Download presentation

Presentation is loading. Please wait.

Published byLorena Rosten Modified over 2 years ago

1
Randomized Algorithms Randomized Algorithms CS648 Lecture 9 Random Sampling part-I (Approximating a parameter) Lecture 9 Random Sampling part-I (Approximating a parameter) 1

2
Overview of the Lecture Randomization Framework for estimation of a parameter 1.Number of balls from a bag 2.Size of transitive closure of a directed graph An Inspirational Problem from Continuous probability

3
AN INSPIRATIONAL PROBLEM FROM CONTINUOUS PROBABILITY

4
0 1

5
0 1 Sampling points on a line segment 0 1

6
Sampling points on a Circle (of circumference 1) 1

7
Transforming a line segment to a circle (just a different perspective) The knot formed by joining the ends of the line segment Give the knot a uniformly random rotation around the circle

8
Transforming a line segment to a circle (just a different perspective) First uniformly random point is the knot.

9
0 1 We have got the answer of the problem (without any knowledge of continuous probability theory) 0 1

11
ESTIMATING THE NUMBER OF BALLS IN A BAG

12
Estimating the number of Balls in a BAG 4 t 1 2 3 5 n j q :c:c : i l l : : : :: :

13
4 t 1 2 3 5 n j q :c:c : i l l : : : :: : Can we use it to design an algorithm ?

14
Estimating the number of Balls in a BAG 4 t 1 2 3 5 n j q :c:c : i l l : : : :: :

15
How good is the estimate ? 2 N 1 N-1 multiple sampling.

16
Multiple samplings to improve accuracy and reduce error probability 21N

17
A better algorithm for estimating the number of balls:

18
21N

19
Final result

20
Randomized framework for estimating a parameter

21
ESTIMATING THE SIZE OF TRANSITIVE CLOSURE OF A DIRECTED GRAPH

22
Estimating size of Transitive Closure of a Directed Graph

25
Randomized Monte Carlo Algorithm for estimating the size of transitive closure of directed graph

26
MIN-Label Problem

29
Inference from the inspirational problem

30
RANDOMIZED MONTE CARLO ALGORITHM FOR ESTIMATING THE SIZE OF TRANSITIVE CLOSURE OF A DIRECTED GRAPH

32
0.45 0.71 0.22 0.53 0.83 0.38

33
0.34 0.14 0.45 0.71 0.22 0.53 0.83 0.28 0.901 0.65 0.265 0.49 0.54 0.74 0.38 0.81 0.63

34
Estimating size of Transitive Closure of a Directed Graph

36
0 1 Can you answer Question 2 now ?

37
Estimating size of Transitive Closure of a Directed Graph

38
Homework Use Chernoff bound to get a high probability bound on the error. Hint: Proceed along similar lines as in the case of estimating number of balls in a bag. Make sincere attempts to do this homework. I shall discuss the same briefly in the beginning of the next class.

Similar presentations

OK

Distributed Algorithms – 2g1513 Lecture 1b – by Ali Ghodsi Models of distributed systems continued and logical time in distributed systems.

Distributed Algorithms – 2g1513 Lecture 1b – by Ali Ghodsi Models of distributed systems continued and logical time in distributed systems.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on dairy farm management Ppt online open channel Ppt on statistics in maths what is the factor Ppt on presidents of india Ppt on chapter 3 atoms and molecules class Ppt on data handling for grade 3 How to make ppt on macbook pro Ppt on atomic structure class 11 Ppt on total internal reflection diagrams Ppt on event handling in javascript what is the syntax