Two Sample Test for Eigendecompositions of Functional Data

2026-03-31

AI Summary

This study addresses the challenge of distinguishing whether trial-to-trial neuronal variability arises from measurement noise or reflects genuine changes in underlying activation patterns. To this end, the authors propose a two-sample test based on the covariance matrix of functional principal component scores, extending it to paired experimental designs. This approach represents the first application of eigen-decomposition to assess structural consistency in functional data, effectively capturing dynamic trial-level variations that conventional dimensionality reduction methods overlook. Simulations demonstrate superior performance over existing techniques across diverse scenarios. When applied to 157 neural trials, the method significantly detected variability in latent activation patterns that cannot be attributed to sampling noise alone.

Abstract

Neuron-level firing data is believed to be governed by latent activation patterns during task completion. Analysing repeated trials of a task allows us to study these patterns, typically by averaging in-vivo neural spikes across trials. However, estimates of underlying latent activation patterns show trial-to-trial variability. Our aim is to determine whether this variation arises from observed data differences or changes in the latent activation patterns themselves. The latter would imply that current approaches overlook meaningful activation changes, necessitating adjustments in dimension reduction and downstream analysis. We propose a test that compares the eigendecompositions of two samples of functional data based on the covariance matrix of scores derived from a functional principal component analysis of the pooled data. Initially developed for independent samples, we later extend the test to paired samples, as necessary for our data. Simulation studies demonstrate its superior power compared to leading methods across various scenarios. In an experiment with 157 trials, we analyse all pairwise comparisons using a permutation approach to test the null hypothesis of shared latent activation patterns across trials. Our findings reveal trial-to-trial variation in latent activation patterns that cannot be attributed to sampling noise.

Problem

• functional data
• eigendecomposition
• two-sample test
• latent activation patterns
• trial-to-trial variability

Innovation

• two-sample test
• functional principal component analysis
• eigendecomposition
• trial-to-trial variability
• paired functional data