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This study introduces a new framework to determine Gaussian process (GP) kernel parameter identifiability for commonly used kernels. This helps researchers correctly interpret GP model parameters in diverse applications.

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Area of Science:

  • Machine Learning
  • Statistical Modeling
  • Time Series Analysis

Background:

  • Gaussian processes (GPs) are versatile tools in machine learning, time series analysis, and spatial statistics.
  • Interpreting GP kernel parameters is crucial for applications like spatial transcriptomics, but their identifiability is often unaddressed.
  • Current research on GP parameter identifiability mainly covers Matérn-type kernels.

Purpose of the Study:

  • To develop a theoretical framework for assessing Gaussian process kernel parameter identifiability.
  • To address the underexplored identifiability of kernels that are holomorphic near zero, widely used in time series.
  • To enable practitioners to distinguish identifiable from non-identifiable GP kernel parameters.

Main Methods:

  • Developed a novel theoretical framework for determining kernel parameter identifiability.
  • Focused on kernels that are holomorphic near zero, including squared exponential, periodic, and rational quadratic kernels.
  • Analyzed the mathematical properties of kernel functions to establish identifiability criteria.

Main Results:

  • Established a method to determine the identifiability of parameters for kernels holomorphic near zero.
  • Provided guidelines for interpreting identifiable GP kernel parameters in practical applications.
  • Identified specific parameters that require cautious interpretation due to non-identifiability.

Conclusions:

  • The novel framework advances the understanding of GP kernel parameter identifiability.
  • Enables more reliable interpretation of GP models in various scientific domains.
  • Supports the development and application of new GP kernels with clearly defined parameter properties.