# A canonical polyadic tensor basis for fast Bayesian estimation of multi-subject brain activation patterns

## TL;DR

This paper introduces a fast Bayesian model using tensor decomposition to analyze brain activity patterns related to working memory in a large dataset.

## Contribution

The novel approach uses a canonical polyadic tensor basis for efficient Bayesian estimation of multi-subject brain activation.

## Key findings

- The model effectively extracts both common and subject-specific brain activation features.
- It enables fast MCMC estimation of population-level activation maps.
- Application to the HCP dataset revealed significant brain signatures for working memory.

## Abstract

Task-evoked functional magnetic resonance imaging studies, such as the Human Connectome Project (HCP), are a powerful tool for exploring how brain activity is influenced by cognitive tasks like memory retention, decision-making, and language processing. A fast Bayesian function-on-scalar model is proposed for estimating population-level activation maps linked to the working memory task. The model is based on the canonical polyadic (CP) tensor decomposition of coefficient maps obtained for each subject. This decomposition effectively yields a tensor basis capable of extracting both common features and subject-specific features from the coefficient maps. These subject-specific features, in turn, are modeled as a function of covariates of interest using a Bayesian model that accounts for the correlation of the CP-extracted features. The dimensionality reduction achieved with the tensor basis allows for a fast MCMC estimation of population-level activation maps. This model is applied to one hundred unrelated subjects from the HCP dataset, yielding significant insights into brain signatures associated with working memory.