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So Much Data Bernard Chazelle Princeton University Princeton University Bernard Chazelle Princeton University Princeton University So Little Time

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So Many Slides Bernard Chazelle Princeton University Princeton University Bernard Chazelle Princeton University Princeton University So Little Time So Little Time (before lunch) (before lunch)

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computation math experimentationalgorithms

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Computers have two problems

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1. They don’t have steering wheels

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2. End of Moore’s Law party’s over !

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computation algorithms experimentation

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32 x 17 224 32 = 544 This is not me

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FFT RSA

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noisy low entropy uncertain unevenly priced big

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noisy low entropy uncertain unevenly priced big

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Biomedical imaging Sloan Digital Sky Survey 4 petabytes (~1MG) (~1MG) 10 petabytes/yr 150 petabytes/yr

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Collected works of Micha Sharir My A(9,9)-th paper

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massive input massive input output Sublinear Algorithms Sample tiny fraction

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Shortest Paths [C-Liu-Magen ’03] New York DelphiDelphi

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Ray Shooting Volume Intersection Point location

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Approximate MST [C-Rubinfeld- Trevisan ’01]

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Reduces to counting connected components

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EE = no. connected components varvar << (no. connected components) 22 whp, is a good estimator of # connected components

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worst case input space average case (uniform)

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worst case

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average case = actuarial view

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“ OK, if you elect NOT to have the surgery, the insurance company offers 6 days and 7 nights in Barbados. “

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arbitrary, unknown random source Self-Improving Algorithms

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Yes ! This could be YOU, too !

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E Tk Optimal expected time for random source time T1 time T2 time T3 time T4

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Clustering [ Ailon-C-Liu-Comandur ’05 ] K-median over Hamming cube

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minimize sum of distances

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[ Kumar-Sabharwal-Sen ’04 ] COST OPT ( 1 + )

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How to achieve linear limiting time? Input space {0,1} dndn prob < O(dn)/KSS Identify core Tail:Tail: Use KSS

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Store sample of precomputed KSS Nearest neighbor Incremental algorithm

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Main difficulty: How to spot the tail?

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encode

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decode

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Data inaccessible before noise What makes you think it’s wrong?

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Data inaccessible before noise must satisfy some property (eg, convex, bipartite) but does not quite

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f(x) = ? x f(x) data f = access function

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f(x) = ? x f(x) f = access function

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f(x) = ? x f(x) But life being what it is…

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f(x) = ? x f(x)

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Humans Define distance from any object to data class

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f(x) = ? x g(x) x 1, x 2,… f ( x 1), f ( x 2),… filter g is access function for:

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Online Data Reconstructio n Online Data Reconstructio n

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Monotone function: [n] R d Filter requires polylog (n) lookups [ Ailon-C-Liu-Comandur ’04 ] [ Ailon-C-Liu-Comandur ’04 ]

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Convex polygon Filter requires : lookups [C-Comandur ’06 ]

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Convex terrain lookups Filter requires :

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Iterated planar separator theorem

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Iterated (weak) planar separator theorem Iterated (weak) planar separator theorem in sublinear time!

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Using epsilon-nets in spaces of unbounded VC dimension reconstruct

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bipartite graph k-connectivity expander

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denoising low-dim attractor sets

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Priced computation & accuracy Priced computation & accuracy spectrometry/cloning/gene chip spectrometry/cloning/gene chip PCR/hybridization/chromatography PCR/hybridization/chromatography gel electrophoresis/blotting gel electrophoresis/blotting spectrometry/cloning/gene chip spectrometry/cloning/gene chip PCR/hybridization/chromatography PCR/hybridization/chromatography gel electrophoresis/blotting gel electrophoresis/blotting 0 1 0 0 10 0 11 1 0 1 0 1 01 1 0 0 1 0 0 01 1 1o 1 0 0 1 0 Linear programming Linear programming

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Pricing data Pricing data Factoring is easy. Here’s why… Gaussian mixture sample: 00100101001001101010101 ….

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Collaborators: Collaborators: Nir Ailon, Seshadri Comandur, Ding Liu Avner Magen, Ronitt Rubinfeld, Luca Trevisan Collaborators: Collaborators: Nir Ailon, Seshadri Comandur, Ding Liu Avner Magen, Ronitt Rubinfeld, Luca Trevisan

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