Suppression of Overfitting in Extraction of Spectral Data from Imaginary Frequency Green Function Using Maximum Entropy Method

TL;DR

This paper introduces a regularization-enhanced maximum entropy method to effectively suppress overfitting and spurious spikes when extracting spectral data from imaginary frequency Green functions, improving spectral accuracy.

Contribution

It proposes a novel regularization term added to the maxEnt loss function, specifically designed to penalize spikiness in spectral functions, addressing overfitting issues.

Findings

Spurious spikes are significantly reduced in spectral functions.

The method works effectively on both artificial and real data.

Spectral accuracy is improved with the new regularization.

Abstract

Although maximum entropy method (maxEnt method) is currently the standard algorithm for extracting real frequency information from imaginary frequency Green function, still this method is beset with overfitting problem, which manifests itself as the spurious spikes in the resultant spectral functions. To address this issue and motivated by the regularization techniques widely used in machine learning and statistics, here we propose to add one more regularization term into the original maxEnt loss function to suppress these redundant spikes. The essence of this extra regularization term is to demand that the resultant spectral functions should pay a price for being spiky. We test our algorithm with both artificial and real data, and find that spurious spikes in the resultant spectral functions can be effectively suppressed by this method.