End of Sprint 5
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Transcript of End of Sprint 5
Collective Inteligence
Enginering
Not Bigger Research Picture (Tom)
Progress
Findings
Proposal
Progress
Reading.
Progress
Investigate Compute Problem.
Progress
Investigate Compute Problem.
Pearson example.
Progress
Investigate Compute Problem.
Pearson example.
Progress
Investigate Compute Problem.
Pearson example.
Store all comparisons = 1/2 N^2
Progress
Investigate Scale
N films
M people
M[(N(N-1)/2] time the algorithm cost
Pearson:
Numerator 2 , 1 *, 1+
Denominator 2 -, 2 ^2, 2 +
M(N) time to compute averages
Can be done on ingest in M(N) time
Progress
Tractible?
A typical P4 - theoretical max of 20-40 G FLOPs,
With L2cach bandwidth, supporting instructions etc. a max of 3-7 G Flop is more realistic. (my further benchmarking show 7GFlop on a dual core centrino)
What could we expect from various technologies
Matrix multiplication is a good estimate.....
Progress
41 mins
17 mins
8 mins
Progress
40 Seconds
Progress
Genial MFlops
Which correlate well with: http://www.ient.rwth-aachen.de/~laurent/genial/benchmark_gemm_4T.html
More investigation details at: http://jira.talis.com/browse/COL-5
Progress
Computation
a 1M x 1M dense matrix multiply results in at least 1M ^ 3 FLOP's = 1E18 = 1 exaflop.
On a single P4 cpu this would take 1E18 / 7E9 = 142E6 seconds or 1653 days.
So even on a matrix 100,000 a theoretical time of 1.65 days.
Of course Comparisons are this
Megaflop 10 6gigaflop 10 9teraflop 10 12petaflop 10 15exaflop 10 18zettaflop 10 21yottaflop 10 24
Progress
Realisation.
Huge compute problem
1M matrix 1650 days
Paralelise?
16.5 days on 100 nodes
1.65 days on 1000 nodes
10M matrix 1,650,000 days
Paralelise?
16,500 days on 100 nodes
1,650 days on 1000 nodes
165 days on 10,000 nodes
Progress
Brute force
IBM's US$133M Roadrunner sustaining over 1petaflops
12,960 IBM PowerXCell 8i CPUs and 6,480 AMD Opteron dual-core processors
PowerXCell 32 GFLOPS (similar to GPU's)
10M matrix = 1000 seconds (100M = 11.6 Days)
Progress
Brute force
Folding@Home (free!) is reached over 4.1 PFLOPS
10M matrix = 25 seconds
ATI Radeon HD 4870 X2 2.4 Teraflops
500 * $500 + 250 *$1000 (each backplane) = $500,000 (331,665) for 1 PFLOP
Progress
Optimisations
Intuitively sparse - Ignore Nulls? How sparse?
True Pearson for linear algebra requires zeros, but Nulls?
Depends on data generally yes
I.e three people A, B, C - A has seen no films in common with B or C
A has seen 10 films, B 5 and C 15
Pearson numerator for B would be 15 and c -25
So C is less similar to A than B is.
So can ignore nulls - tfft!
Progress
600 Elsevier Full Text Articles.
Single core running C++
processes 20 articles / 80,000 terms per second.
Computations way faster than dense matrix.
Only 600 articles 150,000 unique terms.
A little distraction...
Progress
Progress
(from van Rijsbergen, 1979) The most frequent wordsare not the most descriptive
More Optimisation
Word Count (LSA) Characteristics
Be carefull, the lower discriminatory words can provide good information...
(and serendipity)
Progress
Progress
How Sparse?
Term Document Count from 2.18 million DBPedia Abstracts
Progress
Distraction....
Some Least Popular (stemmed) 3 docs each
Accretionari - an increase in a beneficiary's share in an estate
Accordiana - a musical radio series which was heard on CBS in 1934
Accokeek - Located in the southwest corner of Prince George's County
Nazarbayev - President of Kazakhstan
The Most Popular
15938 year
12476 season
11410 state
10758 world
10722 name
Serendipity
Progress
Very Sparse
Turns out to be Zipf Mandelbrot distribution.
[1] G. K. Zipf, Human Behavior and the Principle of Least Effort. (Cam- bridge, Mass., 1949; Addison-; Wesley, 1965).
[2] B. Mandelbrot, An informational theory of the statistical structure of language, in Communication Theory, ed. Willis Jackson. (Better- worths, 1953).
Word Count is .0025% dense
Ignore Null for huge optimisation.
40,000 x less compute
(using uniform density assumption)
Zipf-Mandelbrot has the form:
y = P1/(x+P2)^P3.
Progress
DBPedia words follow Zipf-Mandelbrot
Zoomed in chunk of DBPedia word count
y = P1/(x+P2)^P3
best fit regression (red curve)
with factors
P1 = 874150
P2 = 60.0000
P3 = 1.01000
Progress
Calculate Comparisons.
2.18 million Abstracts 1.3M unique terms.
Fits in 2G ram - (1.3M*2.18M*.000025 * 21 = 1.5G ) (as it is .0025% dense each entry is 21 bytes)
Uniform density assumption
Comparisons computable in few minutes
Not storeable in RAM (3.6 Tbytes!)
Big underestimate
(Stopped the run after 4 hours)
Stored random 100 article sample, and comparing with all 2M others. (0.2Gb) to allow intuitative QA
Progress
Extrapolating Compute Times.
Not 40,000x less compute (.0025% dense)
Word Count is .0025% dense - 40,000 x less compute
Top 1000 most commonly occurring terms the density is 0.78%
Not 128x less (.78% dense)
So use square of area under curve
= Integral of Zipf Mandelbrot Squared
Roughly a power law.
y = (x^P)/N
Progress
DBPedia Abstracs Ops (not including algorithm cost)
Regression using simple power law (P = 2.1 N = 1E0.73)
Progress
Extrapolating Compute Times.
2 Million abstracts
Square of Integral of Zipf Mandelbrot
Predicts calculable in 5.42 Hours
Assuming all in RAM.
But writing Gigs to disk big overhead.
(Not run this yet to prove)
Progress
Loans Data Ops (not including algorithm cost)(proving power law linear regression prediction)
Regression using simple power law (P = 3.5 N = 1E10.15)
Progress
Loans Data
Hereford Libraries.
C++ In memory 'super fast hash'
Processed 19M loans in 1min 20sec.
Producing 269,000 unique borrower and 491,000 unique books.
8 Million unique loan events
Progress
Loans per Individual Nice Zipf Mandelbrot curve
Progress
Zipf Mandelbrot Good Assumption?
Most (all large complex systems?) data that we are likely to process will follow a Zipf-Mandlebrot model.
K. Silagadze shows [1] that these comply...
Clickstreams
Page-rank (Linkage/Centrality)
Citations
Other long tail interactions.
[1]Z. K. Silagadze [physics.soc-ph] 26 Jan 1999 Citations and the Zipf-Mandelbrots law - Budker Institute of Nuclear Physics, 630 090, Novosibirsk, Russia ing.
Findings
Cant Store All Comparisons
50 Tb for 10M matrix ( N^2) for triangle matrix.
Store only meaningfull? Thld = n or f.
Can compute All 2M (squared) Comparisons
In 6 hours (1 core).
Cant Compute 1 Billion Comparisons
287 years (7 days on 20,000 cores 10Billion?).
Zipf Mandelbrot Curve is Usefull.
Can store All(?) raw metrics
n=count - fixedf=factor - Z-M
Findings
Zipf Mandelbrot Curve is Usefull.
Head
Big proportion of compute
Large M1 M2 intersection.
Low discrimination
Body
Good info
Medium compute
Tail
Specialist
Trivial or no compute
Findings
Zipf Mandelbrot Curve is Usefull.
Allows us to make optimisations
In reducing the y axis (and x a bit)
Chop the head off.
Body
Dimensionality reduction
Tail
Chop the tail off
Or Dimensionality reduction
X axis = N^2, Y axis = M
Findings
What about storing meaningfull comparisons.
Solves storage problem
Requires repeated compute problem
Deltas, could affect whole set
Will affect a chunk of the set
Could trade off timely accuracy with batch processing.
Proposal
Store raw curve
Sparse Strorage Bigtable like
Hbase, Hypertable, etc
Unloads indexing and lookup to nodes.
Calculate on the fly
Two indeces Books people and People books
Not 1/2N^2 just 1* Intersect (* M)
Tail Retrieval problem M~0 Intersect~0.
Body Some retrieval and compute.
Head Big retrieval and compute big M big intersect.
Proposal
Pre Compute Head
Store top n
Store any that take more than .5 seconds
Zipf-Mandelbrot retrieval only problem
Dynamic finding them is linear
Store as a cache only when requested?
Depends on acceptible delay?
This Hybrid Scales Better.
Better than Storing all or Computnig all
Proposal
It doesn't scale indefinately.
* scale by 10, * nodes by 100
Dimensionality reduction will HAVE to kick in.
This aproach allows that, but at bigger scles than most
Consider severing head and tail as early aproach.
Only optimised for individual requests.
Given this article find the 10 next similar
What about...Given this corpus find the 100 most similar things
Then set n = infinity (or f=0) and the service will tell you how many days to come back for your results
Proposal
Experimentation
Used Hbase, HDFS, Hadoop
Not using Hadoop yet but is good fit for data ingest
Hadoop not v efficient for comparison but doable.
Used Loan data and binary pearson
Ignoring nulls (and sigma) so counts only.
Quick demo
Proposal
Next Steps
Prove this aproach
Performance Testing.
Hbase over n nodes (perf lab, poss then EC2?).
Timing retrieval vs compute
Good logging
Configurable variables
Multiple 'stores' (data sets).
8M loans now 80M?
Hadoop the ingest if just to save time during trials
OpsPredicted Ops
140177643736920282.7204039
2135545534601664907107.6301639
317842229994162169851509.672014
4202901127390308266375731.97562
5247103441119866530973764.725377
6279949812720790821819083.372186
733161815943973281486734211.08415
841895835332021363369742434.19775
945377145567594944455829660.29513
1049114058085647025877850970.94164
111.#NAN9842678040
121.#NAN1.#NAN0
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