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Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
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Measures of distinguishability between stochastic processes.

Chengran Yang1,2, Felix C Binder3, Mile Gu1,2,4

  • 1School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371.

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We introduce divergence rates, a new family of measures for quantifying how distinguishable two stochastic processes are. This novel approach offers a well-behaved and broadly applicable method for process distinguishability, outperforming existing measures in complex scenarios.

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Area of Science:

  • Statistics
  • Machine Learning
  • Quantitative Finance

Background:

  • Quantifying the distinguishability of stochastic processes is crucial in various scientific and financial domains.
  • Existing measures for process distinguishability often lack universal applicability or ease of use.

Purpose of the Study:

  • To establish a set of requirements for an ideal measure of process distinguishability.
  • To propose a new family of measures, termed divergence rates, that meet these requirements.

Main Methods:

  • Defined a set of criteria for a well-behaved distinguishability measure.
  • Introduced a family of measures called divergence rates.
  • Analyzed the coemission divergence rate, a specific member of this family.

Main Results:

  • The proposed divergence rates satisfy all established requirements for process distinguishability.
  • The coemission divergence rate is computationally efficient.
  • The coemission divergence rate demonstrates robust performance, aligning with existing measures where applicable and outperforming them in challenging scenarios.

Conclusions:

  • Divergence rates offer a versatile and effective approach to quantifying stochastic process distinguishability.
  • The coemission divergence rate provides a practical and reliable tool for applications in machine learning, finance, and beyond.