1©MapR Technologies - Confidential

Online Learning Bayesian bandits and more

2©MapR Technologies - Confidential

whoami – Ted Dunning

Ted Dunningtdunning@maprtech.comtdunning@apache.org@ted_dunning

We’re hiring at MapR

For slides and other info http://www.slideshare.net/tdunning

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Online

ScalableIncremental

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Scalability and Learning

What does scalable mean?

What are inherent characteristics of scalable learning?

What are the logical implications?

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Scalable ≈ On-line

If you squint just right

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unit of work ≈ unit of time

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Learning

State

Infinite Data

Stream

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Pick One

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Now pick again

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A Quick Diversion

You see a coin– What is the probability of heads?– Could it be larger or smaller than that?

I flip the coin and while it is in the air ask again I catch the coin and ask again I look at the coin (and you don’t) and ask again Why does the answer change?– And did it ever have a single value?

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Which One to Play?

One may be better than the other The better coin pays off at some rate Playing the other will pay off at a lesser rate– Playing the lesser coin has “opportunity cost”

But how do we know which is which?– Explore versus Exploit!

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A First Conclusion

Probability as expressed by humans is subjective and depends on information and experience

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A Second Conclusion

A single number is a bad way to express uncertain knowledge

A distribution of values might be better

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I Dunno

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5 and 5

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2 and 10

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The Cynic Among Us

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Demo

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An Example

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An Example

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The Cluster Proximity Features

Every point can be described by the nearest cluster – 4.3 bits per point in this case– Significant error that can be decreased (to a point) by increasing number of

clusters Or by the proximity to the 2 nearest clusters (2 x 4.3 bits + 1 sign

bit + 2 proximities)– Error is negligible– Unwinds the data into a simple representation

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Diagonalized Cluster Proximity

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Lots of Clusters Are Fine

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Surrogate Method

Start with sloppy clustering into κ = k log n clusters Use these clusters as a weighted surrogate for the data Cluster surrogate data using ball k-means

Results are provably high quality for highly clusterable data Sloppy clustering can be done on-line Surrogate can be kept in memory Ball k-means pass can be done at any time

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Algorithm Costs

O(k d log n) per point for Lloyd’s algorithm … not so good for k = 2000, n = 108

Surrogate methods …. O(d log κ) = O(d (log k + log log n)) per point

This is a big deal:– k d log n = 2000 x 10 x 26 = 500,000– log k + log log n = 11 + 5 = 17– 30,000 times faster makes the grade as a bona fide big deal

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30,000 times faster sounds good

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30,000 times faster sounds good

but that isn’t the big news

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30,000 times faster sounds good

but that isn’t the big news

these algorithms do on-line clustering

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Parallel Speedup?

✓

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What about deployment?

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Learning

State

Infinite Data

Stream

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Mapper

State

Data Split

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Mapper

State

Data Split

Need shared memory!

MapperMapper

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whoami – Ted Dunning

We’re hiring at MapR

Ted Dunningtdunning@maprtech.comtdunning@apache.org@ted_dunning

For slides and other infohttp://www.slideshare.net/tdunning