Probabilities-Informed Machine Learning

TL;DR

This paper presents a probabilistically-informed machine learning framework that incorporates domain-specific probabilistic knowledge into training, improving accuracy and robustness across various applications like regression and image denoising.

Contribution

It introduces a novel ML paradigm that embeds probabilistic structure of target variables into the learning process, inspired by domain knowledge and probabilistic principles.

Findings

Enhanced model accuracy in regression and classification tasks

Reduced overfitting and underfitting through probabilistic embedding

Effective application demonstrated in image denoising and real-world problems

Abstract

Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge of the structure of output function, akin to physics-informed ML, but rooted in probabilistic principles rather than physical laws. The proposed approach integrates the probabilistic structure of the target variable (such as its cumulative distribution function) into the training process. This probabilistic information is obtained from historical data or estimated using structural reliability methods during experimental design. By embedding domain-specific probabilistic insights into the learning process, the technique enhances model accuracy and mitigates risks of overfitting and underfitting. Applications in regression, image denoising, and classification demonstrate the approach's effectiveness in addressing real-world problems.