A New Parallel Framework for Machine Learning

Carnegie Mellon

Joseph GonzalezJoint work with

YuchengLow

AapoKyrola

DannyBickson

CarlosGuestrin

GuyBlelloch

JoeHellerstein

DavidO’Hallaron

A New Parallel Framework for Machine Learning

AlexSmola

In ML we face BIG problems

48 Hours a MinuteYouTube

24 Million Wikipedia Pages

750 MillionFacebook Users

6 Billion Flickr Photos

Massive data provides opportunities for rich probabilistic structure …

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Shopper 1 Shopper 2

Cameras Cooking

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Social Network

What are the tools for massive data?

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Parallelism: Hope & ChallengesWide array of different parallel architectures:

New Challenges for Designing Machine Learning Algorithms: Race conditions and deadlocksManaging distributed model state

New Challenges for Implementing Machine Learning Algorithms:Parallel debugging and profilingHardware specific APIs

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GPUs Multicore Clusters Mini Clouds Clouds

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Massive Structured Problems

Advances Parallel Hardware?Thesis:

“Parallel Learning and Inference in Probabilistic Graphical Models”

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Advances Parallel Hardware

“Parallel Learning and Inference in Probabilistic Graphical Models”

GraphLab

Parallel Algorithms forProbabilistic Learning and Inference

Probabilistic Graphical Models

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GraphLab


Advances Parallel Hardware



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Advances Parallel HardwareGraphLab



How will wedesign and implement

parallel learning systems?

Threads, Locks, & Messages

“low level parallel primitives”

We could use ….

Threads, Locks, and MessagesML experts repeatedly solve the same parallel design challenges:

Implement and debug complex parallel systemTune for a specific parallel platformTwo months later the conference paper contains:

“We implemented ______ in parallel.”The resulting code:

is difficult to maintainis difficult to extendcouples learning model to parallel implementation

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Graduate students

Map-Reduce / HadoopBuild learning algorithms on-top of

high-level parallel abstractions

... a better answer:

CPU 1 CPU 2 CPU 3 CPU 4

MapReduce – Map Phase

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Embarrassingly Parallel independent computation

12.9

42.3

21.3

25.8

No Communication needed



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12.9

42.3

21.3

25.8

24.1

84.3

18.4

84.4

Image Features



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Embarrassingly Parallel independent computation

12.9

42.3

21.3

25.8

17.5

67.5

14.9

34.3

24.1

84.3

18.4

84.4

No Communication needed

CPU 1 CPU 2

MapReduce – Reduce Phase

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12.9

42.3

21.3

25.8

24.1

84.3

18.4

84.4

17.5

67.5

14.9

34.3

2226.

26

1726.

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Image Features

Attractive Face Statistics

Not Attractive FaceStatistics

N A A N N N A A N A N A

Attractive FacesNot AttractiveFaces

BeliefPropagation

Label Propagation

KernelMethods

Deep BeliefNetworks

NeuralNetworks

Tensor Factorization

PageRank

Lasso

Map-Reduce for Data-Parallel MLExcellent for large data-parallel tasks!

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Data-Parallel Graph-Parallel

CrossValidation

Feature Extraction

Map Reduce

Computing SufficientStatistics

Is there more toMachine Learning

?

Concrete ExampleLabel Propagation

Profile

Label Propagation AlgorithmSocial Arithmetic:

Recurrence Algorithm:

iterate until convergence

Parallelism:Compute all Likes[i] in parallel

Sue Ann

Carlos

Me

50% What I list on my profile40% Sue Ann Likes10% Carlos Like

40%

10%

50%

80% Cameras20% Biking



I Like:

+60% Cameras, 40% Biking

Properties of Graph Parallel Algorithms

DependencyGraph

IterativeComputation

What I Like

What My Friends Like

Factored Computation

?

BeliefPropagation

Label Propagation

KernelMethods

Deep BeliefNetworks

NeuralNetworks


PageRank

Lasso


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CrossValidation

Feature Extraction

Map Reduce


Map Reduce?

Why not use Map-Reducefor

Graph Parallel Algorithms?

Data DependenciesMap-Reduce does not efficiently express dependent data

User must code substantial data transformations Costly data replication

Inde

pend

ent D

ata

Row

s

Slow

Proc

esso

rIterative Algorithms

Map-Reduce not efficiently express iterative algorithms:

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

CPU 1

CPU 2

CPU 3

Data

Data

Data

Data

Data

Data

Data

CPU 1

CPU 2

CPU 3

Data

Data

Data

Data

Data

Data

Data

CPU 1

CPU 2

CPU 3

Iterations

Barr

ier

Barr

ier

Barr

ier

MapAbuse: Iterative MapReduceOnly a subset of data needs computation:

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

CPU 1

CPU 2

CPU 3

Data

Data

Data

Data

Data

Data

Data

CPU 1

CPU 2

CPU 3

Data

Data

Data

Data

Data

Data

Data

CPU 1

CPU 2

CPU 3

Iterations

Barr

ier

Barr

ier

Barr

ier

MapAbuse: Iterative MapReduceSystem is not optimized for iteration:

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

Data

CPU 1

CPU 2

CPU 3

Data

Data

Data

Data

Data

Data

Data

CPU 1

CPU 2

CPU 3

Data

Data

Data

Data

Data

Data

Data

CPU 1

CPU 2

CPU 3

Iterations

Disk Penalty

Disk Penalty

Disk Penalty

Startup Penalty

Startup Penalty

Startup Penalty

BeliefPropagation

SVM

KernelMethods

Deep BeliefNetworks

NeuralNetworks


PageRank

Lasso


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CrossValidation

Feature Extraction

Map Reduce


Map Reduce?Pregel (Giraph)?

BarrierPregel (Giraph)

Bulk Synchronous Parallel Model:

Compute Communicate

Bulk synchronous computation can be highly inefficient.

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Example: Loopy Belief Propagation

Problem

Loopy Belief Propagation (Loopy BP)

• Iteratively estimate the “beliefs” about vertices– Read in messages– Updates marginal

estimate (belief)– Send updated

out messages• Repeat for all variables

until convergence

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Bulk Synchronous Loopy BP

• Often considered embarrassingly parallel – Associate processor

with each vertex– Receive all messages– Update all beliefs– Send all messages

• Proposed by:– Brunton et al. CRV’06– Mendiburu et al. GECC’07– Kang,et al. LDMTA’10– …

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Sequential Computational Structure

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Hidden Sequential Structure

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Hidden Sequential Structure

• Running Time:

EvidenceEvidence

Time for a singleparallel iteration Number of Iterations

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Optimal Sequential Algorithm

Forward-Backward

Bulk Synchronous2n2/p

p ≤ 2n

RunningTime

2n

Gap

p = 1Optimal Parallel

np = 2 38

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The Splash Operation• Generalize the optimal chain algorithm:

to arbitrary cyclic graphs:

~

1) Grow a BFS Spanning tree with fixed size

2) Forward Pass computing all messages at each vertex

3) Backward Pass computing all messages at each vertex

Data-Parallel Algorithms can be Inefficient

The limitations of the Map-Reduce abstraction can lead to inefficient parallel algorithms.

1 2 3 4 5 6 7 80

100020003000400050006000700080009000

Number of CPUs

Runti

me

in S

econ

ds

Optimized in Memory Bulk Synchronous

Asynchronous Splash BP

BeliefPropagationSVM

KernelMethods

Deep BeliefNetworks

NeuralNetworks


PageRank

Lasso

The Need for a New AbstractionMap-Reduce is not well suited for Graph-Parallelism

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CrossValidation

Feature Extraction

Map Reduce


Pregel (Giraph)

What is GraphLab?

The GraphLab Framework

Scheduler Consistency Model

Graph BasedData Representation

Update FunctionsUser Computation

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Data Graph

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A graph with arbitrary data (C++ Objects) associated with each vertex and edge.

Vertex Data:• User profile text• Current interests estimates

Edge Data:• Similarity weights

Graph:• Social Network

Implementing the Data GraphMulticore Setting

In MemoryChallenge:

Fast lookup, low overhead

Solution:Dense data-structuresFixed Vdata & Edata typesImmutable graph structure

Cluster Setting

In MemoryPartition Graph:

ParMETIS or Random Cuts

Cached Ghosting

Node 1 Node 2

A BC D

A BC D

A B

C D





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label_prop(i, scope){ // Get Neighborhood data (Likes[i], Wij, Likes[j]) scope;

// Update the vertex data

// Reschedule Neighbors if needed if Likes[i] changes then reschedule_neighbors_of(i); }

Update Functions

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An update function is a user defined program which when applied to a vertex transforms the data in the scope of the vertex





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The Scheduler

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CPU 1

CPU 2

The scheduler determines the order that vertices are updated.

e f g

kjih

dcba b

ih

a

i

b e f

j

c

Sche

dule

r

The process repeats until the scheduler is empty.

Choosing a Schedule

GraphLab provides several different schedulersRound Robin: vertices are updated in a fixed orderFIFO: Vertices are updated in the order they are addedPriority: Vertices are updated in priority order

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The choice of schedule affects the correctness and parallel performance of the algorithm

Obtain different algorithms by simply changing a flag! --scheduler=roundrobin --scheduler=fifo --scheduler=priority





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Ensuring Race-Free CodeHow much can computation overlap?

CPU 1 CPU 2

Common Problem: Write-Write Race

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Processors running adjacent update functions simultaneously modify shared data:

CPU1 writes: CPU2 writes:

Final Value

Importance of Consistency

Alternating Least Squares

Importance of Consistency

Build

Test

Debug

Tweak Model

GraphLab Ensures Sequential Consistency

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For each parallel execution, there exists a sequential execution of update functions which produces the same result.

CPU 1

CPU 2

SingleCPU

Parallel

Sequential

time

Consistency Rules

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Guaranteed sequential consistency for all update functions

Data

Full Consistency

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Obtaining More Parallelism

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Edge Consistency

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CPU 1 CPU 2

Safe

Read

Consistency Through R/W LocksRead/Write locks:

Full Consistency

Edge Consistency

Write Write WriteCanonical Lock Ordering

Read Write ReadRead Write

Multicore Setting: Pthread R/W LocksDistributed Setting: Distributed Locking

Prefetch Locks and Data

Allow computation to proceed while locks/data are requested.

Node 2

Consistency Through R/W Locks

Node 1Data GraphPartition

Lock Pipeline





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Anatomy of a GraphLab Program:

1) #include <graphlab.hpp>2) Define C++ Update Function3) Build data graph using the C++ graph object4) Set engine parameters:

1) Scheduler type 2) Consistency model

5) Add initial vertices to the scheduler 6) Run the engine on the graph [Blocking call]7) Final answer is stored in the graph

Algorithms Implemented PageRankLoopy Belief PropagationGibbs SamplingCoEMGraphical Model Parameter LearningProbabilistic Matrix/Tensor FactorizationAlternating Least SquaresLasso with Sparse FeaturesSupport Vector Machines with Sparse FeaturesLabel-Propagation…

Shared MemoryExperiments

Shared Memory Setting16 Core Workstation

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Loopy Belief Propagation

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3D retinal image denoising

Data GraphUpdate Function:

Loopy BP Update EquationScheduler:

SplashBPConsistency Model:

Edge Consistency

Vertices: 1 MillionEdges: 3 Million

Loopy Belief Propagation

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0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

Number of CPUs

Spee

dup

Optimal

Bette

r

SplashBP

15.5x speedup

Gibbs SamplingProtein-protein interaction networks [Elidan et al. 2006]

Provably correct ParallelizationEdge Consistency

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Discrete MRF14K Vertices100K Edges

Backbone

Protein

Interactions

Side-Chain

Gibbs Sampling

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0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

Number of CPUs

Spee

dup

OptimalBe

tter

Chromatic Gibbs Sampler

Carnegie Mellon

An asynchronous Gibbs Sampler that adaptively addresses strong dependencies.

Splash Gibbs Sampler

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Step 1: Grow multiple Splashes in parallel:

ConditionallyIndependent

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Tree-width = 1

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Tree-width = 2

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Step 2: Calibrate the trees in parallel

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Step 3: Sample trees in parallel

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Experimental Results

The Splash sampler outperforms the Chromatic sampler on models with strong dependencies

Likelihood Final Sample

Bette

r

Splash

Chromatic

“Mixing”

BetterSplash

Chromatic

Speedup in Sample Generation

Bette

r

Splash

Chromatic

• Markov logic network with strong dependencies10K Variables 28K Factors

CoEM (Rosie Jones, 2005)Named Entity Recognition Task

the dog

Australia

Catalina Island

<X> ran quickly

travelled to <X>

<X> is pleasant

Hadoop 95 Cores 7.5 hrs

Is “Dog” an animal?Is “Catalina” a place?

Vertices: 2 MillionEdges: 200 Million

0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

Number of CPUs

Spee

dup

Bette

r

Optimal

GraphLab CoEM

CoEM (Rosie Jones, 2005)

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GraphLab 16 Cores 30 min

15x Faster!6x fewer CPUs!

Hadoop 95 Cores 7.5 hrs

Lasso: Regularized Linear Model

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Data matrix,n x d

weights d x 1 Observationsn x 1

5 Features

4 Examples

Shooting Algorithm [Coordinate Descent]• Updates on weight vertices modify

losses on observation vertices.

Requires theFull Consistency ModelFinancial prediction dataset

from Kogan et al [2009].

Regularization

Full Consistency

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Optimal

0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

Number of CPUs

Spee

dup

Bette

r

Dense

Sparse

0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

Number of CPUs

Spee

dup

Relaxing Consistency

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Why does this work? (See Shotgut ICML Paper)

0 2 4 6 8 10 12 14 160

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4

6

8

10

12

14

16

Number of CPUs

Spee

dup

Bette

r Optimal

Dense

Sparse

ExperimentsAmazon EC2

High-Performance Nodes

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Video Cosegmentation

Segments mean the same

Model: 10.5 million nodes, 31 million edges

Gaussian EM clustering + BP on 3D grid

Video Coseg. Speedups

Matrix FactorizationNetflix Collaborative Filtering

Alternating Least Squares Matrix FactorizationModel: 0.5 million nodes, 99 million edges

Netflix

Users

Movies

d

NetflixSpeedup Increasing size of the matrix factorization

The Cost of Hadoop

SummaryAn abstraction tailored to Machine Learning

Targets Graph-Parallel Algorithms

Naturally expressesData/computational dependenciesDynamic iterative computation

Simplifies parallel algorithm designAutomatically ensures data consistencyAchieves state-of-the-art parallel performance on a variety of problems

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Carnegie Mellon

Checkout GraphLab

http://graphlab.org

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Documentation… Code… Tutorials…

Questions & Feedback

[email protected]

Current/Future Work Out-of-core StorageHadoop/HDFS Integration

Graph ConstructionGraph StorageLaunching GraphLab from HadoopFault Tolerance through HDFS Checkpoints

Sub-scope parallelismAddress the challenge of very high degree nodes

Improved graph partitioningSupport for dynamic graph structure

Documents

A New Parallel Framework for Machine Learning