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README.md

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 ## Abstract
 
-The heritability of human connectomes is crucial for understanding the influence of genetic and environmental factors on variations in connectomes, and their implications for behavior and disease. However, current methods for studying heritability assume an associational rather than a causal effect, and rely on modeling assumptions that may not be appropriate for complex, high-dimensional connectomes. To address these limitations, we propose two solutions: first, formalize heritability as causal effects, and identify measurable covariates to control for unmeasured confounding, allowing us to make causal claims. Second, leverage statistical models that capture the underlying structure and dependence within connectomes, enabling us to define different notions of connectome heritability. For example, we remove common structures with increasing complexity across connectomes and test whether heritability exists beyond these commonalities. We then develop a non-parametric test to detect causal heritability and apply it to connectomes estimated from the Human Connectome Project diffusion data. Our investigation provides compelling evidence that genetics play a significant role in shaping connectomes.
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+The heritability of human connectomes is crucial for understanding the influence of genetic and environmental factors on variability in connectomes, and their implications for behavior and disease. However, current methods for studying heritability assume an associational rather than a causal effect, or rely on strong distributional assumptions that may not be appropriate for complex, high-dimensional connectomes. To address these limitations, we propose two solutions: first, we formalize heritability as a problem in causal inference, and identify measured covariates to control for unmeasured confounding, allowing us to make causal claims. Second, we leverage statistical models that capture the underlying structure and dependence within connectomes, enabling us to define different notions of connectome heritability by removing common structures such as scaling of edge weights between connectomes. We then develop a non-parametric test to detect whether causal heritability exists after taking principled steps to adjust for these commonalities, and apply it to diffusion connectomes estimated from the Human Connectome Project. Our findings reveal that heritability can still be detected even after adjusting for potential confounding like neuroanatomy, age, and sex. However, once we address for rescaling between connectomes, our causal tests are no longer significant. These results suggest that previous conclusions on connectome heritability may be driven by rescaling factors. Together, our manuscript highlights the importance for future works to continue to develop data-driven heritability models which faithfully reflect potential confounders and network structure.