On the Complexity of Counterfactual Reasoning

We study the computational complexity of counterfactual reasoning in relation to the complexity of associational and interventional reasoning on structural causal models (SCMs). We show that counterfactual reasoning is no harder than associational or interventional reasoning on fully specified SCMs in the context of two computational frameworks. The first framework is based on the notion of treewidth and includes the classical variable elimination and jointree algorithms. The second framework is based on the more recent and refined notion of causal treewidth which is directed towards models with functional dependencies such as SCMs. Our results are constructive and based on bounding the (causal) treewidth of twin networks -- used in standard counterfactual reasoning that contemplates two worlds, real and imaginary -- to the (causal) treewidth of the underlying SCM structure. In particular, we show that the latter (causal) treewidth is no more than twice the former plus one. Hence, if associational or interventional reasoning is tractable on a fully specified SCM then counterfactual reasoning is tractable too. We extend our results to general counterfactual reasoning that requires contemplating more than two worlds and discuss applications of our results to counterfactual reasoning with a partially specified SCM that is coupled with data. We finally present empirical results that measure the gap between the complexities of counterfactual reasoning and associational/interventional reasoning on random SCMs.Comment: An earlier version of this paper appeared in NeurIPS 2022 workshop, "A causal view on dynamical systems.

Gene Expression Profiling for Diagnosis of Triple-Negative Breast Cancer: A Multicenter, Retrospective Cohort Study

Background: Triple-negative breast cancer (TNBC) accounts for 12–20% of all breast cancers. Diagnosis of TNBC is sometimes quite difficult based on morphological assessment and immunohistochemistry alone, particularly in the metastatic setting with no prior history of breast cancer.Methods: Molecular profiling is a promising diagnostic approach that has the potential to provide an objective classification of metastatic tumors with unknown primary. In this study, performance of a novel 90-gene expression signature for determination of the site of tumor origin was evaluated in 115 TNBC samples. For each specimen, expression profiles of the 90 tumor-specific genes were analyzed, and similarity scores were obtained for each of the 21 tumor types on the test panel. Predicted tumor type was compared to the reference diagnosis to calculate accuracy. Furthermore, rank product analysis was performed to identify genes that were differentially expressed between TNBC and other tumor types.Results: Analysis of the 90-gene expression signature resulted in an overall 97.4% (112/115, 95% CI: 0.92–0.99) agreement with the reference diagnosis. Among all specimens, the signature correctly classified 97.6% of TNBC from the primary site (41/42) and lymph node metastasis (41/42) and 96.8% of distant metastatic tumors (30/31). Furthermore, a list of genes, including AZGP1, KRT19, and PIGR, was identified as differentially expressed between TNBC and other tumor types, suggesting their potential use as discriminatory markers.Conclusion: Our results demonstrate excellent performance of a 90-gene expression signature for identification of tumor origin in a cohort of both primary and metastatic TNBC samples. These findings show promise for use of this novel molecular assay to aid in differential diagnosis of TNBC, particularly in the metastatic setting