Uncertainty-Aware Optimal Treatment Selection for Clinical Time Series

In personalized medicine, the ability to predict and optimize treatment outcomes across various time frames is essential. Additionally, the ability to select cost-effective treatments within specific budget constraints is critical. Despite recent advancements in estimating counterfactual trajectories, a direct link to optimal treatment selection based on these estimates is missing. This paper introduces a novel method integrating counterfactual estimation techniques and uncertainty quantification to recommend personalized treatment plans adhering to predefined cost constraints. Our approach is distinctive in its handling of continuous treatment variables and its incorporation of uncertainty quantification to improve prediction reliability. We validate our method using two simulated datasets, one focused on the cardiovascular system and the other on COVID-19. Our findings indicate that our method has robust performance across different counterfactual estimation baselines, showing that introducing uncertainty quantification in these settings helps the current baselines in finding more reliable and accurate treatment selection. The robustness of our method across various settings highlights its potential for broad applicability in personalized healthcare solutions.

Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes

Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such processes can often be accurately modeled via stochastic differential equations (SDEs), which naturally imply causal relationships via "which variables enter the differential of which other variables". In this paper, we develop a kernel-based test of conditional independence (CI) on "path-space" -- solutions to SDEs -- by leveraging recent advances in signature kernels. We demonstrate strictly superior performance of our proposed CI test compared to existing approaches on path-space. Then, we develop constraint-based causal discovery algorithms for acyclic stochastic dynamical systems (allowing for loops) that leverage temporal information to recover the entire directed graph. Assuming faithfulness and a CI oracle, our algorithm is sound and complete. We empirically verify that our developed CI test in conjunction with the causal discovery algorithm reliably outperforms baselines across a range of settings.

Learning Counterfactually Invariant Predictors

We propose a method to learn predictors that are invariant under counterfactual changes of certain covariates. This method is useful when the prediction target is causally influenced by covariates that should not affect the predictor output. For instance, an object recognition model may be influenced by position, orientation, or scale of the object itself. We address the problem of training predictors that are explicitly counterfactually invariant to changes of such covariates. We propose a model-agnostic regularization term based on conditional kernel mean embeddings, to enforce counterfactual invariance during training. We prove the soundness of our method, which can handle mixed categorical and continuous multi-variate attributes. Empirical results on synthetic and real-world data demonstrate the efficacy of our method in a variety of settings.