Visible and Invisible: Causal Variable Learning and its Application in a Cancer Study

Abstract

Causal visual discovery is a fundamental yet challenging problem in many research fields. Given visual data and the outcome of interest, the goal is to infer the cause-effect relation. Aside from rich visual ('visible') variables, oftentimes, the outcome is also determined by 'invisible' variables, i.e. the variables from non-visual modalities that do not have visual counterparts. This (visible, invisible) combination is particularly common in the clinical domain. Built upon the promising invariant causal prediction (ICP) framework, we propose a novel -ICP algorithm to resolve the (visible, invisible) setting. To efficiently discover -plausible causal variables and to estimate the cause-effect relation, the -ICP is learned under a min-min optimisation scheme. Driven by the need for clinical reliability and interpretability, the -ICP is implemented with a typed neural-symbolic functional language. With the built-in program synthesis method, we can synthesize a type-safe program that is comprehensible to the clinical experts. For concept validation of the -ICP, we carefully design a series of synthetic experiments on the type of visual-perception tasks that are encountered in daily life. To further substantiate the proposed method, we demonstrate the application of -ICP on a real-world cancer study dataset, Swiss CRC. This population-based cancer study has spanned over two decades, including 25k fully annotated tissue micro-array (TMA) images with at least 3k 3k resolution and a broad spectrum of clinical meta data for 533 patients. Both the synthetic and clinical experiments demonstrate the advantages of -ICP over the state-of-the-art methods. Finally, we discuss the limitations and challenges to be addressed in the future.

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