Handling ridiculous amounts of data with probabilistic data structures

C. Titus BrownMichigan State University

Computer Science / Microbiology

Resources

http://www.slideshare.net/c.titus.brown/

Webinar: http://oreillynet.com/pub/e/1784

Source: github.com/ctb/N-grams (this talk): khmer-ngramDNA (the real cheese): khmer

khmer is implemented in C++ with a Python wrapper, which has been awesome for scripting, testing, and general

development. (But man, does C++ suck…)

Lincoln Stein

Sequencing capacity is outscaling Moore’s Law.

Hat tip to Narayan Desai / ANL

We don’t have enough resources or people to analyze data.

Data generation vs data analysis

It now costs about $10,000 to generate a 200 GB sequencing data set (DNA) in about a week.

(Think: resequencing human; sequencing expressed genes; sequencing metagenomes, etc.)

…x1000 sequencers

Many useful analyses do not scale linearly in RAM or CPU with the amount of data.

The challenge?

Massive (and increasing) data generation capacity, operating at a boutique level, with

algorithms that are wholly incapable of scaling to the data volume.

Note: cloud computing isn’t a solution to a sustained scaling problem!! (See: Moore’s Law slide)

Awesomeness

Easy stuff like Google Search

Life’s too short to tackle the easy problems – come to academia!

A brief intro to shotgun assembly

It was the best of times, it was the wor, it was the worst of times, it was the isdom, it was the age of foolishness

mes, it was the age of wisdom, it was th

It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness

…but for 2 bn+ fragments.Not subdivisible; not easy to distribute; memory intensive.

Define a hash function (word => num)

def hash(word): assert len(word) <= MAX_K

value = 0 for n, ch in enumerate(word): value += ord(ch) * 128**n

return value

class BloomFilter(object): def __init__(self, tablesizes, k=DEFAULT_K): self.tables = [ (size, [0] * size) \

for size in tablesizes ] self.k = k

def add(self, word): # insert; ignore collisions val = hash(word) for size, ht in self.tables: ht[val % size] = 1 def __contains__(self, word): val = hash(word) return all( ht[val % size] \

for (size, ht) in self.tables )

class BloomFilter(object): def __init__(self, tablesizes, k=DEFAULT_K): self.tables = [ (size, [0] * size) \

for size in tablesizes ] self.k = k

def add(self, word): # insert; ignore collisions val = hash(word) for size, ht in self.tables: ht[val % size] = 1 def __contains__(self, word): val = hash(word) return all( ht[val % size] \

for (size, ht) in self.tables )

class BloomFilter(object): def __init__(self, tablesizes, k=DEFAULT_K): self.tables = [ (size, [0] * size) \

for size in tablesizes ] self.k = k

def add(self, word): # insert; ignore collisions val = hash(word) for size, ht in self.tables: ht[val % size] = 1 def __contains__(self, word): val = hash(word) return all( ht[val % size] \

for (size, ht) in self.tables )

Storing words in a Bloom filter>>> x = BloomFilter([1001, 1003, 1005])>>> 'oogaboog' in xFalse>>> x.add('oogaboog')>>> 'oogaboog' in xTrue

>>> x = BloomFilter([2])>>> x.add('a')>>> 'a' in x # no false negativesTrue>>> 'b' in xFalse>>> 'c' in x # …but false positivesTrue

Storing words in a Bloom filter>>> x = BloomFilter([1001, 1003, 1005])>>> 'oogaboog' in xFalse>>> x.add('oogaboog')>>> 'oogaboog' in xTrue

>>> x = BloomFilter([2]) # …false positives>>> x.add('a')>>> 'a' in xTrue>>> 'b' in xFalse>>> 'c' in xTrue

Storing text in a Bloom filter

class BloomFilter(object): …def insert_text(self, text):

for i in range(len(text)-self.k+1): self.add(text[i:i+self.k])

def next_words(bf, word): # try all 1-ch extensions prefix = word[1:] for ch in bf.allchars: word = prefix + ch if word in bf: yield ch

# descend into all successive 1-ch extensionsdef retrieve_all_sentences(bf, start): word = start[-bf.k:]

n = -1 for n, ch in enumerate(next_words(bf, word)): ss = retrieve_all_sentences(bf,start + ch) for sentence in ss: yield sentence

if n < 0: yield start

def next_words(bf, word): # try all 1-ch extensions prefix = word[1:] for ch in bf.allchars: word = prefix + ch if word in bf: yield ch

# descend into all successive 1-ch extensionsdef retrieve_all_sentences(bf, start): word = start[-bf.k:]

n = -1 for n, ch in enumerate(next_words(bf, word)): ss = retrieve_all_sentences(bf,start + ch) for sentence in ss: yield sentence

if n < 0: yield start

Storing and retrieving text

>>> x = BloomFilter([1001, 1003, 1005, 1007])

>>> x.insert_text('foo bar baz bif zap!')>>> x.insert_text('the quick brown fox jumped over the lazy

dog')

>>> print retrieve_first_sentence(x, 'foo bar ')foo bar baz bif zap!

>>> print retrieve_first_sentence(x, 'the quic')the quick brown fox jumped over the lazy dog

Sequence assembly

>>> x = BloomFilter([1001, 1003, 1005, 1007])

>>> x.insert_text('the quick brown fox jumped ')>>> x.insert_text('jumped over the lazy dog')

>>> retrieve_first_sentence(x, 'the quic')the quick brown fox jumped over the lazy dog

(This is known as the de Bruin graph approach to assembly; c.f. Velvet, ABySS, SOAPdenovo)

Repetitive strings are the devil

>>> x = BloomFilter([1001, 1003, 1005, 1007])

>>> x.insert_text('na na na, batman!')>>> x.insert_text('my chemical romance: na na na')

>>> retrieve_first_sentence(x, "my chemical")'my chemical romance: na na na, batman!'

Note, it’s a probabilistic data structure

Retrieval errors:

>>> x = BloomFilter([1001, 1003]) # small Bloom filter…>>> x.insert_text('the quick brown fox jumped over the lazy dog’)>>> retrieve_first_sentence(x, 'the quic'),('the quick brY',)

Assembling DNA sequence

• Can’t directly assemble with Bloom filter approach (false connections, and also lacking many convenient graph properties)

• But we can use the data structure to grok graph properties and eliminate/break up data:– Eliminate small graphs (no false negatives!)– Disconnected partitions (parts -> map reduce)– Local graph complexity reduction & error/artifact trimming

…and then feed into other programs.

This is a data reducing prefilter

Right, but does it work??

• Can assemble ~200 GB of metagenome DNA on a single 4xlarge EC2 node (68 GB of RAM) in 1 week ($500).

…compare with not at all on a 512 GB RAM machine.

• Error/repeat trimming on a tricky worm genome: reduction from– 170 GB resident / 60 hrs– 54 GB resident / 13 hrs

How good is this graph representation?

• V. low false positive rates at ~2 bytes/k-mer;– Nearly exact human genome graph in ~5 GB.– Estimate we eventually need to store/traverse 50 billion k-

mers (soil metagenome)

• Good failure mode: it’s all connected, Jim! (No loss of connections => good prefilter)

• Did I mention it’s constant memory? And independent of word size?

• …only works for de Bruijn graphs

Thoughts for the future

• Unless your algorithm scales sub-linearly as you distribute it across multiple nodes (hah!), or your problem size has an upper bound, cloud computing isn’t a long-term solution in bioinformatics

• Synopsis data structures & algorithms (which incl. probabilistic data structures) are a neat approach to parsing problem structure.

• Scalable in-memory local graph exploration enables many other tricks, including near-optimal multinode graph distribution.

Groxel view of knot-like region / Arend Hintze

Acknowledgements:The k-mer gang:

• Adina Howe

• Jason Pell• Rosangela Canino-Koning• Qingpeng Zhang• Arend Hintze

Collaborators:

• Jim Tiedje (Il padrino)

• Janet Jansson, Rachel Mackelprang, Regina Lamendella, Susannah Tringe, and many others (JGI)

• Charles Ofria (MSU)

Funding: USDA NIFA; MSU, startup and iCER; DOE; BEACON/NSF STC; Amazon Education.