Aligning Unpaired Multimodal Data Using Propensity Score Matching

Core Concepts

Propensity score matching can be used to efficiently align unpaired multimodal data by leveraging information about shared latent states and experimental perturbations.

Abstract

The key insights and highlights of the content are:

1. Multimodal representation learning techniques typically rely on paired samples, but paired samples are challenging to collect in many scientific fields. This paper presents an approach to address the challenge of aligning unpaired samples across disparate modalities.

2. The authors draw an analogy between potential outcomes in causal inference and potential views in multimodal observations. This allows them to use Rubin's framework to estimate a common space in which to match samples.

3. The approach assumes the collection of samples that are experimentally perturbed by treatments. It 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.

4. Two alignment techniques that leverage the propensity score distance are explored - shared nearest neighbours (SNN) and optimal transport (OT) matching. The authors find that OT matching results in significant improvements over state-of-the-art alignment approaches.

5. The proposed matching procedure can also be used for cross-modality prediction tasks by estimating a function that translates between modalities using a two-sample stochastic gradient estimator.

6. Experiments on a synthetic multi-modal setting and real-world data from the NeurIPS Multimodal Single-Cell Integration Challenge demonstrate the effectiveness of the propensity score-based matching approach.

Stats

The authors use the following key metrics or figures to support their approach:
"π(z) := P(t|Z = z) ∈[0, 1]T +1"
"I(t, Z(t) | π(Z(t))) = I(t, Z(t) | π(X(t))) = 0"
"If T < d, the propensity score π, restricted to its strictly positive part, is non-injective."

Quotes

"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."
"Our key observation is that the propensity score, defined as p(t|z), satisfies three properties: 1) It provides a common space for matching, 2) it maximally coarsens z, retaining only relevant information and 3) under certain assumptions, it is estimable from observations of individual modalities alone."
"Observing, or accurately inferring z would address the first issue by providing a common space Z in we could match samples. However, inferring the latent variable is hopelessly underspecified without making strong assumptions on the data generating processes of both modalities."

Key Insights Distilled From

Propensity Score Alignment of Unpaired Multimodal Data

by Johnny Xi,Ja... at arxiv.org 04-03-2024

https://arxiv.org/pdf/2404.01595.pdf

Deeper Inquiries

How can the proposed propensity score matching approach be extended to settings with more complex data generation processes, such as when the treatment variable t has a non-trivial effect on the modality-specific noise variables U(e)

The proposed propensity score matching approach can be extended to settings with more complex data generation processes by considering the impact of the treatment variable t on the modality-specific noise variables U(e). In such cases, where the treatment affects the noise variables in addition to the latent variable Z, the propensity score can still serve as a useful proxy for the latent variable.
To extend the approach, one could incorporate the treatment variable's influence on the noise variables into the propensity score estimation process. By training classifiers to predict the treatment variable based on both the observed modality data and the noise variables, one can capture the shared information between the latent variable, treatment, and modality-specific noise. This extended propensity score can then be used to define a distance metric for matching samples across modalities, taking into account the impact of the treatment on the noise variables as well.

What are the theoretical limits of propensity score matching in terms of the dimensionality of the latent space Z and the number of available treatments t

The theoretical limits of propensity score matching in terms of the dimensionality of the latent space Z and the number of available treatments t are crucial considerations for understanding the tradeoffs in matching performance.
In settings where the dimensionality of the latent space Z exceeds the number of available treatments t, the propensity score may not be injective, leading to an indeterminacy in matching. This limitation arises from the compressing nature of the propensity score, which retains only relevant information shared between the latent variable and treatment. As a result, when the number of treatments is insufficient to uniquely identify the latent space, the propensity score may not provide a one-to-one mapping for matching samples accurately.
On the other hand, when the number of treatments t is equal to or greater than the dimensionality of the latent space Z, the propensity score can potentially be injective, allowing for more precise matching. In such cases, the propensity score serves as a minimal representation of shared information, facilitating effective sample alignment across modalities.
Understanding these theoretical limits helps in optimizing the design of experiments and data collection strategies to ensure sufficient perturbations and treatments are available to support accurate propensity score matching.

Can the authors provide more insights into the tradeoffs between these factors and the matching performance

The capability of the propensity score matching approach for cross-modality prediction tasks offers several practical benefits in various applications.
One key advantage is the ability to leverage the aligned samples from different modalities to train predictive models that can translate information between modalities. By estimating a function that maps from one modality to another using the matched samples, the approach enables seamless cross-modality prediction without the need for paired data. This can be particularly useful in scenarios where collecting paired samples is challenging or impractical.
Furthermore, the propensity score matching approach provides a principled way to integrate information from multiple modalities, enhancing the robustness and generalization of predictive models. By incorporating the shared information captured in the propensity score, the cross-modality prediction models can effectively learn the relationships between different data modalities and make accurate predictions across domains.
Overall, the propensity score matching approach for cross-modality prediction tasks offers a versatile and efficient way to leverage multimodal data for various applications, including image analysis, biological studies, and data integration tasks.