Learning and Fourier Analysis Grigory Yaroslavtsev CIS 625: Computational Learning Theory.

Slides:

Advertisements

Similar presentations

1 Property testing and learning on strings and trees Michel de Rougemont University Paris II & LRI Joint work with E. Fischer, Technion, F. Magniez, LRI.

Advertisements

Hardness of testing 3- colorability in bounded degree graphs Andrej Bogdanov Kenji Obata Luca Trevisan.

Property Testing and Communication Complexity Grigory Yaroslavtsev

Lower Bounds for Testing Properties of Functions on Hypergrids Grigory Yaroslavtsev Joint with: Eric Blais (MIT) Sofya Raskhodnikova.

Grigory Yaroslavtsev Joint work with Piotr Berman and Sofya Raskhodnikova.

Approximate List- Decoding and Hardness Amplification Valentine Kabanets (SFU) joint work with Russell Impagliazzo and Ragesh Jaiswal (UCSD)

Of 22 August 29-30, 2011 Rabin ’80: APT 1 Invariance in Property Testing Madhu Sudan Microsoft Research TexPoint fonts used in EMF. Read the TexPoint manual.

1 D. R. Wilton ECE Dept. ECE 6382 Introduction to Linear Vector Spaces Reference: D.G. Dudley, “Mathematical Foundations for Electromagnetic Theory,” IEEE.

Deterministic vs. Non-Deterministic Graph Property Testing Asaf Shapira Tel-Aviv University Joint work with Lior Gishboliner.

Property testing of Tree Regular Languages Frédéric Magniez, LRI, CNRS Michel de Rougemont, LRI, University Paris II.

Foundations of Cryptography Lecture 10 Lecturer: Moni Naor.

Inapproximability Seminar – 2005 David Arnon  March 3, 2005 Some Optimal Inapproximability Results Johan Håstad Royal Institute of Technology, Sweden.

1 Markov Decision Processes: Approximate Equivalence Michel de Rougemont Université Paris II & LRI

Christian Sohler | Every Property of Hyperfinite Graphs is Testable Ilan Newman and Christian Sohler.

Seminar in Foundations of Privacy 1.Adding Consistency to Differential Privacy 2.Attacks on Anonymized Social Networks Inbal Talgam March 2008.

Learning and Testing Submodular Functions Grigory Yaroslavtsev Slides at

Testing the Diameter of Graphs Michal Parnas Dana Ron.

Sparse Random Linear Codes are Locally Decodable and Testable Tali Kaufman (MIT) Joint work with Madhu Sudan (MIT)

Orthogonality and Least Squares

Adi Akavia Shafi Goldwasser Muli Safra

Transforms: Basis to Basis Normal Basis Hadamard Basis Basis functions Method to find coefficients (“Transform”) Inverse Transform.

Some 3CNF Properties are Hard to Test Eli Ben-Sasson Harvard & MIT Prahladh Harsha MIT Sofya Raskhodnikova MIT.

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Fourier Transforms.

Section 6.6 Orthogonal Matrices.

Quantum Mechanics(14/2)Taehwang Son Functions as vectors  In order to deal with in more complex problems, we need to introduce linear algebra. Wave function.

Limits of Local Algorithms in Random Graphs

Gram-Schmidt Orthogonalization

Signals Through Linear Shift-Invariant Systems. Definitions  A system (operator) H is called linear if for every two signals and constants a,b:  A system.

Fourier Series and Transforms Clicker questions. Does the Fourier series of the function f converge at x = 0? 1.Yes 2.No 0 of 5 10.

Primer on Fourier Analysis Dana Moshkovitz Princeton University and The Institute for Advanced Study.

CS654: Digital Image Analysis Lecture 12: Separable Transforms.

AN ORTHOGONAL PROJECTION

Compressive Sampling Jan Pei Wu. Formalism The observation y is linearly related with signal x: y=Ax Generally we need to have the number of observation.

Fourier Series - Recap. Interpretation of Fourier series: expansion in an orthonormal basis. Analogy: orthonormal basis in 3-dimensional space:

MAT 2401 Linear Algebra 5.3 Orthonormal Bases

Chapter 10 Real Inner Products and Least-Square

1 The Mathematics of Quantum Mechanics 3. State vector, Orthogonality, and Scalar Product.

Section 5.1 Length and Dot Product in ℝ n. Let v = ‹v 1, v 2, v 3,..., v n › and w = ‹w 1, w 2, w 3,..., w n › be vectors in ℝ n. The dot product.

Motivation: Wavelets are building blocks that can quickly decorrelate data 2. each signal written as (possibly infinite) sum 1. what type of data? 3. new.

Fast Fourier Sparsity Testing over the Boolean Hypercube Grigory Yaroslavtsev Joint with Andrew Arnold (Waterloo), Arturs Backurs (MIT),

狄彥吾 (Yen-Wu Ti) 華夏技術學院資訊工程系 Property Testing on Combinatorial Objects.

Complexity and Efficient Algorithms Group / Department of Computer Science Testing the Cluster Structure of Graphs Christian Sohler joint work with Artur.

1 MAC 2103 Module 11 lnner Product Spaces II. 2 Rev.F09 Learning Objectives Upon completing this module, you should be able to: 1. Construct an orthonormal.

6 6.3 © 2016 Pearson Education, Inc. Orthogonality and Least Squares ORTHOGONAL PROJECTIONS.

Of 17 Limits of Local Algorithms in Random Graphs Madhu Sudan MSR Joint work with David Gamarnik (MIT) 7/11/2013Local Algorithms on Random Graphs1.

Complexity and Efficient Algorithms Group / Department of Computer Science Testing the Cluster Structure of Graphs Christian Sohler joint work with Artur.

ECE 3323 Principles of Communication Systems Section 3.2 Fourier Transform Properties 1.

MA4229 Lectures 13, 14 Week 12 Nov 1, Chapter 13 Approximation to periodic functions.

References Jain (a text book?; IP per se; available)

On Sample Based Testers

Property Testing (a.k.a. Sublinear Algorithms )

Dana Ron Tel Aviv University

Elementary Linear Algebra

Warren Center for Network and Data Sciences

Linear Transformations

Tight Fourier Tails for AC0 Circuits

Subhash Khot Dept of Computer Science NYU-Courant & Georgia Tech

Local Error-Detection and Error-correction

CIS 700: “algorithms for Big Data”

Linear sketching with parities

Fourier Series Prof. Woonchul Ham

Linear sketching over

Algebraic Property Testing

Linear sketching with parities

Theorems about LINEAR MAPPINGS.

Lecture 21: B Spline Curve

CIS 700: “algorithms for Big Data”

Sublinear Algorihms for Big Data

Great Moments of Theory at UC Berkeley (visit day edition)

Presentation transcript:

Learning and Fourier Analysis Grigory Yaroslavtsev CIS 625: Computational Learning Theory

Fourier Analysis and Learning

Boolean Functions

Fourier Expansion

Orthonormal Basis: Proof

Functions = Vectors, Inner Product

Fourier Coefficients

Parsevel’s Theorem

Plancharel’s Theorem

Basic Fourier Analysis

Convolution

Convolution: Proof of Property 3

Approximate Linearity

Property Testing [Goldreich, Goldwasser, Ron; Rubinfeld, Sudan] NO YES Randomized Algorithm YES NO Property Tester Don’t care

Linearity Testing Linear Non- linear Linearity Tester Don’t care

Linearity Testing [Blum, Luby, Rubinfeld]

Linearity Testing: Analysis

Linearity Testing: Analysis Continued

Local Correction

Thanks!