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Estimating Predictive Rate-Distortion Curves via Neural Variational Inference.

Michael Hahn1, Richard Futrell2

  • 1Department of Linguistics, Stanford University, Stanford, CA 94305, USA.

Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

We introduce Neural Predictive Rate-Distortion (NPRD), a new method to estimate the Predictive Rate-Distortion curve for complex processes like natural language. NPRD scales effectively, offering improved bounds over existing techniques.

Keywords:
Predictive Rate–Distortioninformation bottlenecknatural languageneural variational inference

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Area of Science:

  • Information Theory
  • Machine Learning
  • Computational Linguistics

Background:

  • The Predictive Rate-Distortion (PRD) curve measures the trade-off between past information compression and future prediction accuracy.
  • Current PRD estimation methods struggle with complex processes like natural language due to large alphabets and unknown causal states.
  • Existing methods based on clustering or known causal states lack scalability.

Purpose of the Study:

  • To develop a scalable method for estimating the PRD curve for complex stochastic processes.
  • To leverage neural networks for estimating PRD curves where analytical solutions are intractable.
  • To provide improved PRD bounds for natural language processing.

Main Methods:

  • Introduced Neural Predictive Rate-Distortion (NPRD), a novel estimation technique.
  • Utilized the universal approximation capabilities of neural networks.
  • Computed a variational bound on the PRD curve using only time series data.

Main Results:

  • NPRD demonstrates scalability for processes with large alphabets and long dependencies.
  • The method was validated on processes with analytically known PRD curves.
  • NPRD provided improved PRD bounds for natural language compared to sequence clustering.

Conclusions:

  • NPRD offers a scalable approach to estimating the PRD curve for complex systems.
  • The PRD curve is a more effective characterization tool than statistical complexity for highly complex processes like natural language.
  • This work advances the application of information theory to natural language and other complex data.