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Dynamic Graph
Embedding on
Event Streams
Massimo Perini
Advisors: P. Carbone, V. Kalavri, G.Ramponi
Machine learning on graphs
⬡ Incorporate graph structure information
into a machine learning model
⬡ Capture the graph topology and other
graph relevant graph information
2
GraphSAGE
⬡ Each node embedding is represented by
the aggregation of its features and
those of its neighborhood.
⬡ Learns how to aggregate features from
a node neighborhood.
3
Graph representation - GraphSAGE
4
5
GraphSAGE
D Aggregate
A
B
C
E
F
G
Aggregate
Aggregate
D Aggregate
A
B
A
C
E
Aggregate
B
F
G
Aggregate D Aggregate
A
B
Layer 1 Layer 2
h0
-> h1
h1
-> h2
Problems
⬡ Inductive neural networks are trained
using static graphs
⬡ Available systems perform inference
using a batch approach
⬡ We will focus on a supervised vertex
classification task
6
7
Pipeline
Labelled graph stream
Unlabelled graph
stream
Train
model
Inference
embeddings
8
Train
Labelled
graph stream
Unlabelled
graph stream
Train
model
Inference
embeddings
Dynamic dataset
⬡ Typical training from static datasets:
random sampling
⬡ Dynamic dataset: trains more old
samples
⬡ Idea: learn more from some samples
than from others
9
Dynamic dataset
⬡ We can measure how unexpected is a
vertex
∙ How much the model can’t predict it
⬡ Vertices are selected using this value
⬡ New vertices get maximum priority
10
Sampling probabilities and vertex classes
11
12
Inference
Labelled
graph stream
Unlabelled
graph stream
Train
model
Inference
embeddings
Duplicate computations
13
A
B
E
G
D
D
B
E
A
G
G
D
B
E
A
G
G
D
G
Graph updates
⬡ Recomputes only the sections of the
dependency trees affected by changes.
⬡ The recomputed dependency hierarchy
contains the newly added, changed or
removed node.
14
Graph updates
15
A
B
E
G
D
A
B
E
G
D
A
B
E
G
D
h1
h1 h2
h2
h2
h2
Let’s scale!
Problems with batch approaches
⬡ The straggler task determines the runtime
⬡ New mutations are not processed while
computation is ongoing
⬡ No low-latency real-time processing
17
Asynchronous distributed
version
⬡ Each vertex stores the vectors of the
neighboring vertices up to the
maximum depth
⬡ Node communicates the computed
features to neighbors.
⬡ Neighbors replace the vectors and
perform the aggregation again
18
State
⬡ Stores in the managed per-vertex keyed
state:
∙ Vertex adjacency list (used to send
messages to adjacent vertices)
∙ Vertex and neighbours vectors
∙ Neural networks layers (trained
parameters)
19
Message passing - addition
20
E
D
A
F
E
C
B
A CB
EDF
D
F
E
A CB
EDF
D
A
A
C
E
A
A
D
h0
h1
h0
h1
h1
A CB
EDF
h1
h1
B A
C
B
E
h1
Iterations
⬡ Asynchronous iteration allows
message-passing between different
vertices of a keyed stream
21
A CB
EDF
E A D
hE
1
hE
0
hE
1
hE
0
hE
1hE
1
Keyed state
Window Operator
Windowing policy
⬡ A neural network layer is a matrix: each
vertex needs to run matrix multiplications
⬡ Bottleneck if a vertex receives too many
messages in a short amount of time
⬡ We use per-vertex session windows with
a maximum window length
22
Neural network execution
⬡ Neural networks require fast linear
algebra operations
⬡ Implemented using Breeze:
∙ Uses a wrapper for low-level BLAS
∙ Used in Flink ML and Spark MLLib too
23
Execution plan
24
Graph
Source
Flat Map
Forward
Window
Hash
Filter Filter
ForwardForward
Iteration
Sink
Iteration
Source
Hash
Map
Data sink
Forward
Forward
Stream of edges
A key represents a vertex
of the graph
Opposite filter conditions:
the operator filters new
vertex embeddings and
neighbours messages
Vertex prediction
Message passing
between vertices
Forward
Preprocessing
Dynamic model
⬡ Once a new model is deployed, the
system needs to run again the inference
on the graph
⬡ Can be implemented without an explicit
barrier
25
Dynamic model
26
A CB
EDF
A CB
EDF
A CB
EDF
h1
New
model
The new model is
broadcasted
(broadcasted
state paradigm)
Once each vertex
receives the
model, emits the
new vector at
“depth 0”
Once a vertex receives the
“depth 0” vectors from the
neighbours, it aggregates
them. It then sends the
“depth 1” result to
neighbours
h0
Execution plan
27
Graph
Source
Flat Map
Forward
Window
Hash
Filter Filter
ForwardForward
Iteration
Sink
Iteration
Source
Hash
Map
Data sink
Forward
Forward
Forward
Model
Source
Forward
Map
Co-process-Broadcast-Keyed
BroadcastHash
Computes graph
updates
Defines per-vertex
windows of incoming
messages
Message passing
between vertices
Solving Iteration Deadlocks
28
Flat Map
Forward
Window
Hash
Filter Filter
ForwardForward
Iteration
Sink
Iteration
Source
Hash
Map
Data sink
Forward
Forward
Forward
Model
Source
Forward
Map
Co-process-Broadcast-Keyed
BroadcastHash
Window
⬡ Problem:
∙ Backpressure on
feedback-edge
∙ All channels in loop block
indefinitely
⬡ Solution:
∙ New
PrioritizedUnionInputGate*
∙ Max priority on feedback
input
∙ Min priority on regular input
∙ *http://tiny.cc/fu1xdz (hotfix by senorcarbone for Flink 1.7)
Experiments
Datasets
⬡ Pubmed Diabetes (dynamic vertex
addition, publication network)
⬡ Reddit (dynamic edge addition, social
network)
30
citation
paper
Same user
comment on
both posts
post
topics
Communities
(“subreddits”)
Baselines
⬡ Offline: Train over the full graph with
multiple epochs every 10 steps
⬡ No-Rehearsal: Train over the new
vertices only.
⬡ Random: Train over a uniform random
sample selected on the full graph
31
F1 Macro - Reddit 32
F1 Macro - Pubmed
F1 score
Training time
33
Scalability - Throughput
34
Pubmed dataset Reddit dataset
Delay - Pubmed
35
Delay - Reddit
36
Thank you

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