Strata NYC 2015: Sketching Big Data with Spark: randomized algorithms for large-scale data analytics

Sketching Big Data with Spark

Reynold Xin @rxin Sep 29, 2015 @ Strata NY

About Databricks

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Spark

Count-min sketch

Approximate frequent items

Taylor Swift

“Spark is the Taylor Swift of big data software.” - Derrick Harris, Fortune

Who is this guy?

Co-founder & architect for Spark at Databricks Former PhD student at UC Berkeley AMPLab A “systems” guy, which means I won’t be showing equations and this talk might be the easiest to consume in HDS

This talk

1.  Develop intuitions on these sketches so you know when to use it

2.  Understand how certain parts in distributed data processing (e.g. Spark) work

Sketch: Reynold’s not-so-scientific definition

1. Use small amount of space to summarize a large dataset. 2. Go over each data point once, a.k.a. “streaming algorithm”, or “online algorithm” 3. Parallelizable, but only small amount of communication

What for?

Exploratory analysis Feature engineering Combine sketch and exact to speed up processing

Sketches in Spark

Set membership (Bloom filter) Cardinality (HyperLogLog) Histogram (count-min sketch) Frequent pattern mining

Frequent items Stratified Sampling …

This Talk

Set membership (Bloom filter) Cardinality (HyperLogLog) Histogram (count-min sketch) Frequent pattern mining

Frequent items Stratified Sampling …

Set membership

Set membership

Identify whether an item is in a set e.g. “You have bought this item before”

Exact set membership

Track every member of the set •  Space: size of data •  One pass: yes •  Parallelizable & communication: size of data

Approximate set membership

Take 1. Use a 32-bit integer hash map to track •  ~4 bytes per record •  Max 4 billion items

Take 2. Hash items to 256 buckets

•  Memory usage only 256 bits •  Good if num records is small •  Bad if num records is large (256+ items, collision rate 100%!)

Bloom filter

Bloom filter algorithm •  k hash functions •  hash item into k separate positions •  if any of the k positions is not set, then item is not in set

Properties •  ~500MB needed to have 10% error rate on 1 billion items •  See http://hur.st/bloomfilter?n=1000000000&p=0.1 •  False positives possible

Use case beyond exploration

SELECT * FROM A join B on A.key = B.key 1.  Assume A and B are both large, i.e. “shuffle join” 2.  Some rows in A might not have matched rows in B 3.  Wouldn’t it be nice if we only need to shuffle rows that match?

Answer: use a bloom filter to filter the ones that don’t match

Frequent items

Frequent Items

Find items more frequent than 1/k

Source: http://www.macfreek.nl/memory/Letter_Distribution

4,474

3,146

2,352

1,749

1,293 1,248 1,107 1,094 1,065

907 835 793 789 737 598 582 517 482 447 444 420 409 409 405 400 381 378 369 367 366

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000 Tw

itter

follo

wer

s in

thou

sand

s

Twitter Followers of NBA teams (in 1,000s), September 2015

Source: http://www.statista.com/statistics/240386/twitter-followers-of-national-basketball-association-teams/

Frequent Items

Exploration •  Identify important members in a network •  E.g. “the”, LA Lakers, Taylor Swift

Feature Engineering •  Identify outliers •  Ignore low frequency items

Frequent Items: Exact Algorithm

SELECT  item,  count(*)  cnt  FROM  corpus  GROUP  BY  item  HAVING  cnt  >  k  *  cnt  

•  Space: linear to |item| •  One pass: no (two passes) •  Parallelizable & communication: linear to |item|

Example 1: Find Items Frequency > ½ (k=2)

draw

Put back if any pair of balls are the same color

draw

Remove if balls are all different color

Example 1: Find Items Frequency > 1/2

Blue ball left (frequent item)

Example 2: Find Items Frequency > ½ (k=2)

draw

draw

draw

1 ball left (frequent item)

How do we implement this?

Maintain a hash table of counts

Increment for every ball we see

0 => 1

Increment for every ball we see

1 => 2

Increment for every ball we see

0 => 4

Increment for every ball we see

0 => 4

Increment for every ball we see

4

0 => 1

When the hash table has k items, remove 1 from each item and remove the item if count = 0

4 => 3

1 => 0

3

3

0 => 1

2

2

0 => 1

1

Implementation

Maintains a hash table of counts •  For each item, increment its count •  If hash table size == k:

– decrement 1 from each item; and –  remove items whose count == 0

Parallelization: merge hash tables of max size k

Comparing Exact vs Approximate

Naïve Exact Sketch

# Passes 2 1

Memory |item| k

Communication |item| k

Comparing Exact vs Approximate

Naïve Exact Sketch Smart Exact

# Passes 2 1 2 (1st pass using sketch)

Memory |item| k k

Communication |item| k k

Quiz: an example with false positive?

K = 3

How to use it in Spark?

Frequent items for multiple columns independently •  df.stat.freqItems([“columnA”,  “columnB”,  …])  

Frequent items for composite keys

•  df.stat.freqItems(struct(“columnA”,  “columnB”))  

Stratified sampling

Bernoulli sampling & Variance

Sample US population (300m) using rate 0.000002 (~600) •  Wyoming (0.5m) should have 1 •  Bernoulli sampling likely leads to Wyoming having 0

Intuition: uniform sampling leads to ~ 600 samples.

•  i.e. it might be 600, or 601, or 599, or … •  Impact on WY when going from 600 to 601 is much larger than that on CA’s

Stratified sampling

Existing “exact” algorithms •  Draw-by-draw •  Selection-rejection •  Reservoir •  Random sort

Either sequential or expensive (full global sort)

Random sort

Example: sampling probability p = 0.1 on 100 items. 1.  Generate random keys

•  (0.644, t1), (0.378, t2), … (0.500, t99), (0.471, t100)

2.  Sort and select the smallest 10 items

•  (0.028, t94), (0.029, t44), …, (0.137, t69), …, (0.980, t26), (0.988, t60)

Heuristics

Qualitatively speaking •  If u is “much larger” than p, then t is “unlikely” to be selected •  If u is “much smaller” than p, then it is “likely” to be selected

Set two thresholds q1 and q2, such that: •  If u < q1, accept t directly •  If u > q2, reject t directly •  Otherwise, put t in a buffer to be sorted

Spark’s stratified sampling algorithm

Combines “exact” and “sketch” to achieve parallelization & low memory overhead df.stat.sampleByKeyExact(col,  fractions,  seed)    

Xiangrui Meng. Scalable Simple Random Sampling and Stratified Sampling. ICML 2013  

This Talk

Set membership (Bloom filter) Cardinality (HyperLogLog) Histogram (count-min sketch) Frequent pattern mining

Frequent items Stratified Sampling …

Conclusion

Sketches can be useful in exploration, feature engineering, as well as building faster exact algorithms. We are building a lot of these into Spark so you don’t need to reinvent the wheel!

Thank you. Meetup tonight @ Civic Hall, 6:30pm  156 5th Avenue, 2nd floor, New York, NY