# A False Discovery Rate Control Method Using a Fully Connected Hidden Markov Random Field for Neuroimaging Data

arXiv: https://arxiv.org/abs/2505.20688 · HTML: https://mlsanity.com/paper/2505.20688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 66 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 9 of 9)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [Higher Order Conditional Random Fields in Deep Neural Networks](https://mlsanity.com/paper/1511.08119/) (2015)
- [False discovery rate smoothing](https://mlsanity.com/paper/1411.6144/) (2014)
- [NeuralFDR: Learning Discovery Thresholds from Hypothesis Features](https://mlsanity.com/paper/1711.01312/) (2017)
- [Multiple Testing for Neuroimaging via Hidden Markov Random Field](https://mlsanity.com/paper/1404.1371/) (2014)
- [Corrections for multiple comparisons in voxel-based lesion-symptom mapping](https://mlsanity.com/paper/1612.04345/) (2016)
- [Efficient Relaxations for Dense CRFs with Sparse Higher Order Potentials](https://mlsanity.com/paper/1805.09028/) (2018)
- [DeepFDR: A Deep Learning-based False Discovery Rate Control Method for Neuroimaging Data](https://mlsanity.com/paper/2310.13349/) (2023)

## Abstract (arXiv)

False discovery rate (FDR) control methods are essential for voxel-wise multiple testing in neuroimaging data analysis, where hundreds of thousands or even millions of tests are conducted to detect brain regions associated with disease-related changes. Classical FDR control methods (e.g., BH, q-value, and LocalFDR) assume independence among tests and often lead to high false non-discovery rates (FNR). Although various spatial FDR control methods have been developed to improve power, they still fall short of jointly addressing three major challenges in neuroimaging applications: capturing complex spatial dependencies, maintaining low variability in both false discovery proportion (FDP) and false non-discovery proportion (FNP) across replications, and achieving computational scalability for high-resolution data. To address these challenges, we propose fcHMRF-LIS, a powerful, stable, and scalable spatial FDR control method for voxel-wise multiple testing. It integrates the local index of significance (LIS)-based testing procedure with a novel fully connected hidden Markov random field (fcHMRF) designed to model complex spatial structures using a parsimonious parameterization. We develop an efficient expectation-maximization algorithm incorporating mean-field approximation, the Conditional Random Fields as Recurrent Neural Networks (CRF-RNN) technique, and permutohedral lattice filtering, reducing the time complexity from quadratic to linear in the number of tests. Extensive simulations demonstrate that fcHMRF-LIS achieves accurate FDR control, lower FNR, reduced variability in FDP and FNP, and a higher number of true positives compared to existing methods. Applied to an FDG-PET dataset from the Alzheimer's Disease Neuroimaging Initiative, fcHMRF-LIS identifies neurobiologically relevant brain regions and offers notable advantages in computational efficiency.