PyCon 2011 talk - ngram assembly with Bloom filters

Handling ridiculous amounts of data with probabilistic data structures
C. Titus Brown
Michigan 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-ngram
DNA (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)

Life’s too short to tackle the easy problems – come to academia!
Easy stuff like Google Search
Awesomeness

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 )

Storing words in a Bloom filter
>>> x = BloomFilter([1001, 1003, 1005])
>>> 'oogaboog' in x
False
>>> x.add('oogaboog')
>>> 'oogaboog' in x
True
>>> x = BloomFilter([2])
>>> x.add('a')
>>> 'a' in x # no false negatives
True
>>> 'b' in x
False
>>> 'c' in x # …but false positives
True

Storing words in a Bloom filter
>>> x = BloomFilter([1001, 1003, 1005])
>>> 'oogaboog' in x
False
>>> x.add('oogaboog')
>>> 'oogaboog' in x
True
>>> x = BloomFilter([2]) # …false positives
>>> x.add('a')
>>> 'a' in x
True
>>> 'b' in x
False
>>> 'c' in x
True

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 extensions
def 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 bazbif zap!')
>>> x.insert_text('the quick brown fox jumped over the lazy dog')
>>> print retrieve_first_sentence(x, 'foo bar ')
foo bar bazbif 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 jumpedover 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('nanana, batman!')
>>> x.insert_text('my chemical romance: nanana')
>>> retrieve_first_sentence(x, "my chemical")
'my chemical romance: nanana, 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 allon 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!), oryour 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 / ArendHintze

Acknowledgements:
The k-mer gang:
Adina Howe
Jason Pell
RosangelaCanino-Koning
Qingpeng Zhang
ArendHintze
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.

PyCon 2011 talk - ngram assembly with Bloom filters

by c.titus.brown

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