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Apache SystemML -
Declarative Large-Scale
Machine Learning
Romeo Kienzler (IBM Waston IoT)
Berthold Reinwald (IBM Almaden Research Center)
Frederick R. Reiss (IBM Almaden Research Center)
Matthias Rieke (IBM Analytics)
Swiss Data Science Conference 16 - ZHAW - Winterthur
–Assembler vs. Python?
“High-level programming”
Why another lib?
• Custom machine learning algorithms
• Declarative ML
• Transparent distribution on data-parallel framework
• Scale-up
• Scale-out
• Cost-based optimiser generates low level execution
plans
Why on Spark?
• Unification of SQL, Graph, Stream, ML
• Common RDD structure
• General DAG execution engine
• lazy evaluation
• distributed in-memory caching
200920082007
2007-2008: Multiple
projects at IBM
Research – Almaden
involving machine
learning on Hadoop.
2010
2009-2010: Through
engagements with
customers, we observe
how data scientists
create ML solutions.
2009: We form a
dedicated team
for scalable ML
2014201320122011
Research
20162015
June 2015: IBM
Announces open-
source SystemML
September 2015:
Code available on
Github
November 2015:
SystemML enters
Apache incubation
June 2016:
Second Apache
release (0.10)
February 2016:
First release (0.9) of
Apache SystemML
SystemML at
Moved from Hadoop MapReduce to Spark
SystemML supports both frameworks
Exact same code
300X faster on 1/40th as many nodes
R or
Python
Data
Scientist
Results
Systems
Programmer
Scala
Products
Customers
i
j
Customer i
bought
product j.
Alternating Least Squares
Products
Customers
i
j
Customer i
bought
product j.
Alternating Least Squares
Products
Customers
i
j
Customer i
bought
product j.
Alternating Least Squares
Products
Customers
i
j
Customer i
bought
product j.
Products Factor
CustomersFactor
Products
Customers
i
j
Customer i
bought
product j.
Products Factor
CustomersFactor
Products
Customers
i
j
Customer i
bought
product j.
Products Factor
CustomersFactor
Products
Customers
i
j
Customer i
bought
product j.
Products Factor
CustomersFactor
Multiply these
two factors to
produce a less-
sparse matrix.
×
Products
Customers
i
j
Customer i
bought
product j.
Products Factor
CustomersFactor
Multiply these
two factors to
produce a less-
sparse matrix.
×
New nonzero
values become
product
suggestions.
Apache SystemML - Declarative Large-Scale Machine Learning
U"="rand(nrow(X),"r,"min"="01.0,"max"="1.0);""
V"="rand(r,"ncol(X),"min"="01.0,"max"="1.0);""
while(i"<"mi)"{"
"""i"="i"+"1;"ii"="1;"
"""if"(is_U)"
""""""G"="(W"*"(U"%*%"V"0"X))"%*%"t(V)"+"lambda"*"U;"
"""else"
""""""G"="t(U)"%*%"(W"*"(U"%*%"V"0"X))"+"lambda"*"V;"
"""norm_G2"="sum(G"^"2);"norm_R2"="norm_G2;"""""
"""R"="0G;"S"="R;"
"""while(norm_R2">"10E09"*"norm_G2"&"ii"<="mii)"{"
"""""if"(is_U)"{"
"""""""HS"="(W"*"(S"%*%"V))"%*%"t(V)"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""U"="U"+"alpha"*"S;"""
"""""}"else"{"
"""""""HS"="t(U)"%*%"(W"*"(U"%*%"S))"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""V"="V"+"alpha"*"S;"""
"""""}"
"""""R"="R"0"alpha"*"HS;"
"""""old_norm_R2"="norm_R2;"norm_R2"="sum(R"^"2);"
"""""S"="R"+"(norm_R2"/"old_norm_R2)"*"S;"
"""""ii"="ii"+"1;"
"""}"""
"""is_U"="!"is_U;"
}"
U"="rand(nrow(X),"r,"min"="01.0,"max"="1.0);""
V"="rand(r,"ncol(X),"min"="01.0,"max"="1.0);""
while(i"<"mi)"{"
"""i"="i"+"1;"ii"="1;"
"""if"(is_U)"
""""""G"="(W"*"(U"%*%"V"0"X))"%*%"t(V)"+"lambda"*"U;"
"""else"
""""""G"="t(U)"%*%"(W"*"(U"%*%"V"0"X))"+"lambda"*"V;"
"""norm_G2"="sum(G"^"2);"norm_R2"="norm_G2;"""""
"""R"="0G;"S"="R;"
"""while(norm_R2">"10E09"*"norm_G2"&"ii"<="mii)"{"
"""""if"(is_U)"{"
"""""""HS"="(W"*"(S"%*%"V))"%*%"t(V)"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""U"="U"+"alpha"*"S;"""
"""""}"else"{"
"""""""HS"="t(U)"%*%"(W"*"(U"%*%"S))"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""V"="V"+"alpha"*"S;"""
"""""}"
"""""R"="R"0"alpha"*"HS;"
"""""old_norm_R2"="norm_R2;"norm_R2"="sum(R"^"2);"
"""""S"="R"+"(norm_R2"/"old_norm_R2)"*"S;"
"""""ii"="ii"+"1;"
"""}"""
"""is_U"="!"is_U;"
}"
U"="rand(nrow(X),"r,"min"="01.0,"max"="1.0);""
V"="rand(r,"ncol(X),"min"="01.0,"max"="1.0);""
while(i"<"mi)"{"
"""i"="i"+"1;"ii"="1;"
"""if"(is_U)"
""""""G"="(W"*"(U"%*%"V"0"X))"%*%"t(V)"+"lambda"*"U;"
"""else"
""""""G"="t(U)"%*%"(W"*"(U"%*%"V"0"X))"+"lambda"*"V;"
"""norm_G2"="sum(G"^"2);"norm_R2"="norm_G2;"""""
"""R"="0G;"S"="R;"
"""while(norm_R2">"10E09"*"norm_G2"&"ii"<="mii)"{"
"""""if"(is_U)"{"
"""""""HS"="(W"*"(S"%*%"V))"%*%"t(V)"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""U"="U"+"alpha"*"S;"""
"""""}"else"{"
"""""""HS"="t(U)"%*%"(W"*"(U"%*%"S))"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""V"="V"+"alpha"*"S;"""
"""""}"
"""""R"="R"0"alpha"*"HS;"
"""""old_norm_R2"="norm_R2;"norm_R2"="sum(R"^"2);"
"""""S"="R"+"(norm_R2"/"old_norm_R2)"*"S;"
"""""ii"="ii"+"1;"
"""}"""
"""is_U"="!"is_U;"
}"
U"="rand(nrow(X),"r,"min"="01.0,"max"="1.0);""
V"="rand(r,"ncol(X),"min"="01.0,"max"="1.0);""
while(i"<"mi)"{"
"""i"="i"+"1;"ii"="1;"
"""if"(is_U)"
""""""G"="(W"*"(U"%*%"V"0"X))"%*%"t(V)"+"lambda"*"U;"
"""else"
""""""G"="t(U)"%*%"(W"*"(U"%*%"V"0"X))"+"lambda"*"V;"
"""norm_G2"="sum(G"^"2);"norm_R2"="norm_G2;"""""
"""R"="0G;"S"="R;"
"""while(norm_R2">"10E09"*"norm_G2"&"ii"<="mii)"{"
"""""if"(is_U)"{"
"""""""HS"="(W"*"(S"%*%"V))"%*%"t(V)"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""U"="U"+"alpha"*"S;"""
"""""}"else"{"
"""""""HS"="t(U)"%*%"(W"*"(U"%*%"S))"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""V"="V"+"alpha"*"S;"""
"""""}"
"""""R"="R"0"alpha"*"HS;"
"""""old_norm_R2"="norm_R2;"norm_R2"="sum(R"^"2);"
"""""S"="R"+"(norm_R2"/"old_norm_R2)"*"S;"
"""""ii"="ii"+"1;"
"""}"""
"""is_U"="!"is_U;"
}"
U"="rand(nrow(X),"r,"min"="01.0,"max"="1.0);""
V"="rand(r,"ncol(X),"min"="01.0,"max"="1.0);""
while(i"<"mi)"{"
"""i"="i"+"1;"ii"="1;"
"""if"(is_U)"
""""""G"="(W"*"(U"%*%"V"0"X))"%*%"t(V)"+"lambda"*"U;"
"""else"
""""""G"="t(U)"%*%"(W"*"(U"%*%"V"0"X))"+"lambda"*"V;"
"""norm_G2"="sum(G"^"2);"norm_R2"="norm_G2;"""""
"""R"="0G;"S"="R;"
"""while(norm_R2">"10E09"*"norm_G2"&"ii"<="mii)"{"
"""""if"(is_U)"{"
"""""""HS"="(W"*"(S"%*%"V))"%*%"t(V)"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""U"="U"+"alpha"*"S;"""
"""""}"else"{"
"""""""HS"="t(U)"%*%"(W"*"(U"%*%"S))"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""V"="V"+"alpha"*"S;"""
"""""}"
"""""R"="R"0"alpha"*"HS;"
"""""old_norm_R2"="norm_R2;"norm_R2"="sum(R"^"2);"
"""""S"="R"+"(norm_R2"/"old_norm_R2)"*"S;"
"""""ii"="ii"+"1;"
"""}"""
"""is_U"="!"is_U;"
}"
Every line has a clear purpose!
https://github.com/apache/spark/blob/master/
mllib/src/main/scala/org/apache/spark/mllib/
recommendation/ALS.scala
25 lines’ worth of algorithm…
…mixed with 800 lines of performance code
https://github.com/apache/spark/blob/master/
mllib/src/main/scala/org/apache/spark/mllib/
recommendation/ALS.scala
U"="rand(nrow(X),"r,"min"="01.0,"max"="1.0);""
V"="rand(r,"ncol(X),"min"="01.0,"max"="1.0);""
while(i"<"mi)"{"
"""i"="i"+"1;"ii"="1;"
"""if"(is_U)"
""""""G"="(W"*"(U"%*%"V"0"X))"%*%"t(V)"+"lambda"*"U;"
"""else"
""""""G"="t(U)"%*%"(W"*"(U"%*%"V"0"X))"+"lambda"*"V;"
"""norm_G2"="sum(G"^"2);"norm_R2"="norm_G2;"""""
"""R"="0G;"S"="R;"
"""while(norm_R2">"10E09"*"norm_G2"&"ii"<="mii)"{"
"""""if"(is_U)"{"
"""""""HS"="(W"*"(S"%*%"V))"%*%"t(V)"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""U"="U"+"alpha"*"S;"""
"""""}"else"{"
"""""""HS"="t(U)"%*%"(W"*"(U"%*%"S))"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""V"="V"+"alpha"*"S;"""
"""""}"
"""""R"="R"0"alpha"*"HS;"
"""""old_norm_R2"="norm_R2;"norm_R2"="sum(R"^"2);"
"""""S"="R"+"(norm_R2"/"old_norm_R2)"*"S;"
"""""ii"="ii"+"1;"
"""}"""
"""is_U"="!"is_U;"
}"
U"="rand(nrow(X),"r,"min"="01.0,"max"="1.0);""
V"="rand(r,"ncol(X),"min"="01.0,"max"="1.0);""
while(i"<"mi)"{"
"""i"="i"+"1;"ii"="1;"
"""if"(is_U)"
""""""G"="(W"*"(U"%*%"V"0"X))"%*%"t(V)"+"lambda"*"U;"
"""else"
""""""G"="t(U)"%*%"(W"*"(U"%*%"V"0"X))"+"lambda"*"V;"
"""norm_G2"="sum(G"^"2);"norm_R2"="norm_G2;"""""
"""R"="0G;"S"="R;"
"""while(norm_R2">"10E09"*"norm_G2"&"ii"<="mii)"{"
"""""if"(is_U)"{"
"""""""HS"="(W"*"(S"%*%"V))"%*%"t(V)"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""U"="U"+"alpha"*"S;"""
"""""}"else"{"
"""""""HS"="t(U)"%*%"(W"*"(U"%*%"S))"+"lambda"*"S;"
"""""""alpha"="norm_R2"/"sum"(S"*"HS);"
"""""""V"="V"+"alpha"*"S;"""
"""""}"
"""""R"="R"0"alpha"*"HS;"
"""""old_norm_R2"="norm_R2;"norm_R2"="sum(R"^"2);"
"""""S"="R"+"(norm_R2"/"old_norm_R2)"*"S;"
"""""ii"="ii"+"1;"
"""}"""
"""is_U"="!"is_U;"
}"
SystemML:
compile and run at scale
no performance code needed!
0
5000
10000
15000
20000
1.2GB (sparse
binary)
12GB 120GB
RunningTime(sec)
R
MLLib
SystemML
>24h>24h
OOM
OOM
Architecture
SystemML
Optimizer
High-Level
Algorithm
Parallel
Spark
Program
Architecture
High-Level Operations (HOPs)
General representation of statements in the data
analysis language
Low-Level Operations (LOPs)
General representation of operations in the
runtime framework
High-level language front-ends
Multiple execution
environments
Cost
Based
Optimizer
Apache SystemML - Declarative Large-Scale Machine Learning
W
S
U
U × S
*( (
t(U) t(U)×(W*(U×S)))(
×
Large dense
intermediate
Can compute
directly from U,
S, and W!
t(U)(%*%((W(*((U(%*%(S))(
wdivmm
WU S
1.2GB

sparse
800MB

dense
800MB

dense
800MB

dense
(weighted divide matrix multiplication)
%*%
WU S
*t()
%*%
1.2GB

sparse
80GB

dense
80GB

dense
800MB

dense
800MB

dense
800MB

dense
800MB

dense
All operands
fit into heap
! use one
node
WDivMM
(MapWDivMM)
Apache SystemML - Declarative Large-Scale Machine Learning
Browse the
source!
Browse the
source!
Try out
some
tutorials!
Browse the
source!
Try out
some
tutorials!
Contribute to
the project!
Browse the
source!
Try out
some
tutorials!
Contribute to
the project!Download the
binary release!
Demo

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