Propensity Score Alignment of Unpaired Multimodal Data (2404.01595v2)

Abstract: Multimodal representation learning techniques typically rely on paired samples to learn common representations, but paired samples are challenging to collect in fields such as biology where measurement devices often destroy the samples. This paper presents an approach to address the challenge of aligning unpaired samples across disparate modalities in multimodal representation learning. We draw an analogy between potential outcomes in causal inference and potential views in multimodal observations, which allows us to use Rubin's framework to estimate a common space in which to match samples. Our approach assumes we collect samples that are experimentally perturbed by treatments, and uses this to estimate a propensity score from each modality, which encapsulates all shared information between a latent state and treatment and can be used to define a distance between samples. We experiment with two alignment techniques that leverage this distance -- shared nearest neighbours (SNN) and optimal transport (OT) matching -- and find that OT matching results in significant improvements over state-of-the-art alignment approaches in both a synthetic multi-modal setting and in real-world data from NeurIPS Multimodal Single-Cell Integration Challenge.

• The paper introduces a novel alignment method using propensity score estimation to map unpaired multimodal samples into a common space.
• It demonstrates effectiveness by leveraging Shared Nearest Neighbours and Optimal Transport to achieve superior matching accuracy in both synthetic and real datasets.
• The study provides theoretical insights linking causal inference and latent space coarsening, paving the way for advanced multimodal integration techniques.

Essay on "Propensity Score Alignment of Unpaired Multimodal Data"

The paper "Propensity Score Alignment of Unpaired Multimodal Data," by Johnny Xi and Jason Hartford, presents a novel approach to address the inherent challenges of aligning unpaired samples across different modalities in multimodal representation learning. This is particularly relevant in fields such as biology, where measurement processes can often be destructive, leading to unpaired data. The paper introduces a method that leverages classical causal inference concepts, specifically Rubin's framework, to establish a common space for matching samples, thus presenting a solution to the problem of unpaired multimodal data.

Methodology Overview

The authors draw a compelling analogy between potential outcomes in causal inference and potential views in multimodal observations. This analogy permits them to utilize Rubin's causal model to estimate a shared space. The method relies on the computation of the propensity score, which encapsulates all shared information between a latent state and a treatment, facilitating the definition of distances between samples from different modalities.

To tackle the alignment of unpaired data, the authors propose two alignment techniques that exploit this computed distance: Shared Nearest Neighbours (SNN) and Optimal Transport (OT) matching. Optimal Transport, in particular, is shown to outperform other state-of-the-art alignment methods significantly, demonstrating its efficacy in both synthetic settings and real-world data from the NeurIPS Multimodal Single-Cell Integration Challenge.

Theoretical Foundations

A critical contribution of this paper is the theoretical underpinning that supports the proposed method. The authors prove that the propensity score, as computed within each modality, not only provides a common space but also maximally coarsens the latent space, effectively capturing all relevant shared information. This is achieved under the assumption that each sampled modality does not incur treatment, indicating that experimental perturbations affect the latent state itself rather than confounding noise variables intrinsic to a particular modality.

Moreover, the paper outlines conditions where matching is theoretically feasible, demonstrating that the propensity score's dimensionality needs to at least match the latent variables to maintain injectivity. Hence, a challenge remains when the latent space dimensionality exceeds the number of treatments, echoing known impossibility theorems within causal inference.

Experimental Results

Empirical validation on both synthetic and real-world datasets shows the proposed method's substantial advantages. For instance, in synthetic datasets, the OT matching approach using propensity scores not only yielded significant improvements in alignment precision but also generalized well in downstream tasks such as cross-modality prediction tasks. In real-world CITE-seq data, the method outperformed alternative approaches like SCOT and VAE-based alignments in metrics evaluating matching accuracy, such as FOSCTTM and the trace metric.

An interesting outcome of the experiments is the enhanced generalization capability observed when using soft matching, which sampled over probable couplings between modalities. This capability indicated that the method might inherently filter out modality-specific noise, thus providing a purer form of the shared latents between datasets.

Implications and Future Directions

The implications of this research extend to several domains that deal with multimodal data, offering a robust framework that could be generalized beyond biological data. This propensity-informed alignment could potentially revolutionize how researchers approach unpaired data in other complex systems, reducing reliance on infeasible paired data collection methods.

Future investigations could focus on further refining the conditions under which the propensity score remains informative or developing methods that can cope with less than ideal treatment scenarios or non-random missing data types. Moreover, the theoretical insights regarding injectivity tied to the number of perturbations provide fertile ground for further exploration in causal representation learning.

In conclusion, the paper makes a significant contribution to the field of multimodal data analysis by providing a theoretically sound and empirically validated method for aligning unpaired multimodal data, potentially influencing future research directions and applications across diverse scientific domains.