The Problem  K-means clustering Which Algorithms Really Matter

Which Algorithms Really Matter? ©MapR Technologies 2013 1

Me, Us  Ted Dunning, Chief Application Architect, MapR Committer PMC member, Mahout, Zookeeper, Drill Bought the beer at the first HUG  MapR Distributes more open source components for Hadoop Adds major technology for performance, HA, industry standard API’s  Info Hash tag - #mapr See also - @ApacheMahout @ApacheDrill @ted_dunning and @mapR ©MapR Technologies 2013 2

Topic For Today  What is important? What is not?  Why?  What is the difference from academic research?  Some examples ©MapR Technologies 2013 4

What is Important?  Deployable  Robust  Transparent  Skillset and mindset matched?  Proportionate ©MapR Technologies 2013 5

What is Important?  Deployable – Clever prototypes don’t count if they can’t be standardized  Robust  Transparent  Skillset and mindset matched?  Proportionate ©MapR Technologies 2013 6

What is Important?  Deployable –  Robust –  Clever prototypes don’t count Mishandling is common Transparent – Will degradation be obvious?  Skillset and mindset matched?  Proportionate ©MapR Technologies 2013 7

What is Important?  Deployable –  Robust –  Will degradation be obvious? Skillset and mindset matched? –  Mishandling is common Transparent –  Clever prototypes don’t count How long will your fancy data scientist enjoy doing standard ops tasks? Proportionate – Where is the highest value per minute of effort? ©MapR Technologies 2013 8

Academic Goals vs Pragmatics  Academic goals – – –  Reproducible Isolate theoretically important aspects Work on novel problems Pragmatics – – – – – Highest net value Available data is constantly changing Diligence and consistency have larger impact than cleverness Many systems feed themselves, exploration and exploitation are both important Engineering constraints on budget and schedule ©MapR Technologies 2013 9

Example 1: Making Recommendations Better ©MapR Technologies 2013 10

Recommendation Advances  What are the most important algorithmic advances in recommendations over the last 10 years?  Cooccurrence analysis?  Matrix completion via factorization?  Latent factor log-linear models?  Temporal dynamics? ©MapR Technologies 2013 11

The Winner – None of the Above  What are the most important algorithmic advances in recommendations over the last 10 years? 1. Result dithering 2. Anti-flood ©MapR Technologies 2013 12

The Real Issues  Exploration  Diversity  Speed  Not the last fraction of a percent ©MapR Technologies 2013 13

Result Dithering  Dithering is used to re-order recommendation results – Re-ordering is done randomly  Dithering is guaranteed to make off-line performance worse  Dithering also has a near perfect record of making actual performance much better ©MapR Technologies 2013 14

Result Dithering  Dithering is used to re-order recommendation results – Re-ordering is done randomly  Dithering is guaranteed to make off-line performance worse  Dithering also has a near perfect record of making actual performance much better “Made more difference than any other change” ©MapR Technologies 2013 15

Simple Dithering Algorithm  Generate synthetic score from log rank plus Gaussian s = logr + N(0, e )  Pick noise scale to provide desired level of mixing Dr µ r exp e  Typically e Î [ 0.4, 0.8]  Oh… use floor(t/T) as seed ©MapR Technologies 2013 16

Example … ε = 0.5 1 1 1 1 1 1 1 2 4 2 3 2 ©MapR Technologies 2013 2 2 4 2 6 2 2 1 1 1 1 1 6 3 3 4 2 3 3 3 2 5 5 3 5 8 2 3 3 5 4 5 7 3 4 4 3 5 6 15 4 24 6 7 3 4 2 7 17 4 7 7 7 16 7 12 6 9 7 7 12 13 6 11 13 9 17 5 4 8 13 8 17 16 34 10 19 5 13 14 17 5 6 6 16

Example … ε = log 2 = 0.69 1 1 1 1 1 1 1 2 2 3 11 1 ©MapR Technologies 2013 2 8 3 2 5 2 3 4 3 4 1 8 8 14 8 10 33 7 5 11 1 1 2 7 3 15 2 7 15 3 23 8 4 2 4 3 9 3 10 3 2 5 9 3 6 10 5 22 18 15 2 5 8 9 4 7 1 7 11 7 11 7 22 7 6 11 19 4 44 8 15 3 2 6 10 4 14 29 6 2 9 33 14 14 33

Exploring The Second Page ©MapR Technologies 2013 19

Lesson 1: Exploration is good ©MapR Technologies 2013 20

Example 2: Bayesian Bandits ©MapR Technologies 2013 21

Bayesian Bandits  Based on Thompson sampling  Very general sequential test  Near optimal regret  Trade-off exploration and exploitation  Possibly best known solution for exploration/exploitation  Incredibly simple ©MapR Technologies 2013 22

Thompson Sampling  Select each shell according to the probability that it is the best  Probability that it is the best can be computed using posterior é ù P(i is best) = ò I êE[ri | q ] = max E[rj | q ]ú P(q | D) dq ë û j  But I promised a simple answer ©MapR Technologies 2013 23

Thompson Sampling – Take 2  Sample θ q ~ P(q | D)  Pick i to maximize reward i = argmax E[rj | q ] j  Record result from using i ©MapR Technologies 2013 24

Fast Convergence 0.12 0.11 0.1 0.09 0.08 regret 0.07 0.06 ε- greedy, ε = 0.05 0.05 0.04 Bayesian Bandit with Gam m a- Norm al 0.03 0.02 0.01 0 0 100 200 300 400 500 600 n ©MapR Technologies 2013 25 700 800 900 1000 1100

Thompson Sampling on Ads An Empirical Evaluation of Thompson Sampling - Chapelle and Li, 2011 ©MapR Technologies 2013 26

Bayesian Bandits versus Result Dithering  Many useful systems are difficult to frame in fully Bayesian form  Thompson sampling cannot be applied without posterior sampling  Can still do useful exploration with dithering  But better to use Thompson sampling if possible ©MapR Technologies 2013 27

Lesson 2: Exploration is pretty easy to do and pays big benefits. ©MapR Technologies 2013 28

Example 3: On-line Clustering ©MapR Technologies 2013 29

The Problem  K-means clustering is useful for feature extraction or compression  At scale and at high dimension, the desirable number of clusters increases  Very large number of clusters may require more passes through the data  Super-linear scaling is generally infeasible ©MapR Technologies 2013 30

The Solution  Sketch-based algorithms produce a sketch of the data  Streaming k-means uses adaptive dp-means to produce this sketch in the form of many weighted centroids which approximate the original distribution  The size of the sketch grows very slowly with increasing data size  Many operations such as clustering are well behaved on sketches Fast and Accurate k-means For Large Datasets. Michael Shindler, Alex Wong, Adam Meyerson. Revisiting k-means: New Algorithms via Bayesian Nonparametrics . Brian Kulis, Michael Jordan. ©MapR Technologies 2013 31

An Example ©MapR Technologies 2013 32

An Example ©MapR Technologies 2013 33

The Cluster Proximity Features  Every point can be described by the nearest cluster – –  Or by the proximity to the 2 nearest clusters (2 x 4.3 bits + 1 sign bit + 2 proximities) – –  4.3 bits per point in this case Significant error that can be decreased (to a point) by increasing number of clusters Error is negligible Unwinds the data into a simple representation Or we can increase the number of clusters (n fold increase adds log n bits per point, decreases error by sqrt(n) ©MapR Technologies 2013 34

Diagonalized Cluster Proximity ©MapR Technologies 2013 35

Lots of Clusters Are Fine ©MapR Technologies 2013 36

Typical k-means Failure Selecting two seeds here cannot be fixed with Lloyds Result is that these two clusters get glued together ©MapR Technologies 2013 37

Streaming k-means Ideas  By using a sketch with lots (k log N) of centroids, we avoid pathological cases  We still get a very good result if the sketch is created – – in one pass with approximate search  In fact, adaptive dp-means works just fine  In the end, the sketch can be used for clustering or … ©MapR Technologies 2013 38

Lesson 3: Sketches make big data small. ©MapR Technologies 2013 39

Recommendations Alice Bob Charles ©MapR Technologies 2013 Alice got an apple and a puppy Bob got an apple Charles got a bicycle 42

Co-occurrence Matrix: Items by Items How do you tell which co-occurrences are useful?. 1 2 1 1 2 ©MapR Technologies 2013 1 0 - 0 1 1 46 0 0

Indicator Matrix: Anomalous Co-Occurrence Result: The marked row will be added to the indicator field in the item document… ✔ ✔ ©MapR Technologies 2013 48

Indicator Matrix That one row from indicator matrix becomes the indicator field in the Solr document used to deploy the recommendation engine. ✔ id: t4 title: puppy desc: The sweetest little puppy ever. keywords: puppy, dog, pet indicators: (t1) Note: data for the indicator field is added directly to meta-data for a document in Solr index. You don’t need to create a separate index for the indicators. ©MapR Technologies 2013 49

Looking Inside LucidWorks Real-time recommendation query and results: Evaluation What to recommend if new user listened to 2122: Fats Domino & 303: Beatles? Recommendation is “1710 : Chuck Berry” 52 ©MapR Technologies 2013 52

Lesson 4: Recursive search abuse pays Search can implement recs Which can implement search ©MapR Technologies 2013 54

Me, Us  Ted Dunning, Chief Application Architect, MapR Committer PMC member, Mahout, Zookeeper, Drill Bought the beer at the first HUG  MapR Distributes more open source components for Hadoop Adds major technology for performance, HA, industry standard API’s  Info Hash tag - #mapr See also - @ApacheMahout @ApacheDrill @ted_dunning and @mapR ©MapR Technologies 2013 57