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Robust Universal Inference.

Amichai Painsky1, Meir Feder2

  • 1The Industrial Engineering Department, Tel Aviv University, Tel Aviv 6997801, Israel.

Entropy (Basel, Switzerland)
|July 2, 2021

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a new framework for learning from limited data, focusing on a class of reasonable models rather than a single best-fit model. It offers robust estimation with minimax guarantees, improving worst-case performance in scientific inference.

Keywords:
estimation theoryminimax estimationminimax riskstatistical inferenceuniversal prediction

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Area of Science:

  • Statistical Learning Theory
  • Machine Learning
  • Information Theory

Background:

  • Learning from finite samples is crucial in science, but data acquisition is often costly.
  • Traditional methods seek a single best-fit model, which can be inaccurate with limited data.
  • This poses challenges for scientific inference in data-scarce environments.

Purpose of the Study:

  • To develop an alternative framework for learning and inference with limited samples.
  • To address the limitations of single-model estimation in data-constrained scenarios.
  • To provide robust estimation schemes with theoretical guarantees.

Main Methods:

  • Defining a class of "reasonable" models instead of a single estimated model.
  • Utilizing a minimax estimator to control worst-case performance within the model class.
  • Developing a robust estimation scheme offering minimax guarantees, even when the true model is outside the class.

    • Main Results:

    • The proposed framework improves worst-case performance compared to existing alternatives.
    • Demonstrated effectiveness across various experimental setups.
    • Established connections to universal prediction, redundancy-capacity theorem, and channel capacity theory.

    Conclusions:

    • The new approach offers a more robust and reliable method for scientific inference with limited data.
    • Minimax estimation within a defined model class provides strong theoretical guarantees.
    • This framework enhances decision-making and model selection in data-limited scientific research.