Invariant Risk Minimisation for Cross-Organism Inference: Substituting Mouse Data for Human Data in Human Risk Factor Discovery

Human medical data can be challenging to obtain due to data privacy concerns, difficulties conducting certain types of experiments, or prohibitive associated costs. In many settings, data from animal models or in-vitro cell lines are available to help augment our understanding of human data. However, this data is known for having low etiological validity in comparison to human data. In this work, we augment small human medical datasets with in-vitro data and animal models. We use Invariant Risk Minimisation (IRM) to elucidate invariant features by considering cross-organism data as belonging to different data-generating environments. Our models identify genes of relevance to human cancer development. We observe a degree of consistency between varying the amounts of human and mouse data used, however, further work is required to obtain conclusive insights. As a secondary contribution, we enhance existing open source datasets and provide two uniformly processed, cross-organism, homologue gene-matched datasets to the community.

On Invariance Penalties for Risk Minimization

The Invariant Risk Minimization (IRM) principle was first proposed by Arjovsky et al. [2019] to address the domain generalization problem by leveraging data heterogeneity from differing experimental conditions. Specifically, IRM seeks to find a data representation under which an optimal classifier remains invariant across all domains. Despite the conceptual appeal of IRM, the effectiveness of the originally proposed invariance penalty has recently been brought into question. In particular, there exists counterexamples for which that invariance penalty can be arbitrarily small for non-invariant data representations. We propose an alternative invariance penalty by revisiting the Gramian matrix of the data representation. We discuss the role of its eigenvalues in the relationship between the risk and the invariance penalty, and demonstrate that it is ill-conditioned for said counterexamples. The proposed approach is guaranteed to recover an invariant representation for linear settings under mild non-degeneracy conditions. Its effectiveness is substantiated by experiments on DomainBed and InvarianceUnitTest, two extensive test beds for domain generalization.

M-decomposability, elliptical unimodal densities, and applications to clustering and kernel density estimation

Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-decomposable density via a mixture of unimodal densities. Finally, we demonstrate the application of M-decomposability to clustering and kernel density estimation, using real and simulated data. Our results show that M-decomposability can be used as a non-parametric criterion to locate modes in probability densities.