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Randomized neural networks for learning stochastic dependences.

V S Borkar1, P Gupta

  • 1Dept. of Comput. Sci. & Autom., Indian Inst. of Sci., Bangalore.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|February 7, 2008
PubMed
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This study introduces a new loss function for learning variable dependence from data. The method approximates unknown functions using feedforward neural networks, extending to Markov chains.

Area of Science:

  • Machine Learning
  • Statistical Inference
  • Stochastic Processes

Background:

  • Learning the dependence between random variables is crucial in statistical modeling.
  • Standard function learning techniques fail when samples of uniformly distributed random variables are unavailable.
  • Existing methods lack efficient ways to approximate complex dependencies.

Purpose of the Study:

  • To develop a novel method for learning the dependence between random variables from finite, independently identically distributed (i.i.d.) data.
  • To address the challenge of unavailable samples for uniformly distributed random variables in function approximation.
  • To extend the learning methodology to both countable and continuous state-space Markov chains.

Main Methods:

  • Transforming the dependence learning problem into learning a function involving an unknown variable and a uniformly distributed variable.

Related Experiment Videos

  • Proposing a novel loss function whose minimizer approximates the target function.
  • Employing combination feedforward neural networks for function representation.
  • Extending the approach to handle countable and continuous state-space Markov chains.

    • Main Results:

    • The proposed loss function enables approximation of the desired function despite unavailable uniform random variable samples.
    • Successive approximation results guide the selection of feedforward neural networks for learning.
    • The method is effectively extended to Markov chain models.
    • Simulation studies demonstrate the efficacy of the proposed learning approach.

    Conclusions:

    • A novel and effective method for learning variable dependence from i.i.d. data has been developed.
    • The approach overcomes limitations of standard techniques by introducing a new loss function.
    • The methodology shows promise for applications in statistical inference and stochastic processes, including Markov chains.