Log-Gaussian gamma processes for training Bayesian neural networks in Raman and CARS spectroscopies

Area of Science:

• Spectroscopy
• Machine Learning
• Data Science

Background:

• Limited real-world spectral data hinders neural network training.
• Raman and Coherent Anti-Stokes Raman Scattering (CARS) spectroscopy generate complex datasets.

Purpose of the Study:

• To generate synthetic Raman and CARS spectral datasets for neural network training.
• To develop a robust method for estimating spectral parameters and associated uncertainties.

Main Methods:

• Utilized gamma-distributed random variables and log-Gaussian modeling for synthetic data generation.
• Employed Markov chain Monte Carlo (MCMC) for parameter estimation and Bayesian posterior distribution.
• Modeled background functions using Gaussian processes.
• Trained Bayesian neural networks (BNNs) to estimate gamma process parameters.

Main Results:

• Successfully generated synthetic Raman and CARS spectra.
• BNNs accurately estimated underlying spectral signatures and provided uncertainty quantification.
• Results aligned with deterministic estimates on experimental pigment and biochemical samples.

Conclusions:

• The proposed approach effectively generates synthetic spectral data for BNNs.
• This method enhances spectral analysis by providing uncertainty estimates.
• Applicable to various spectroscopic applications with limited data.