Multimodal data integration and cross-modal querying via orchestrated approximate message passing

TL;DR

This paper introduces a data-driven approximate message passing algorithm for integrating multimodal data and constructing valid prediction sets for partially observed new subjects, demonstrated on synthetic and real datasets.

Contribution

It develops a novel orchestrated approximate message passing method for statistically optimal multimodal data integration and prediction in dependent multifactor models.

Findings

Achieves statistically optimal signal recovery in multimodal data integration.

Constructs asymptotically valid prediction sets for new subjects.

Demonstrates effectiveness on synthetic and real single-cell datasets.

Abstract

The need for multimodal data integration arises naturally when multiple complementary sets of features are measured on the same sample. Under a dependent multifactor model, we develop a fully data-driven orchestrated approximate message passing algorithm for integrating information across these feature sets to achieve statistically optimal signal recovery. In practice, these reference data sets are often queried later by new subjects that are only partially observed. Leveraging on asymptotic normality of estimates generated by our data integration method, we further develop an asymptotically valid prediction set for the latent representation of any such query subject. We demonstrate the prowess of both the data integration and the prediction set construction algorithms on both synthetic examples and real world single-cell datasets.