Inference on the Significance of Modalities in Multimodal Generalized Linear Models

TL;DR

This paper introduces a new statistical inference method for assessing the significance of individual modalities in high-dimensional multimodal generalized linear models, using an entropy-based metric and deviance-based testing.

Contribution

It proposes a novel entropy-based metric and a deviance-based statistical test for evaluating modality significance in high-dimensional multimodal models, with theoretical guarantees and practical validation.

Findings

The proposed method accurately assesses modality significance in simulations.

It provides reliable confidence intervals and p-values for high-dimensional data.

Applied to neuroimaging data, it demonstrates practical utility and robustness.

Abstract

Despite the popular of multimodal statistical models, there lacks rigorous statistical inference tools for inferring the significance of a single modality within a multimodal model, especially in high-dimensional models. For high-dimensional multimodal generalized linear models, we propose a novel entropy-based metric, called the expected relative entropy, to quantify the information gain of one modality in addition to all other modalities in the model. We propose a deviance-based statistic to estimate the expected relative entropy, prove that it is consistent and its asymptotic distribution can be approximated by a non-central chi-squared distribution. That enables the calculation of confidence intervals and p-values to assess the significance of the expected relative entropy for a given modality. We numerically evaluate the empirical performance of our proposed inference tool by simulations and apply it to a multimodal neuroimaging dataset to demonstrate its good performance on various high-dimensional multimodal generalized linear models.