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Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

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Accelerated Stochastic Power Iteration.

Christopher De Sa¹, Bryan He¹, Ioannis Mitliagkas¹

¹Department of Computer Science, Stanford University.

Proceedings of Machine Learning Research

|June 13, 2019

Summary

This summary is machine-generated.

This study introduces a novel momentum-enhanced power iteration for stochastic Principal Component Analysis (PCA). It achieves optimal sample and iteration complexity, accelerating PCA computation in both online and offline settings.

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Area of Science:

Machine Learning
Optimization Algorithms
Data Analysis

Background:

Principal Component Analysis (PCA) is crucial in machine learning.
Existing methods like power iteration and Lanczos have limitations in stochastic settings.
Online stochastic PCA often lacks iteration efficiency.

Purpose of the Study:

To develop a PCA algorithm with optimal sample and iteration complexity.
To accelerate stochastic PCA computation using momentum.
To generalize the approach to other non-convex optimization problems.

Main Methods:

A modified power iteration with a momentum term.
Novel variance analysis to identify acceleration breaking points.
Integration with variance reduction techniques for stochastic PCA.

Main Results:

Achieved optimal sample and iteration complexity for stochastic PCA.
Demonstrated that naive momentum application does not guarantee acceleration.
Developed accelerated online and offline stochastic PCA algorithms with iteration complexity.

Conclusions:

The proposed method offers significant acceleration for stochastic PCA.
The approach is generalizable to various non-convex optimization problems.
Parallel implementation translates acceleration to wall-clock time savings.