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.

/pdf/distributed-optimization-and-statistical-learning-via-the-8s9gtddw0d.pdf

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

Proximal splitting algorithms play a central role in finding the numerical solution of convex optimization problems. This paper addresses the problem of stereo matching of multi-component images by jointly estimating the disparity and the illumination variation. The global formulation being non-convex, the problem is addressed by solving a sequence of convex relaxations. Each convex relaxation is non trivial and involves many constraints aiming at imposing some regularity on the solution. Experiments demonstrate that the method is efficient and provides better results compared with other approaches.

/pdf/a-parallel-proximal-splitting-method-for-disparity-4xu9vqhhmi.pdf

A Parallel Proximal Splitting Method for Disparity Estimation from Multicomponent Images Under Illumination Variation

During the last five years, several convex optimization algorithms have been proposed for solving inverse problems. Most of the time, they allow us to minimize a criterion composed of two terms one of which permits to “stabilize” the solution. Different choices are possible for the so-called regularization term, which plays a prominent role for solving ill-posed problems. While a total variation regularization introduces staircase effects, a wavelet regularization may bring other kinds of visual artefacts. A compromise can be envisaged combining these regularization functions. In the context of Poisson data, we propose in this paper an algorithm to achieve the minimization of the associated (possibly constrained) convex optimization problem.

/pdf/hybrid-regularization-for-data-restoration-in-the-presence-2cjuyzpgcg.pdf

Hybrid regularization for data restoration in the presence of Poisson noise

Adaptive lifting schemes using variable-size block segmentation

Multiple description coding (MDC) is a joint source-channel coding technique specifically designed for real-time multimedia applications over best effort switched packet networks (such as Internet), in order to cope with packet losses due to transmission errors or network congestion. Error resilience of transmitted bitstreams is thus significantly increased, but this does not solve problems like bitstream adaptation to bandwidth variations or receiver characteristics, which are in turn addressed by scalable coding techniques. In this paper, we present a new method of multiple description coding of scalable video, combining the scalability features with MDC. We propose a redundant motion-compensated temporal scheme related to Haar multiresolution analysis. We also present an equivalent lifting implementation leading to simple central and lateral decoders.

Redundant multiresolution analysis for multiple description video coding

Extended forms of contrast functions are introduced to provide statistical measures of independence for orthogonal mixtures. We also define semicontrasts based on second-order statistics which, in some cases, may be sufficient to separate the mixed sources. The corresponding criteria are then used to obtain an optimized representation of a stochastic process in an orthonormal basis of wavelet packets or local cosines.

Jean-Christophe Pesquet

Papers

A Parallel Proximal Splitting Method for Disparity Estimation from Multicomponent Images Under Illumination Variation

Hybrid regularization for data restoration in the presence of Poisson noise

Adaptive lifting schemes using variable-size block segmentation

Redundant multiresolution analysis for multiple description video coding

Independence/decorrelation measures with applications to optimized orthonormal representations