Presentation on experimental setup for verigying - "Slow Learners are Fast"

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This document summarizes a student's machine learning project on a Cell processor supervised by Dr. Eric McCreath. The student, Robin Srivastava, evaluated a parallel online machine learning algorithm on a Cell processor and dual-core Intel machine. The project used logistic regression with delayed updates on a text classification problem involving classifying emails as spam or ham. Memory requirements for the algorithm exceeded what the Cell's SPE could support, so feature space was reduced and extra preprocessing was done. Results showed the parallel implementation on the Cell was faster than the serial implementation on the Intel dual-core.

Technology

Machine Learning on Cell Processor

Supervisor: Dr. Eric McCreath
Student: Robin Srivastava

Background and Motivation
Machine
Learning

Batch Online
Learning Learning

HAM

Email-N ……..… email-2 Email-1

SPAM

Background and Motivation
Machine
Learning

Sequential
Batch Online in Nature
Learning Learning

HAM

Email-N ……..… email-2 Email-1

SPAM

Object
  Performance evaluation of a parallel online machine
learning algorithm (Langford et. al. [1])
  Target Machines
  Cell Processor: One 3 GHz 64-bit IBM PowerPC, six
specialized co-processors
  Intel Dual Core Machine: 2GHz dual core processor, 1.86 GB
of main memory

Stochastic Gradient Descent
  Step 1: Initialize weight vector w0 with some arbitrary
values
  Step 2: Update the weight vector as follows

w (t +1) = w t − η∇E ( w t )

where ∇E is the gradient of error function and η is the
learning rate
€
  Step 3: Follow Step 2 for all the units for data
€ €

Delayed Stochastic Gradient Descent
  Step 1: Initialize weight vector w0 with some arbitrary
values
  Step 2: Update the weight vector as follows

w (t +1) = w t − η∇E ( w t−τ )

where ∇E is the gradient of error function and η is the
learning rate
€
  Step 3: Follow Step 2 for all the units for data
€ €

Implementation
  Dataset – TREC 2007 Public Corpus
  Number of mail: 75,419
  Each mail classified as either ‘ham’ or ‘spam’
  Pre-processing
  Total number of features extracted: 2,218,878
  Pre-processed email format

<Number of features><space><index>:<count><space>…………..<index>:<count>

Memory Requirement
  Algorithm Implemented
  Online Logistic Regression with delayed update
  Requirement per level of parallelization
  Two private copy of weight vectors
  Two shared copy of weight vectors
  Two error gradients
  Required Dimension for each = Number of features = 2,218,878
  Data type: Float (On Cell takes 4 bytes)
  Total = (6 x 2218878) x 4 = 53,253,072 bytes = 50.78 MB
  Size occupied by other auxiliary variables
  Alternatively
  Make only shared copy use the full dimension
  Total size = (2 x 2218878) x 4 = 16.9 MB + others

Limitations on Cell
  Memory limitation of SPE
  Available: 256 KB
  Required: approx. 51 MB
  Work Around:
  Reduced the number of features
  Done one more level of pre-processing
  SIMD limitation
  The time wasted in preparing the data for SIMD surpassed its
benefits for this implementation

Results
  Serial implementation of logistic regression on Intel Dual
core took 36.93 and 36.45 sec respectively for two
consecutive executions.
  Parallel implementation using stochastic gradient process

Results (contd.)
  Performance on Cell

Time in microseconds

References
①  John Langford, Alexander J. Samola and Martin Zinkevich.
Slow learners are fast published in Journal of Machine
Learning Research 1(2009)
②  Michael Kistler, Michael Perrone, Fabrizio Petrini. Cell
Multiprocessor Communication Network: Built for Speed.
③  Thomas Chen , Ram Raghavan , Jason Dale and Eiji Iwata. Cell
Broadband Engine Architecture and its first implementation
④  Jonathan Bartlett. Programming high-performance
applications on the Cell/B.E. processor, Part 6: Smart buffer
management with DMA transfers
⑤  Introduction to Statistical Machine Learning, 2010 course
assignment 1
⑥  Christopher Bishop, Pattern Recognition and Machine
Learning.

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Presentation on experimental setup for verigying - "Slow Learners are Fast"

1. Machine Learning on Cell Processor Supervisor: Dr. Eric McCreath Student: Robin Srivastava

2. Background and Motivation Machine Learning Batch Online Learning Learning HAM Email-N ……..… email-2 Email-1 SPAM

3. Background and Motivation Machine Learning Sequential Batch Online in Nature Learning Learning HAM Email-N ……..… email-2 Email-1 SPAM

4. Object   Performance evaluation of a parallel online machine learning algorithm (Langford et. al. [1])   Target Machines   Cell Processor: One 3 GHz 64-bit IBM PowerPC, six specialized co-processors   Intel Dual Core Machine: 2GHz dual core processor, 1.86 GB of main memory

5. Stochastic Gradient Descent   Step 1: Initialize weight vector w0 with some arbitrary values   Step 2: Update the weight vector as follows w (t +1) = w t − η∇E ( w t ) where ∇E is the gradient of error function and η is the learning rate €   Step 3: Follow Step 2 for all the units for data € €

6. Delayed Stochastic Gradient Descent   Step 1: Initialize weight vector w0 with some arbitrary values   Step 2: Update the weight vector as follows w (t +1) = w t − η∇E ( w t−τ ) where ∇E is the gradient of error function and η is the learning rate €   Step 3: Follow Step 2 for all the units for data € €

7. Implementation Model Complete Dataset

8. Implementation   Dataset – TREC 2007 Public Corpus   Number of mail: 75,419   Each mail classified as either ‘ham’ or ‘spam’   Pre-processing   Total number of features extracted: 2,218,878   Pre-processed email format <Number of features><space><index>:<count><space>…………..<index>:<count>

9. Memory Requirement   Algorithm Implemented   Online Logistic Regression with delayed update   Requirement per level of parallelization   Two private copy of weight vectors   Two shared copy of weight vectors   Two error gradients   Required Dimension for each = Number of features = 2,218,878   Data type: Float (On Cell takes 4 bytes)   Total = (6 x 2218878) x 4 = 53,253,072 bytes = 50.78 MB   Size occupied by other auxiliary variables   Alternatively   Make only shared copy use the full dimension   Total size = (2 x 2218878) x 4 = 16.9 MB + others

10. Limitations on Cell   Memory limitation of SPE   Available: 256 KB   Required: approx. 51 MB   Work Around:   Reduced the number of features   Done one more level of pre-processing   SIMD limitation   The time wasted in preparing the data for SIMD surpassed its benefits for this implementation

11. Results   Serial implementation of logistic regression on Intel Dual core took 36.93 and 36.45 sec respectively for two consecutive executions.   Parallel implementation using stochastic gradient process

12. Results (contd.)   Performance on Cell Time in microseconds

13. References ①  John Langford, Alexander J. Samola and Martin Zinkevich. Slow learners are fast published in Journal of Machine Learning Research 1(2009) ②  Michael Kistler, Michael Perrone, Fabrizio Petrini. Cell Multiprocessor Communication Network: Built for Speed. ③  Thomas Chen , Ram Raghavan , Jason Dale and Eiji Iwata. Cell Broadband Engine Architecture and its first implementation ④  Jonathan Bartlett. Programming high-performance applications on the Cell/B.E. processor, Part 6: Smart buffer management with DMA transfers ⑤  Introduction to Statistical Machine Learning, 2010 course assignment 1 ⑥  Christopher Bishop, Pattern Recognition and Machine Learning.

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