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An R-Based Landscape Validation of a Competing Risk Model

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Published on: September 16, 2022

Cross validation in stochastic analytic continuation.

Gabe Schumm¹, Sibin Yang¹, Anders W Sandvik¹

¹Department of Physics, <a href="https://ror.org/05qwgg493">Boston University</a>, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.

Physical Review. E

|December 18, 2024

Summary

This summary is machine-generated.

Stochastic analytic continuation (SAC) of quantum Monte Carlo (QMC) data can now identify spectral functions more accurately. A new cross-validation technique helps select the best spectrum from multiple possibilities.

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Area of Science:

Computational Physics
Quantum Many-Body Theory
Statistical Mechanics

Background:

Stochastic analytic continuation (SAC) is crucial for linking quantum Monte Carlo (QMC) data to measurable dynamic response functions.
Recent SAC advancements enable high-fidelity resolution of spectral functions with sharp features like peaks and edges.
The ill-posed nature of analytic continuation often results in multiple valid spectral representations.

Purpose of the Study:

To introduce an unbiased cross-validation technique for selecting the most probable spectral function from various parametrizations and constraints.
To enhance the reliability of stochastic analytic continuation by incorporating model selection principles from machine learning and statistics.

Main Methods:

Implementation of a cross-validation technique adapted from machine learning and statistics.
Application of the method to imaginary-time data from QMC simulations.
Testing with synthetic data generated from artificial spectra to validate performance.

Main Results:

Demonstration of the cross-validation technique's effectiveness in identifying the most likely spectrum.
Successful application to both QMC-generated and synthetic data.
Validation of the method's ability to handle spectral functions with sharp features.

Conclusions:

The proposed cross-validation method provides an unbiased approach for model selection in analytic continuation.
This technique significantly improves the identification of spectral features from numerical data.
The procedure is broadly applicable to various numerical analytic continuation methods beyond SAC.