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Related Experiment Videos

Always Good Turing: asymptotically optimal probability estimation.

Alon Orlitsky1, Narayana P Santhanam, Junan Zhang

  • 1Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA 92093, USA. alon@ucsd.edu

Science (New York, N.Y.)
|October 18, 2003
PubMed
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Researchers analyzed probability estimators, finding that the Good-Turing estimator has low attenuation. A new estimator was developed with an attenuation of 1, ensuring it does not underestimate sequence probabilities.

Area of Science:

  • Statistics
  • Information Theory
  • Computer Science

Background:

  • The Good-Turing estimator, developed during Enigma code decryption, is a key method for probability estimation from data samples.
  • Understanding the limitations of probability estimators is crucial for accurate data analysis and sequence probability assignments.

Purpose of the Study:

  • To define and analyze the attenuation of probability estimators.
  • To compare the attenuation of common estimators, including the Good-Turing estimator.
  • To develop a novel estimator with minimal attenuation.

Main Methods:

  • Defining attenuation as the maximum ratio of probabilities assigned by any distribution versus the estimator.
  • Evaluating the attenuation of existing common estimators.

Related Experiment Videos

  • Deriving a new probability estimator with a specific attenuation property.

    • Main Results:

    • Some common probability estimators exhibit infinite attenuation.
    • The Good-Turing estimator demonstrates low, but greater than 1, attenuation.
    • A new estimator was successfully derived with an attenuation of 1.

    Conclusions:

    • The newly derived estimator asymptotically avoids underestimating sequence probabilities.
    • This new estimator offers improved theoretical guarantees compared to existing methods.
    • The concept of attenuation provides a valuable metric for evaluating probability estimators.