l01 - 6.896 Sublinear Time Algorithms February 6, 2007...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6.896 Sublinear Time Algorithms February 6, 2007 Lecture 1 Lecturer: Ronitt Rubinfeld Scribe: Chih-yu Chao 1 Testing Global Properties of Distributions We will begin by considering how to test properties of distributions over large domains. We assume that the only access we have to the distributions is via samples of the distribution, and we will focus on the number of samples required in order to answer our questions about the distribution. We will begin by studying the sample complexity of determining whether two distributions are identical, or far apart according to some measure of distance. 1.1 Closeness Figure 1 : The black box that outputs the distribution of p Here, we will first define the closeness of distributions. Suppose we are given a distribution p in domain D , where | D | = n , and probabilities ( p 1 , . . . p n ), such that p x = Pr[ p outputs x ] unknown to the algorithm, x D p x = 1. We will consider algorithms that are given oracle access to a independent identical distribution p (see Figure 1) each time we press the button on the black box, we get a sample i with probability p i . We would like to consider the L 1 distance between two distributions: Definition 1 ( L 1 distance) | p q | 1 = X x | p x q x | Another common measure is the L 2 distance, defined as follows....
View Full Document

Page1 / 5

l01 - 6.896 Sublinear Time Algorithms February 6, 2007...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online