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

Convex Analysisの二,三の進展について

We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD).We present two distribution free tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.

/pdf/a-kernel-two-sample-test-2mr8hwo4ml.pdf

A kernel two-sample test

On robust estimation of the location parameter

1 Introduction to Wavelets 2 A Multiresolution Formulation of Wavelet Systems 3 Filter Banks and the Discrete Wavelet Transform 4 Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases 5 The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients 6 Regularity, Moments, and Wavelet System Design 7 Generalizations of the Basic Multiresolution Wavelet System 8 Filter Banks and Transmultiplexers 9 Calculation of the Discrete Wavelet Transform 10 Wavelet-Based Signal Processing and Applications 11 Summary Overview 12 References Bibliography Appendix A Derivations for Chapter 5 on Scaling Functions Appendix B Derivations for Section on Properties Appendix C Matlab Programs Index

Introduction to Wavelets and Wavelet Transforms: A Primer

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

In this paper we investigate conditions on the features of a continuous kernel so that it may approximate an arbitrary continuous target function uniformly on any compact subset of the input space. A number of concrete examples are given of kernels with this universal approximating property.

Universal Kernels

Gearbox fault diagnosis using empirical mode decomposition and Hilbert spectrum

Sequence alignment is a long standing problem in bioinformatics The Basic Local Alignment Search Tool (BLAST) is one of the most popular and fundamental alignment tools The explosive growth of biological sequences calls for speedup of sequence alignment tools such as BLAST To this end, we develop high speed BLASTN (HS-BLASTN), a parallel and fast nucleotide database search tool that accelerates MegaBLAST--the default module of NCBI-BLASTN HS-BLASTN builds a new lookup table using the FMD-index of the database and employs an accurate and effective seeding method to find short stretches of identities (called seeds) between the query and the database HS-BLASTN produces the same alignment results as MegaBLAST and its computational speed is much faster than MegaBLAST Specifically, our experiments conducted on a 12-core server show that HS-BLASTN can be 22 times faster than MegaBLAST and exhibits better parallel performance than MegaBLAST HS-BLASTN is written in C++ and the related source code is available at https://githubcom/chenying2016/queries under the GPLv3 license

/pdf/high-speed-blastn-an-accelerated-megablast-search-tool-1wxlcbocf3.pdf

High speed BLASTN: an accelerated MegaBLAST search tool

We propose an alternative B-spline approach for empirical mode decompositions for nonlinear and nonstationary signals. Motivated by this new approach, we derive recursive formulas of the Hilbert transform of B-splines and discuss Euler splines as spline intrinsic mode functions in the decomposition. We also develop the Bedrosian identity for signals having vanishing moments. We present numerical implementations of the B-spline algorithm for an earthquake signal and compare the numerical performance of this approach with that given by the standard empirical mode decomposition. Finally, we discuss several open mathematical problems related to the empirical mode decomposition.

A B-spline approach for empirical mode decompositions

This paper introduces a novel framework for the study of the total-variation model for image denoising. In the model, the denoised image is the proximity operator of the total-variation evaluated at a given noisy image. The total-variation can be viewed as the composition of a convex function (the ?1 norm for the anisotropic total-variation or the ?2 norm for the isotropic total-variation) with a linear transformation (the first-order difference operator). These two facts lead us to investigate the proximity operator of the composition of a convex function with a linear transformation. Under the assumption that the proximity operator of a given convex function (e.g., the ?1 norm or the ?2 norm) can be readily obtained, we propose a fixed-point algorithm for computing the proximity operator of the composition of the convex function with a linear transformation. We then specialize this fixed-point methodology to the total-variation denoising models. The resulting algorithms are compared with the Goldstein?Osher split-Bregman denoising algorithm. An important advantage of the fixed-point framework leads us to a convenient analysis for convergence of the proposed algorithms as well as a platform for us to develop efficient numerical algorithms via various fixed-point iterations. Our numerical experience indicates that the methods proposed here perform favorably.

https://iopscience.iop.org/article/10.1088/0266-5611/27/4/045009/pdf

Yuesheng Xu

Papers

Universal Kernels

Gearbox fault diagnosis using empirical mode decomposition and Hilbert spectrum

High speed BLASTN: an accelerated MegaBLAST search tool

A B-spline approach for empirical mode decompositions

Proximity algorithms for image models: denoising