SGD on Hadoop for Big dATA & Huge Models

SGD ON HADOOPFOR BIG DATA & HUGE MODELSAlex Beutel

Based on work done with Abhimanu Kumar, Vagelis Papalexakis, Partha Talukdar, Qirong Ho, Christos Faloutsos, and Eric Xing

Outline

1. When to use SGD for distributed learning

2. Optimization• Review of DSGD• SGD for Tensors• SGD for ML models – topic modeling, dictionary learning, MMSB

3. Hadoop1. General algorithm

2. Setting up the MapReduce body

3. Reducer communication

4. Distributed normalization

5. “Always-On SGD” – How to deal with the straggler problem

4. Experiments

When distributed SGD is useful

Collaborative FilteringPredict movie preferences

Topic ModelingWhat are the topics of webpages,

tweets, or status updatesDictionary Learning

Remove noise or missing pixels from images

Tensor DecompositionFind communities in temporal graphs

300 Million Photos uploaded to Facebook per day!

1 Billion users on Facebook

400 million tweets per day

Gradient Descent

Stochastic Gradient Descent (SGD)

Stochastic Gradient Descent (SGD)

DSGD for Matrices (Gemulla, 2011)

XU

V

≈Users

Movies

Genres


XU

V

≈Independent!


Independent Blocks


Partition your data & model into d × d blocks

Results in d=3 strata

Process strata sequentially, process blocks in each stratum in parallel

TENSORS

What is a tensor?• Tensors are used for structured data > 2 dimensions• Think of as a 3D-matrix

Subject

Verb

Object

For example:

Derek Jeter plays baseball

Tensor Decomposition

≈U

V

W

X


≈U

V

W

X


≈U

V

W

X

Independent

Not Independent


For d=3 blocks per stratum, we require d2=9 strata

Coupled Matrix + Tensor Decomposition

XY

Subject

Verb

Object

Document


≈U

V

W

XY

A


CONSTRAINTS & PROJECTIONS

Example: Topic Modeling

Documents

Words

Topics

Constraints

• Sometimes we want to restrict response:• Non-negative

• Sparsity

• Simplex (so vectors become probabilities)

• Keep inside unit ball

How to enforce? Projections• Example: Non-negative

More projections• Sparsity (soft thresholding):

• Simplex

• Unit ball

Dictionary Learning• Learn a dictionary of concepts and a sparse

reconstruction• Useful for fixing noise and missing pixels of images

Sparse encoding

Within unit ball

Mixed Membership Network Decomp.

• Used for modeling communities in graphs (e.g. a social network)

Simplex

Non-negative

IMPLEMENTING ON HADOOP

High level algorithm

for Epoch e = 1 … T do

for Subepoch s = 1 … d2 do

Let be the set of blocks in stratum s

for block b = 1 … d in parallel do

Run SGD on all points in block

end

end

end

Stratum 1 Stratum 2 Stratum 3 …

Bad Hadoop Algorithm: Subepoch 1

Run SGD on Update:

Run SGD on Update:

Run SGD on Update:

ReducersMappers

U2 V1 W3

U3 V2 W1

U1 V3 W2

Bad Hadoop Algorithm: Subepoch 2

Run SGD on Update:

Run SGD on Update:

Run SGD on Update:

ReducersMappers

U2 V1 W2

U3 V2 W3

U1 V3 W1

Hadoop Challenges• MapReduce is typically very bad for iterative algorithms

• T × d2 iterations

• Sizable overhead per Hadoop job• Little flexibility

High Level Algorithm

V1

V2

V3

U1 U

2 U3

W 1

W 2

W 3

V1

V2

V3

U1 U

2 U3

W 1

W 2

W 3

U1 V1 W1 U2 V2 W2 U3 V3 W3


V1

V2

V3

U1 U

2 U3

W 1

W 2

W 3

V1

V2

V3

U1 U

2 U3

W 1

W 2

W 3

U1 V1 W1 U2 V2 W2 U3 V3 W3


V1

V2

V3

U1 U

2 U3

W 1

W 2

W 3

V1

V2

V3

U1 U

2 U3

W 1

W 2

W 3

U1 V1 W3 U2 V2 W1 U3 V3 W2


V1

V2

V3

U1 U

2 U3

W 1

W 2

W 3

V1

V2

V3

U1 U

2 U3

W 1

W 2

W 3

U1 V1 W2 U2 V2 W3 U3 V3 W1

Hadoop Algorithm

Process points:

Map each point

to its block

with necessary info to order

Reducers

Mappers

Partition &

Sort

Use:PartitionerKeyComparatorGroupingComparator

Hadoop Algorithm

Process points:

Map each point

to its block


Reducers

Mappers

Partition &

Sort

…

…

Hadoop Algorithm

Process points:

Map each point

to its block


U1 V1 W1

Run SGD on Update:

U2 V2 W2

Run SGD on Update:

U3 V3 W3

Run SGD on Update:

Reducers

Mappers

…

…

Partition &

Sort

Hadoop Algorithm

Process points:

Map each point

to its block


U1 V1 W1

Run SGD on Update:

U2 V2 W2

Run SGD on Update:

U3 V3 W3

Run SGD on Update:

Reducers

Mappers

Partition &

Sort

…

…

Hadoop Algorithm

Process points:

Map each point

to its block


U1 V1

Run SGD on Update:

U2 V2

Run SGD on Update:

U3 V3

Run SGD on Update:

Reducers

Mappers

Partition &

Sort

…

…

HDFS

HDFS

W2

W1

W3

Hadoop Summary

1. Use mappers to send data points to the correct reducers in order

2. Use reducers as machines in a normal cluster

3. Use HDFS as the communication channel between reducers

Distributed Normalization

Documents

Words

Topics

π1 β1

π2 β2

π3 β3

Distributed Normalization

π1 β1

π2 β2π3 β3

σ(1)

σ(2)

σ(3)

σ(b) is a k-dimensional vector, summing the terms of βb

σ(1)

σ(1)

σ(3)

σ(3)

σ(2) σ(2)

Transfer σ(b) to all machinesEach machine calculates σ:

Normalize:

Barriers & Stragglers

Process points:

Map each point

to its block


Run SGD on

Run SGD on

Run SGD on

Reducers

Mappers

Partition &

Sort

…

…U1 V1

Update:

U2 V2

Update:

U3 V3

Update:

HDFS

HDFS

W2

W1

W3

Wasting time waiting!

Solution: “Always-On SGD”For each reducer:

Run SGD on all points in current block Z

Shuffle points in Z and decrease step size Check if other reducers

are ready to syncRun SGD on points in Z

againIf not ready to sync

Wait

If not ready to sync

Sync parameters and get new block Z

“Always-On SGD”

Process points:

Map each point

to its block


Run SGD on

Run SGD on

Run SGD on

Reducers

Partition &

Sort

…

…U1 V1

Update:

U2 V2

Update:

U3 V3

Update:

HDFS

HDFS

W2

W1

W3

Run SGD on old points again!

“Always-On SGD”

First SGD pass of block Z

Extra SGD Updates

Read Parameters from HDFS

Write Parameters to HDFS

Reducer 1

Reducer2

Reducer 3

Reducer 4

EXPERIMENTS

FlexiFaCT (Tensor Decomposition)Convergence

FlexiFaCT (Tensor Decomposition)Scalability in Data Size

FlexiFaCT (Tensor Decomposition)Scalability in Tensor Dimension

Handles up to 2 billion parameters!

FlexiFaCT (Tensor Decomposition)Scalability in Rank of Decomposition

Handles up to 4 billion parameters!

FlexiFaCT (Tensor Decomposition)Scalability in Number of Machines

Fugue (Using “Always-On SGD”)Dictionary Learning: Convergence

Fugue (Using “Always-On SGD”)Community Detection: Convergence

Fugue (Using “Always-On SGD”)Topic Modeling: Convergence

Fugue (Using “Always-On SGD”)Topic Modeling: Scalability in Data Size

Fugue (Using “Always-On SGD”)Topic Modeling: Scalability in Rank

Fugue (Using “Always-On SGD”)Topic Modeling: Scalability over Machines

Fugue (Using “Always-On SGD”)Topic Modeling: Number of Machines

Fugue (Using “Always-On SGD”)

Key Points• Flexible method for tensors & ML models• Can use stock Hadoop through using HDFS for

communication• When waiting for slower machines, run updates on old

data again

Questions?

Alex [email protected]://alexbeutel.com