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

State-of-the-art methods for solving smooth optimization problems are nonlinear conjugate gradient, low memory BFGS, and majorize–minimize (MM) subspace algorithms. The MM subspace algorithm that has been introduced more recently has shown good practical performance when compared with other methods on various optimization problems arising in signal and image processing. However, to the best of our knowledge, no general result exists concerning the theoretical convergence rate of the MM subspace algorithm. This paper aims at deriving such convergence rates both for batch and online versions of the and in particular, discusses the influence of the choice of the subspace.

https://hal.archives-ouvertes.fr/hal-01373641/document

Convergence Rate Analysis of the Majorize–Minimize Subspace Algorithm

Background
Inferring gene networks from high-throughput data constitutes an important step in the discovery of relevant regulatory relationships in organism cells. Despite the large number of available Gene Regulatory Network inference methods, the problem remains challenging: the underdetermination in the space of possible solutions requires additional constraints that incorporate a priori information on gene interactions.

/pdf/brane-cut-biologically-related-a-priori-network-enhancement-3badt6iy23.pdf

BRANE Cut: biologically-related a priori network enhancement with graph cuts for gene regulatory network inference.

TV-like constraints/regularizations are useful tools in variational methods for multicomponent image restoration. In this paper, we design more sophisticated non-local TV constraints which are derived from the structure tensor. The proposed approach allows us to measure the non-local variations, jointly for the different components, through various l1,p matrix norms with p ≥ 1. The related convex constrained optimization problems are solved through a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments carried out for color images demonstrate the interest of considering a Non-Local Structure Tensor TV and show that the proposed epigraphical projection method leads to significant improvements in terms of convergence speed over existing numerical solutions.

/pdf/an-epigraphical-convex-optimization-approach-for-3vwbyd9w5z.pdf

An epigraphical convex optimization approach for multicomponent image restoration using non-local structure tensor

The paper deals with blind source separation of images. The model which is adopted here is a convolutive multi-dimensional one. Recent results about polynomial matrices in several indeterminates are used to prove the invertibility of the mixing process. We then extend an iterative blind source separation method to the multi-dimensional case and show that it still applies if the source spectra vanish on an interval. Based on experimental observations we then discuss problems arising when we want to separate natural images: the sources are non i.i.d. and have a band limited spectrum; a scalar filtering indeterminacy thus remains after separation.

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An Iterative Blind Source Separation Method for Convolutive Mixtures of Images

We propose a 2D generalization to the M-band case of the dual-tree structure (initially proposed by N.G. Kingsbury and further investigated by I.W. Selesnick) based on a Hilbert pair of wavelets. We particularly address the construction of the dual basis and the resulting directional analysis. We revisit the necessary preprocessing stage in the M-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed M-band decomposition is demonstrated via image denoising comparisons.

https://hal-upec-upem.archives-ouvertes.fr/hal-00621891/document

Jean-Christophe Pesquet

Papers

Convergence Rate Analysis of the Majorize–Minimize Subspace Algorithm

BRANE Cut: biologically-related a priori network enhancement with graph cuts for gene regulatory network inference.

An epigraphical convex optimization approach for multicomponent image restoration using non-local structure tensor

An Iterative Blind Source Separation Method for Convolutive Mixtures of Images

2D dual-tree M-band wavelet decomposition