research and Development Program of China; The Beijing Science and Technology Project; and Major Projects of National Science and Technology on New Drug Creation and Development.

Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study

Reference [11] investigated the almost sure weak convergence of block-coordinate fixed point algorithms and discussed their applications to nonlinear analysis and optimization. This algorithmic framework features random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and it allows for stochastic errors in the evaluation of the operators. The present paper establishes results on the mean-square and linear convergence of the iterates. Applications to monotone operator splitting and proximal optimization algorithms are presented.

Stochastic Quasi-Fej\'er Block-Coordinate Fixed Point Iterations With Random Sweeping II: Mean-Square and Linear Convergence

Due to the great interest of stereo images in several applications, it becomes mandatory to improve the efficiency of existing coding techniques. For this purpose, many research works have been developed. The basic idea behind most of the reported methods consists of applying an inter-view prediction via the estimated disparity map followed by a separable wavelet transform. In this paper, we propose to use a two-dimensional non separable decomposition based on the concept of vector lifting scheme. Furthermore, we focus on the optimization of all the lifting operators employed with the left and right images. Experimental results carried out on different stereo images show the benefits which can be drawn from the proposed coding method.

https://hal.archives-ouvertes.fr/hal-00734457/document

ℓ 1 -adapted non separable vector lifting schemes for stereo image coding

This paper presents a new scheme to perform the canonical polyadic decomposition (CPD) of a symmetric tensor. We first formulate the CPD problem as a truncated moment problem, where a measure has to be recovered knowing some of its moments. The support of the measure is discrete and encodes the CPD. The support is then retrieved by solving a polynomial system. Using algebraic results, our method resorts only to classical linear algebra operations (eigenvalue method and Schur reordered factorization). This new viewpoint offers theoretical guarantees on the retrieved decomposition. Finally experimental results show the validity of our method and a better reconstruction accuracy compared to classic CPD algorithms.

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A Moment-Based Approach for Guaranteed Tensor Decomposition

In this paper we address the problem of deconvolution of an image corrupted with Poisson noise by reformulating the restoration process as a constrained minimization of a suitable regularized data fidelity function. The minimization step is performed by means of an interior-point approach, in which the constraints are incorporated within the objective function through a barrier penalty and a forward-backward algorithm is exploited to build a minimizing sequence. The key point of our proposed scheme is that the choice of the regularization, barrier and step-size parameters defining the interior point approach is automatically performed by a deep learning strategy. Numerical tests on Poisson corrupted benchmark datasets show that our method can obtain very good performance when compared to a state-of-the-art variational deblurring strategy.

A Hybrid Interior Point - Deep Learning Approach for Poisson Image Deblurring

A statistical method for detecting and/or localizing nonstationarities in a process observed over a time interval T is presented. Stationarity is induced by taking a wavelet transform of the process. A parametric model is fitted to the result. The error incurred in fitting the model is shown to preserve the singularity manifested in the transform. The error is then used to establish a statistical detection test that is free of any prior knowledge about the class of signals being analyzed, and of any user input. >

Jean-Christophe Pesquet

Papers

Stochastic Quasi-Fej\'er Block-Coordinate Fixed Point Iterations With Random Sweeping II: Mean-Square and Linear Convergence

ℓ 1 -adapted non separable vector lifting schemes for stereo image coding

A Moment-Based Approach for Guaranteed Tensor Decomposition

A Hybrid Interior Point - Deep Learning Approach for Poisson Image Deblurring

Multiscale detection of nonstationary signals