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Parametric inference in the large data limit using maximally informative models.

Justin B Kinney1, Gurinder S Atwal

  • 1Simons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A. jkinney@cshl.edu.

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Researchers developed a new statistical inference method to infer system filters from high-dimensional signals. This approach circumvents the need for precise noise function knowledge by maximizing mutual information, simplifying complex data analysis.

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Area of Science:

  • Statistical Inference
  • Computational Neuroscience
  • Systems Biology

Background:

  • Inferring system filters (S to R) from high-dimensional signals (S) and noisy measurements (M) is crucial in fields like neuroscience and transcriptional regulation.
  • Traditional likelihood-based inference requires accurate knowledge of the noise function (R to M), which is often unknown or approximated, leading to biased results.

Purpose of the Study:

  • To develop a novel statistical inference method that bypasses the need for a pre-characterized noise function.
  • To enable accurate filter inference even when noise characteristics are not fully known.
  • To explore the fundamental substructure within parameter spaces in statistical inference.

Main Methods:

  • Proposed a method based on maximizing mutual information (I[M; R]) between observed measurements and predicted representations in the large data limit.
  • Demonstrated that maximizing mutual information is equivalent to maximizing all valid dependence measures under the data processing inequality, given the correct filter is explored.
  • Derived a systematic method to identify and analyze unconstrained directions in parameter space, termed 'diffeomorphic modes'.

Main Results:

  • Successfully circumvented the requirement for a priori noise function knowledge in statistical inference.
  • Showed that maximizing mutual information provides a robust alternative to likelihood-based inference with unknown noise functions.
  • Identified and provided a method for deriving 'diffeomorphic modes', revealing hidden parameter space substructure.

Conclusions:

  • Maximizing mutual information offers a powerful, data-driven approach for inferring system filters, particularly when noise functions are uncertain.
  • The concept of diffeomorphic modes highlights a fundamental aspect of parameter space structure obscured by traditional methods.
  • This work advances statistical inference techniques applicable to complex, high-dimensional biological systems.