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Echo State Hoeffding Tree Learning
Diego Marr´on (dmarron@ac.upc.edu)
Jesse Read (jesse.read@telecom-paristech.fr)
Albert Bifet (albert.bifet@telecom-paristech.fr)
Talel Abdessalem (talel.abdessalem@telecom-paristech.fr)
Eduard Ayguad´e (eduard.ayguade@bsc.es)
Jos´e R. Herrero (josepr@ac.upc.edu)
ACML 2016
Hamilton, New Zeland

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Introduction ESHT Evaluations Conclusions
Introduction
• Real-time classification of Big Data streams is becoming
essential in a variety of application domains.
• Real-time classification imposes some challenges:
• Deal with potentially infinite streams
• Strong temporal dependences
• React to changes on the stream
• Response time and memory are bounded
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Introduction ESHT Evaluations Conclusions
Real Time Classification
• In real-time classification:
• Hoeffding Tree (HT) is the streaming state-of-the art decision
tree
• HTs are powerful and easy–to–deploy (no hyper-parameter to
tune)
• But, they are unable to capture strong temporal dependences
• Recurrent Neural Networks (RNN) are very popular nowadays
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Introduction ESHT Evaluations Conclusions
Recurrent Neural Networks
• Recurrent Neural Networks (RNNs) are the state-of-the-art in
handwriting recognition, speech recognition, natural language
processing among others
• They are able to capture time dependences
• But their use for data streams is not straight forward
• Very sensitive to hyper-parameters configuration
• Training requires many iterations over data...
• ...and large amount of time
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Introduction ESHT Evaluations Conclusions
RNN: Echo State Network
• A type of Recurrent Neural Network
• Echo State Layer (ESL):
• Dynamics only driven by the input
• Requires very few computations
• Easy to understand hyper-parameters
• Can capture time dependences
• ESN also requires the hyper-parameters needed by the NN
• Gradient Descent methods have slow convergence
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Introduction ESHT Evaluations Conclusions
Contribution
• Objective:
• Need to model the evolution of the stream over time
• Reduce number of hyper-parameters
• Reduce amount of samples needed to learn
• In this work we present the ESHT:
• Combination of HT + ESL
• To learn temporal dependences in data streams in real-time
• Requires less hyper-parameters than the ESN
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Introduction ESHT Evaluations Conclusions
ESHT
• Echo State Layer (ESL):
• Only needs two hyper-parameters:
• Alpha (α): weights events in X(n) importance over new ones
• Density: Wres is a sparse matrix with given density
• Encodes time-dependences
• FIMT-DD: Hoeffding tree for regression
• Works out-of-the-box: no hyper-parameters tuning
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Introduction ESHT Evaluations Conclusions
ESHT: Evaluation Methodology
• We propose the ESHT to learn character-stream functions:
• Counter (skipped in this presentation)
• lastIndexOf
• emailFilter
• lastIndexOf Evaluation:
• Study the effects of hyper-parameters: α and density
• Alpha (α): weights events in X(n) importance over new ones
• Density: Wres is a sparse matrix with given density
• Use 1,000 neurons on the ESL
• emailFilter evaluation:
• We focus on the speed of learning
• Use outcomes from previous evaluations to configure the
ESHT for this task
• Metrics:
• Cumulative loss
• We consider an error if |yt − ˆy| >= 0.5
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Introduction ESHT Evaluations Conclusions
Input format
• Input is a vector of floats
• Number of attributes = number of input symbols
• Attribute representing current symbol set to 0.5
• Other attributes are set to zero
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Introduction ESHT Evaluations Conclusions
LastIndexOf
• Counts the number of time steps since the current symbol was
last observed
• Input stream is randomly generated
• We 2,3 and 4 symbols
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Introduction ESHT Evaluations Conclusions
LastIndexOf: Vector vs Scalar Input
• Vector input improves accuracy in all cases
• Specially with 4 symbols
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α
Accuracy(%)
2symbols density=0.4
2symbols-vec density=0.4
3symbols density=0.4
3symbols-vec density=0.4
4symbols density=0.4
4symbols-vec density=0.4
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Introduction ESHT Evaluations Conclusions
LastIndexOf: Alpha and Density vs Accuracy
• Lower values of alpha (α) have low accuracy
• There is no clear correlation between accuracy and density
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Alpha (α)
Accuracy(%)
2symbols density=0.1
2symbols density=0.4
3symbols density=0.1
3symbols density=0.4
4symbols density=0.1
4symbols density=0.4
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13.
Introduction ESHT Evaluations Conclusions
EmailFilter
• ESHT configuration:
• ESL: 4,000 neurons
• α = 1.0 and density = 0.1
• Outputs the length on the next space character
• Dataset: 20 newsgroups dataset
• Extracted 590 characters and repeated them 8 times
• To reduce the memory usage we used an input vector of 4
symbols
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Introduction ESHT Evaluations Conclusions
EmailFilter: Recurrence vs Non Recurrence
• Non-recurrent methods (FIMT-DD and NN) fail to capture
temporal dependences
• NN defaults to majority class
Algorithm Density α Learning rate Loss Accuracy (%)
FIMT-DD - - - 4,119.7 91.61
NN - - 0.8 2,760 97.80
ESN1 0.2 1.0 0.1 1,032 98.47
ESN2 0.7 1.0 0.1 850 98.47
ESHT 0.1 1.0 - 180 99.75
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Introduction ESHT Evaluations Conclusions
EmailFilter: ESN vs ESHT
• After 500 samples the ESHT loss is close to 0 (and 0 loss
after the 1,000 samples)
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# Samples
CummulativeLoss
ESN1
ESN2
ESHT
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Introduction ESHT Evaluations Conclusions
Conclusions and Future Work
• Conclusions:
• We presented the ESHT to learn temporal dependences in data
streams in real-time
• The ESHT requires less hyper-parameters than the ESN
• Our proof-of-concept implementation is able to learn faster
than an ESN (Most of them at first shot)
• Future Work:
• We are currently reimplementing our prototype so we can test
larger input sequences
• We need to study the effects of the initial state vanishing in
large sequences
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17.
Thank you

18.
Echo State Hoeffding Tree Learning
Diego Marr´on (dmarron@ac.upc.edu)
Jesse Read (jesse.read@telecom-paristech.fr)
Albert Bifet (albert.bifet@telecom-paristech.fr)
Talel Abdessalem (talel.abdessalem@telecom-paristech.fr)
Eduard Ayguad´e (eduard.ayguade@bsc.es)
Jos´e R. Herrero (josepr@ac.upc.edu)
ACML 2016
Hamilton, New Zeland

19.
ESHT: Module Architecture
• In each evaluation we use the following architecture
• Label generator implements the function to be learnt
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Counter: Introduction
• Stream of zeros and ones randomly generated
• Input is a scalar
• Two variants:
• Option1: Outputs cumulative count
• Option2: Outputs total count on the next zero
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Counter: Cumulative Loss
• After 200 samples the loss is stable
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# Samples
CummulativeLoss
Op1(density=0.3,α=1.0)
Op1(density=1.0,α=0.7)
Op2(density=0.8,α=1.0)
Op2(density=0.8,α=0.7)
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Counter: Alpha and Density vs Accuracy
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23.
EmailFilter: ASCII to 4 symbols Table
ASCII Domain 4-Symbols Domain
Original Symbols Target Symbol Target Symbol Index
[t n r]+ Single space 0
[a-zA-Z0-9] x 1
@ @ 2
. . 3
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