# Correntropy-Based Improper Likelihood Model for Robust Electrophysiological Source Imaging

arXiv: https://arxiv.org/abs/2408.14843 · HTML: https://mlsanity.com/paper/2408.14843/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 27 Aug 2024.

## Builds on (most cited first, 6 of 6)

- [General Bayesian Loss Function Selection and the use of Improper Models](https://mlsanity.com/paper/2106.01214/) (2021)
- [Restricted Minimum Error Entropy Criterion for Robust Classification](https://mlsanity.com/paper/1909.02707/) (2019)
- [Correntropy-Based Logistic Regression with Automatic Relevance Determination for Robust Sparse Brain Activity Decoding](https://mlsanity.com/paper/2207.09693/) (2022)
- [Bias-Compensated Normalized Maximum Correntropy Criterion Algorithm for System Identification with Noisy Input](https://mlsanity.com/paper/1711.08677/) (2017)
- [Partial Maximum Correntropy Regression for Robust Trajectory Decoding from Noisy Epidural Electrocorticographic Signals](https://mlsanity.com/paper/2106.13086/) (2021)
- [Adaptive sparseness for correntropy-based robust regression via automatic relevance determination](https://mlsanity.com/paper/2302.00082/) (2023)

## Built on by (most cited first, 1 of 1)

- [Robust Sparse Bayesian Learning Based on Minimum Error Entropy for Noisy High-Dimensional Brain Activity Decoding](https://mlsanity.com/paper/2508.11657/) (2025)

## Abstract (arXiv)

Bayesian learning provides a unified skeleton to solve the electrophysiological source imaging task. From this perspective, existing source imaging algorithms utilize the Gaussian assumption for the observation noise to build the likelihood function for Bayesian inference. However, the electromagnetic measurements of brain activity are usually affected by miscellaneous artifacts, leading to a potentially non-Gaussian distribution for the observation noise. Hence the conventional Gaussian likelihood model is a suboptimal choice for the real-world source imaging task. In this study, we aim to solve this problem by proposing a new likelihood model which is robust with respect to non-Gaussian noises. Motivated by the robust maximum correntropy criterion, we propose a new improper distribution model concerning the noise assumption. This new noise distribution is leveraged to structure a robust likelihood function and integrated with hierarchical prior distributions to estimate source activities by variational inference. In particular, the score matching is adopted to determine the hyperparameters for the improper likelihood model. A comprehensive performance evaluation is performed to compare the proposed noise assumption to the conventional Gaussian model. Simulation results show that, the proposed method can realize more precise source reconstruction by designing known ground-truth. The real-world dataset also demonstrates the superiority of our new method with the visual perception task. This study provides a new backbone for Bayesian source imaging, which would facilitate its application using real-world noisy brain signal.