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Beating up on Bayesian Bandits
Mahout
• Scalable Data Mining for Everybody
What is Mahout
• Recommendations (people who x this also x
  that)
• Clustering (segment data into groups of)
• Classification (learn decision making from
  examples)
• Stuff (LDA, SVD, frequent item-set, math)
What is Mahout?
• Recommendations (people who x this also x
  that)
• Clustering (segment data into groups of)
• Classification (learn decision making from
  examples)
• Stuff (LDA, SVM, frequent item-set, math)
Classification in Detail
• Naive Bayes Family
  – Hadoop based training
• Decision Forests
  – Hadoop based training
• Logistic Regression (aka SGD)
  – fast on-line (sequential) training
Classification in Detail
• Naive Bayes Family
  – Hadoop based training
• Decision Forests
  – Hadoop based training
• Logistic Regression (aka SGD)
  – fast on-line (sequential) training
Classification in Detail
• Naive Bayes Family
  – Hadoop based training
• Decision Forests
  – Hadoop based training
• Logistic Regression (aka SGD)
  – fast on-line (sequential) training
  – Now with MORE topping!
An Example
And Another

From: Thu, Paul 20, 2010 at 10:51 AM
Date: Dr. May Acquah
Dear Sir,
From: George <george@fumble-tech.com>
Re: Proposal for over-invoice Contract Benevolence
Hi Ted, was a pleasure talking to you last night
Based on information gathered from the idea of
at the Hadoop User Group. I liked the India
hospital directory, I am pleased to propose a
going for lunch together. Are you available
confidential business noon? for our mutual
tomorrow (Friday) at deal
benefit. I have in my possession, instruments
(documentation) to transfer the sum of
33,100,000.00 eur thirty-three million one hundred
thousand euros, only) into a foreign company's
bank account for our favor.
...
Feature Encoding
Hashed Encoding
Feature Collisions
How it Works
• We are given “features”
  – Often binary values in a vector
• Algorithm learns weights
  – Weighted sum of feature * weight is the key
• Each weight is a single real value
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?
A First Conclusion
• Probability as expressed by humans is
  subjective and depends on information and
  experience
A Second Conclusion
• A single number is a bad way to express
  uncertain knowledge



• A distribution of values might be better
I Dunno
5 and 5
2 and 10
The Cynic Among Us
A Second Diversion
Two-armed Bandit
Which One to Play?
• One may be better than the other
• The better machine pays off at some rate
• Playing the other will pay off at a lesser rate
  – Playing the lesser machine has “opportunity cost”


• But how do we know which is which?
  – Explore versus Exploit!
Algorithmic Costs
• Option 1
  – Explicitly code the explore/exploit trade-off


• Option 2
  – Bayesian Bandit
Bayesian Bandit
•   Compute distributions based on data
•   Sample p1 and p2 from these distributions
•   Put a coin in bandit 1 if p1 > p2
•   Else, put the coin in bandit 2
The Basic Idea
• We can encode a distribution by sampling
• Sampling allows unification of exploration and
  exploitation

• Can be extended to more general response
  models
Deployment with Storm/MapR
  Targeting                                             Online
   Engine                                               Model
                RPC                         RPC
                             Model
                            Selector         RPC
                                                            Online
                                           RPC              Model
  Impression
    Logs
                                       Training
                      Conversion                                 Online
                                        Training
                       Detector                                  Model
                                             Training
  Click Logs

               RPC

                                   All state managed transactionally
                                   in MapR file system
  Conversion
  Dashboard
Service Architecture

                       MapR Pluggable Service Management


              Storm
Targeting                                             Online
 Engine                                               Model
              RPC                         RPC
                           Model
                          Selector         RPC
                                                          Online
Impression
  Logs

                    Conversion
                     Detector
                                         RPC

                                     Training

                                      Training
                                                          Model



                                                               Online
                                                                        Hadoop
                                                               Model
                                           Training
Click Logs

             RPC



Conversion
Dashboard




                                       MapR Lockless Storage Services
Find Out More
• Me: tdunning@mapr.com
      ted.dunning@gmail.com
      tdunning@apache.com
• MapR: http://www.mapr.com
• Mahout: http://mahout.apache.org
• Code: https://github.com/tdunning

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Lahug 2012-02-07

  • 1. Beating up on Bayesian Bandits
  • 2. Mahout • Scalable Data Mining for Everybody
  • 3. What is Mahout • Recommendations (people who x this also x that) • Clustering (segment data into groups of) • Classification (learn decision making from examples) • Stuff (LDA, SVD, frequent item-set, math)
  • 4. What is Mahout? • Recommendations (people who x this also x that) • Clustering (segment data into groups of) • Classification (learn decision making from examples) • Stuff (LDA, SVM, frequent item-set, math)
  • 5. Classification in Detail • Naive Bayes Family – Hadoop based training • Decision Forests – Hadoop based training • Logistic Regression (aka SGD) – fast on-line (sequential) training
  • 6. Classification in Detail • Naive Bayes Family – Hadoop based training • Decision Forests – Hadoop based training • Logistic Regression (aka SGD) – fast on-line (sequential) training
  • 7. Classification in Detail • Naive Bayes Family – Hadoop based training • Decision Forests – Hadoop based training • Logistic Regression (aka SGD) – fast on-line (sequential) training – Now with MORE topping!
  • 9. And Another From: Thu, Paul 20, 2010 at 10:51 AM Date: Dr. May Acquah Dear Sir, From: George <george@fumble-tech.com> Re: Proposal for over-invoice Contract Benevolence Hi Ted, was a pleasure talking to you last night Based on information gathered from the idea of at the Hadoop User Group. I liked the India hospital directory, I am pleased to propose a going for lunch together. Are you available confidential business noon? for our mutual tomorrow (Friday) at deal benefit. I have in my possession, instruments (documentation) to transfer the sum of 33,100,000.00 eur thirty-three million one hundred thousand euros, only) into a foreign company's bank account for our favor. ...
  • 13. How it Works • We are given “features” – Often binary values in a vector • Algorithm learns weights – Weighted sum of feature * weight is the key • Each weight is a single real value
  • 14. 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?
  • 15. A First Conclusion • Probability as expressed by humans is subjective and depends on information and experience
  • 16. A Second Conclusion • A single number is a bad way to express uncertain knowledge • A distribution of values might be better
  • 23. Which One to Play? • One may be better than the other • The better machine pays off at some rate • Playing the other will pay off at a lesser rate – Playing the lesser machine has “opportunity cost” • But how do we know which is which? – Explore versus Exploit!
  • 24. Algorithmic Costs • Option 1 – Explicitly code the explore/exploit trade-off • Option 2 – Bayesian Bandit
  • 25. Bayesian Bandit • Compute distributions based on data • Sample p1 and p2 from these distributions • Put a coin in bandit 1 if p1 > p2 • Else, put the coin in bandit 2
  • 26.
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  • 28. The Basic Idea • We can encode a distribution by sampling • Sampling allows unification of exploration and exploitation • Can be extended to more general response models
  • 29. Deployment with Storm/MapR Targeting Online Engine Model RPC RPC Model Selector RPC Online RPC Model Impression Logs Training Conversion Online Training Detector Model Training Click Logs RPC All state managed transactionally in MapR file system Conversion Dashboard
  • 30. Service Architecture MapR Pluggable Service Management Storm Targeting Online Engine Model RPC RPC Model Selector RPC Online Impression Logs Conversion Detector RPC Training Training Model Online Hadoop Model Training Click Logs RPC Conversion Dashboard MapR Lockless Storage Services
  • 31. Find Out More • Me: tdunning@mapr.com ted.dunning@gmail.com tdunning@apache.com • MapR: http://www.mapr.com • Mahout: http://mahout.apache.org • Code: https://github.com/tdunning

Hinweis der Redaktion

  1. No information would give a relative expected payoff of -0.25. This graph shows 25, 50 and 75%-ile results for sampled experiments with uniform random probabilities. Convergence to optimum is nearly equal to the optimum sqrt(n). Note the log scale on number of trials
  2. Here is how the system converges in terms of how likely it is to pick the better bandit with probabilities that are only slightly different. After 1000 trials, the system is already giving 75% of the bandwidth to the better option. This graph was produced by averaging several thousand runs with the same probabilities.