Comparison of eigeninference based on one- and two-point Green's functions

Area of Science:

• Computational physics
• Statistical mechanics
• Data analysis

Background:

• Eigeninference is crucial for analyzing large datasets.
• Existing methods, like those using fluctuations and two-point Green's functions, face challenges with speed and stability.

Purpose of the Study:

• To compare the efficiency and stability of two eigeninference methods.
• To introduce and validate a novel eigeninference approach using one-point Green's functions and Padé approximants.
• To investigate eigeninference for various data distributions, including Wishart distributions.

Main Methods:

• Developed an eigeninference method utilizing one-point Green's functions and Padé approximants.
• Analyzed a comparative method based on fluctuations and two-point Green's functions.
• Investigated eigeninference for real-valued and complex-valued correlated Wishart distributions.
• Introduced eigeninference based on spectral moments of negative orders for positive spectra.

Main Results:

• The one-point Green's function method demonstrated superior speed, being orders of magnitude faster than the two-point Green's function method.
• Identified a source of instability in the two-point Green's function method, linked to spurious modes in the variance operator estimator.
• Confirmed the advantage of the one-point Green's function method across different data distributions.

Conclusions:

• The eigeninference method based on one-point Green's functions and Padé approximants is significantly more efficient and stable.
• The identified instability in the two-point Green's function method highlights its limitations for large-scale data analysis.
• The proposed method offers a robust and scalable solution for eigeninference problems.