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Fixed-Rate Universal Lossy Source Coding and Model Identification: Connection with Zero-Rate Density Estimation and

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Summary

This study connects density estimation and universal lossy source coding. A novel skeleton estimator framework achieves joint coding and model identification for broader density classes, extending prior work.

Keywords:
L1-totally bounded classesfixed-rate lossy source codingjoint coding and modelinglearning with rate constraintsthe skeleton estimatoruniversal source coding

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Area of Science:

  • Information Theory
  • Machine Learning
  • Data Compression

Background:

  • Density estimation with data-rate constraints is crucial for efficient data handling.
  • Raginsky's 2008 work established a joint objective for fixed-rate universal lossy source coding and model identification.
  • Existing methods often require strong assumptions on density classes.

Purpose of the Study:

  • To establish a formal link between constrained density estimation and joint source coding/model identification.
  • To derive conditions for achieving Raginsky's joint objective.
  • To extend the applicability of universal lossy source coding and model identification to new density classes.

Main Methods:

  • Utilizing an equivalent learning formulation.
  • Introducing the skeleton estimator, a rate-constrained learning scheme.
  • Analyzing the performance in both parametric and non-parametric density settings.

Main Results:

  • A necessary and sufficient condition for achievability of the joint objective is derived.
  • The skeleton estimator optimally adapts learning parameters for the coding and modeling problem.
  • The framework successfully extends to non-parametric L1-totally bounded densities.
  • In the parametric case, a prior assumption is removed without performance loss.

Conclusions:

  • The skeleton estimator provides a unified framework for rate-constrained density estimation and joint source coding/model identification.
  • This work significantly broadens the scope of applicable density classes for these information-theoretic problems.
  • The findings offer improved performance and applicability in both parametric and non-parametric scenarios.