Alfred V. Aho
aho@cs.columbia.edu
Lecture 2: Design and
Implementation
of Lambda Expressions in Java 8
CS E69981: Advanced Topics in
Programming Languages and Compilers
September 15, 2014
Outline
1.
What is the lambda calculus?
2.
What is functional prog
COMS E69989 F15
Lecture 16:
EarthMover Distance
1
Administrivia, Plan
Administrivia:
NO CLASS next Tuesday 11/3 (holiday)
Plan:
EarthMover Distance
Scriber?
2
EarthMover Distance
Definition:
Given two sets of points in a metric space
= min cos
We shall assume that x = 1. Recall that we dened Zi = ri x = m xj rij , where rij are
j=1
i.i.d. random variables drawn from N (0, 1). Also recall that for Z = [Z1 . . . Zk ], we have
2
2]
E[ Z
=k
Lemma 1.
2
2
Pr[ Z
2 +O(k3 )
k(1 + )2 ] = ek
2
2
Proof. L
Graph Stream Algorithms: A Survey
Andrew McGregor
University of Massachusetts
mcgregor@cs.umass.edu
ABSTRACT
Over the last decade, there has been considerable interest in designing algorithms for processing massive
graphs in the data stream model. The ori
Lecture 8: Fourier Basics for
Boolean functions.
Linearity testing.
Lecturer: Ronitt Rubinfeld
Spring 2013
6.893: Sublinear Algorithms
Why Boolean?
Truth table of a function (complexity theory)
Concept to be learned (machine learning)
Subset of the Bo
Constr Approx
DOI 10.1007/s003650079003x
A Simple Proof of the Restricted Isometry Property
for Random Matrices
Richard Baraniuk Mark Davenport
Ronald DeVore Michael Wakin
Received: 17 May 2006 / Revised: 18 January 2007 / Accepted: 5 February 2007
S
An Automatic Inequality Prover and Instance Optimal Identity
Testing
Gregory Valiant
Stanford University
valiant@stanford.edu
Paul Valiant
Brown University
pvaliant@gmail.com
January 2, 2015
Abstract
We consider the problem of verifying the identity of a
CS 229r: Algorithms for Big Data
Fall 2013
Lecture 9 October 1, 2013
Prof. Jelani Nelson
1
Scribe: Colin Lu
Overview
In the last lecture we proved several space lower bounds for streaming algorithms using the communication complexity model, and some ideas
Estimating Lp Norms
Piotr Indyk
MIT
Lp Norm Estimation
Vector x:
1 2 .m
A stream is a sequence of updates (i,a)
xi=xi+a
Want to estimate xp up to 1
Last week, we have seen how to do that for:
x0 : variant of FlajoletMartin
x2 : AlonMatiasSze
Sublinear Graph
Approximation Algorithms
Krzysztof Onak
IBM Research
SublinearTime Algorithms
BIG
DATA
SublinearTime Algorithms
Sublineartime algorithms:
Fast answer based on inspecting
a tiny fraction of the input
Focus: Parameters of Graphs
Want to i
CS 229r: Algorithms for Big Data
Fall 2013
Lecture 14 Thursday, Oct 17 2013
Prof. Jelani Nelson
1
Scribe: Aleksandar Makelov
Overview
Today, well be looking at subspace embeddings, and how to use them to get fast algorithms for
least squares regression. N
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CS 229r: Algorithms for Big Data
Fall 2013
Lecture 15 October 24, 2013
Prof. Jelani Nelson
1
Scribe: Mark Bun
Overview
In this lecture we started the fourth module of the course, on compressed sensing. We gave an
overview of the general idea and goals of
CSE 522: Sublinear (and Streaming) Algorithms
Spring 2014
Lecture 7: Testing Distributions
April 21, 2014
Lecturer: Paul Beame
1
Scribe: Paul Beame
Testing Uniformity of Distributions
We return today to property testing and a surprising application of F2
AF
T
CS49: Data Stream Algorithms
Lecture Notes, Fall 2011
Amit Chakrabarti
Dartmouth College
DR
Latest Update: October 14, 2014
AF
T
Acknowledgements
These lecture notes began as rough scribe notes for a Fall 2009 offering of the course Data
Stream Algor
COMS E69989
F15
Lecture 15:
Least Square
Regression
Metric Embeddings
1
Administrivia, Plan
PS2:
Pick up after class
120>144 auto extension
Plan:
Least Squares Regression (finish)
Metric Embeddings
reductions for distances
2
Least Square Regressi
Alfred V. Aho
aho@cs.columbia.edu
CS E69981: Advanced Topics in
Programming Languages and
Compilers
Lecture 1 Introduction to
Course
September 8, 2014
Lecture Outline
1.
Introduction to course
2.
Course overview
3.
Prerequisites and background text
4.
Co
Swift: a reactionary
language?
Kevin Roark Jr.
Im going to be talking about Apple a lot.
I just want to make it clear that I am not obsessed with
Apple. I think it is a somewhatquestionable corporation
that can make very good things but that can also hav
JIT Compilation
Louis Croce
Columbia University
A look at how it stacks up against standard compilation procedures as
well as its optimization techniques, drawbacks and security issues. We
will take a brief tour
COMS E69989
F15
Lecture
3:
Frequency Moments: ,
Heavy Hitters
1
Administrivia, Plan
Piazza: signup!
PS1 releazed
Scriber?
Plan:
Frequency Moments
Heavy Hitters
2
Part 1: Frequency Moments
Let be frequency of
IP
Lecture 1: count one
1
Lecture 2:
COMS E69989 F15
Lecture 22:
Linearity Testing
Sparse Fourier
Transform
1
Administrivia, Plan
Thu: no class. Happy Thanksgiving!
Tue, Dec 1st:
Sergei Vassilvitskii (Google Research) on
MapReduce model and algorithms
Im away until next Thu, Dec 3rd
Of
Algorithmic Techniques
for Massive Data (COMS
69989)
Alex Andoni
1
Algorithms
Happy when your algorithm is fast
Golden standard:
linear time O(input size) time and
space.
COMS E4231
2
Algorithms for massive data
Computer resources < data
Access data
Lecture 5:
Precision Sampling
(cont),
Streaming for Graphs
1
Plan
Precision Sampling (continuation)
Streaming for graphs
Scriber?
2
Precision Sampling:
Algorithm
Precision Sampling Lemma: can get
with 90% success:
O(1) additive error and 1.5 multipli
COMS E69989 F15
Lecture 4:
CountSketch
High Frequencies
1
Plan
Scriber?
Plan:
CountMin/CountSketch (continuing from
last time)
High frequency moments via Precision
Sampling
2
Part 1:
CountMin/CountSketch
Let be frequency of
Last lecture:
2nd momen