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Implementing Gaussian process inference with neural networks.

Marcus Frean1, Matt Lilley, Phillip Boyle

  • 1Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand. marcus@mcs.vuw.ac.nz

International Journal of Neural Systems
|November 23, 2006
PubMed
Summary
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Gaussian processes offer superior regression capabilities compared to backpropagation neural networks. A novel recurrent neural network trained with Hebbian learning mimics Gaussian process predictions, simplifying complex models.

Area of Science:

  • Machine Learning
  • Computational Neuroscience
  • Artificial Intelligence

Background:

  • Gaussian processes (GPs) are effective for regression tasks.
  • Bayesian neural networks (BNNs) exhibit GP-like behavior with infinite hidden neurons.
  • Backpropagation neural networks (BPNNs) are a common alternative for regression.

Purpose of the Study:

  • To introduce a novel recurrent neural network (RNN) architecture.
  • To demonstrate that this RNN can replicate Gaussian process regression predictions.
  • To explore a more efficient alternative to infinite hidden unit feed-forward networks.

Main Methods:

  • A simple recurrent neural network (RNN) architecture was designed.
  • Connection weights were trained using one-shot Hebbian learning.

Related Experiment Videos

  • The network was analyzed as a dynamical system relaxing to a stable state.

    • Main Results:

    • The trained RNN generates predictions identical to Gaussian process regression.
    • This finite recurrent network effectively replaces an infinite-hidden-unit feed-forward network.
    • Hebbian learning provides a one-shot training method for the recurrent system.

    Conclusions:

    • Recurrent neural networks trained with Hebbian learning can achieve Gaussian process regression performance.
    • A finite recurrent architecture offers a computationally efficient alternative to infinite feed-forward networks.
    • This approach bridges the gap between dynamical systems and Gaussian process models in machine learning.