Tutorial Information Note Download Here Friday, July 29, 2011: 9:00am.12:00pm, 2:00pm.5:00pm Topics: Learning theory Tutorial lecturers: Steve Smale, Ding-Xuan Zhou 9:00am-10:00am: Tutorial lecture by Steve Smale Framework of the least squares regression, empirical risk minimization, hypothesis space, reproducing kernel Hilbert space, sample error, probability inequalities, covering number, approximation error. 10:00am-10:30am: break/discussion/questions 10:30am-11:30am: Tutorial lecture by Ding-Xuan Zhou Kernel methods in learning theory, regularization scheme, representor theorem, reduction of optimization problems, binary classification, support vector machine, misclassification error, Bayes rule, separable distributions, comparison theorem, regularization error, error bounds. 11:30am-12:00am: break/discussion/questions 2:00pm-3:00pm: Tutorial lecture by Ding-Xuan Zhou Dimensionality reduction, Laplacian eigenmap, spectral clustering, kernel PCA, semi-supervised learning on manifolds, online learning. 3:00pm-3:30pm break/discussion/questions 3:30pm-4:30pm: Tutorial lecture by Ding-Xuan Zhou LASSO, elastic net, sparsity kernel projection machine, empirical feature, gradient learning and variable selection. 4:30pm-5:00pm: break/discussion/questions Extended list of references: F. Cucker and S. Smale, On the mathematical foundations of learning, Bull. Amer. Math. Soc. {\bf 39} (2001), 1--49. F. Cucker and D. X. Zhou, Learning Theory: An Approximation Theory Viewpoint, Cambridge University Press, 2007. N. Cristianini and J. Shawe-Taylor, An Introduction to Support Vector Machines, Cambridge University Press, 2000. V. Vapnik, Statistical Learning Theory, John Wiley \& Sons, 1998. T. Evgeniou, M. Pontil, and T. Poggio, Regularization networks and support vector machines, Adv. Comput. Math. {\bf 13} (2000), 1--50. B. Sch\"olkopf and A. J. Smola, Learning with Kernels, MIT Press, Cambridge, 2002. D. X. Zhou, Capacity of reproducing kernel spaces in learning theory, IEEE Trans. Inform. Theory {\bf 49} (2003), 1743--1752. M. Belkin and P. Niyogi, Laplacian eigenmaps for dimensionality reduction and data representation, Neural Comput. {\bf 15} (2003), 1373-1396. U. von Luxburg, M. Belkin, and O. Bousquet, Consistency of spectral clustering, Ann. Stat. {\bf 36} (2008), 555--586. S. Smale and Ding-Xuan Zhou, Geometry on probability spaces, Constr. Approx. {\bf 30} (2009), 311--323. M. Belkin and P. Niyogi, Semisupervised learning on Riemannian manifolds, Machine Learning {\bf 56} (2004), 209--239. Y. Ying and Ding-Xuan Zhou, Online regularized classification algorithms, IEEE Trans. Inform. Theory {\bf 52} (2006), 4775--4788. R. Tibshirani, Regression shrinkage and selection via the lasso, J. Royal. Statist. Soc. B {\bf 58} (1996), 267--288. H. Zou, T. Hastie, Regularization and variable selection via the elastic net, J. Royal. Statist. Soc. B {\bf 67} (2005), 301--320. S. Mukherjee and D. X. Zhou, Learning coordinate covariances via gradients, J. Machine Learning Research {\bf 7} (2006), 519--549. Saturday, July 30, 2011: 9:00am.12:00pm, 2:00pm.5:00pm Topics: MRA based wavelet frame and applications Tutorial lecturer: Zuowei Shen Link of tutorial materials online: http://www.math.nus.edu.sg/~matzuows/IASLectureNotes.pdf One of the major driving forces in the area of applied and computational harmonic analysis during the last two decades is the development and the analysis of redundant systems that produce sparse approximations for classes of functions of interest. Such redundant systems include wavelet frames, ridgelets, curvelets and shearlets, to name a few. This series of talks focuses on tight wavelet frames that are derived from multiresolution analysis and their applications in imaging. The pillar of this theory is the unitary extension principle and its various generalizations, hence we will first give in details on the theory that leads to the unitary extension principles. The extension principles allow for systematic constructions of wavelet frames that can be tailored to, and effectively used in, various problems in imaging science. We will discuss some of these applications of wavelet frames in details. The discussion will include frame-based image analysis and restorations, image inpainting, image denoising, image deblurring and blind deblurring, image decomposition, segmentation and CT image reconstruction. Sunday, July 31, 2011: 9:00am.12:00am Topics: Algorithms of wavelets and framelets Tutorial lecturer: Bin Han Link of tutorial materials online: http://www.ualberta.ca/~bhan/notes.pdf 9:00am-10:00am: Some basic aspects on wavelets and framelets. More precisely, discrete wavelet/framelet transform, properties such as perfect reconstruction, sparsity, and stability, multilevel wavelet transform, oblique extension principle, variants of discrete wavelet transform, wavelet transform for data on bounded interval. 10:00am-10:30am: break/discussion/questions 10:30am-11:30am: Design of wavelet and framelet filter banks. Interpolatory filters, orthogonal filter banks, symmetric complex orthogonal wavelet filter banks, biorthogonal wavelet filter banks, tight framelet filter banks, and dual framelet filter banks. 11:30am-12:00pm: break/discussion/questions