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

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

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

Sparsity inducing penalizations are useful tools in variational methods for machine learning. In this paper, we design a learning algorithm for multiclass support vector machines that allows us to enforce sparsity through various nonsmooth regularizations, such as the mixed l
 1, p
-norm with p ≥ 1. The proposed constrained convex optimization approach involves an epigraphical constraint for which we derive the closed-form expression of the associated projection. This sparse multiclass SVM problem can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments carried out for handwritten digits demonstrate the interest of considering nonsmooth sparsity-inducing regularizations and the efficiency of the proposed epigraphical projection method.

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Epigraphical proximal projection for sparse multiclass SVM

Primal-dual proximal optimization methods have recently gained much interest for dealing with very large-scale data sets encoutered in many application fields such as machine learning, computer vision and inverse problems [1–3]. In this work, we propose a novel random block-coordinate version of such algorithms allowing us to solve a wide array of convex variational problems. One of the main advantages of the proposed algorithm is its ability to solve composite problems involving large-size matrices without requiring any inversion. In addition, the almost sure convergence to an optimal solution to the problem is guaranteed. We illustrate the good performance of our method on a mesh denoising application.

A random block-coordinate primal-dual proximal algorithm with application to 3D mesh denoising

The geometry-texture decomposition of images produced by X-Ray Computed Tomography (CT) is a challenging inverse problem which is usually performed in two steps: reconstruction and decomposition Decomposition can be used for instance to produce an approximate segmentation of the image, but this one can be compromised by artifacts and noise arising from the acquisition and reconstruction processes We propose a geometry-texture decomposition based on a TV-Laplacian model, well-suited for segmentation and edge detection The corresponding joint reconstruction and decomposition task from CT data is then formulated as a convex constrained minimization problem We use our recently introduced proximal interior point method to solve this inverse problem in a reliable manner Numerical experiments on realistic images of material samples illustrate the practical efficiency of the proposed approach Our algorithm indeed compares favorably with a state-of-the-art method

/pdf/geometry-texture-decomposition-reconstruction-using-a-35ut9f5yhl.pdf

Geometry-Texture Decomposition/Reconstruction Using a Proximal Interior Point Algorithm

Oversampled transforms are useful tools for data analysis, since redundancy increases freedom in the choice of the processing. We propose here a framework for oversampled lapped transform of images. More specifically, we establish conditions for perfect reconstruction of 2D data using non-separable windows. We also provide an example of a transform which relies on this approach. We also show the benefit of this technique in directional filtering applications encountered in the field of seismic data processing.

/pdf/a-non-separable-2d-complex-modulated-lapped-transform-and-3mnvz5i05s.pdf

A non-separable 2D complex modulated lapped transform and its applications to seismic data filtering

In this letter, we revisit a number of concepts that have recently proven to be useful in multiresolution signal analysis, specifically by replacing the now classical linear-scale transition operators by nonlinear ones. More precisely, we address the problem of designing appropriate operators associated to nonlinear filter banks using multiscale analysis. We first establish a connection between nonlinear filter banks and partial differential equations operators used in scale-space theory. Toward this end, we propose specific structures of nonlinear three-band decompositions ensuring a perfect reconstruction. The behavior of the proposed structures is analyzed for a step-like signal in a high SNR scenario, and a simulation is proposed for a more complex scenario.

Jean-Christophe Pesquet

Papers

Epigraphical proximal projection for sparse multiclass SVM

A random block-coordinate primal-dual proximal algorithm with application to 3D mesh denoising

Geometry-Texture Decomposition/Reconstruction Using a Proximal Interior Point Algorithm

A non-separable 2D complex modulated lapped transform and its applications to seismic data filtering

A nonlinear diffusion-based three-band filter bank