This paper studies the problem of Continuous-Time Counterfactual Quantile Learning (CT-CQL) for risk-sensitive policy optimization. In many real-world applications such as patient blood pressure monitoring, financial market analysis, and autonomous driving, data is high-frequency and continuously evolving. However, most existing causal inference methods focus on expectation-based or discrete-time counterfactual reasoning, which fail to capture fine-grained temporal dynamics. As a result, policies optimized under these frameworks may overlook critical risks—e.g., a treatment policy with good average outcomes may still expose patients to life-threatening episodes. To overcome these limitations, we propose CT-CQL, a framework built upon a novel identification theory and featuring three key components: (1) modeling full counterfactual outcome distributions via Stochastic Differential Equations (SDEs) governed by the Fokker–Planck Equation (FPE); (2) enhancing robustness through a minimax objective that minimizes FPE residuals under adversarial perturbations; and (3) mitigating confounding bias using a double-robust AIPW loss. CT-CQL enables robust policy optimization by identifying optimal intervention strategies that maximize expected utility while adhering to real-world budget and safety constraints. Experiments on widely-used benchmarks and the real-world MIMIC-III dataset demonstrate the validation and superiority of the proposed method. The project is available at: https://github.com/Eliza-YiHe/CT-CQL/

Treatment effect estimation from observational data is a fundamental problem in causal inference, and its critical challenge is to address the confounding bias arising from the confounders. The effectiveness of the conventional methods proposed to solve this problem depends on the unconfoundedness assumption. In practice, however, the unconfoundedness assumption is frequently violated since we cannot guarantee that all the confounders are measured. To this end, recent studies suggest using auxiliary network architectures to mine information about unmeasured confounders in the data to relax this assumption. However, these methods cannot address the confounding bias from unmeasured confounders unrelated to the network information. Inspired by the insight that some neighboring features that influence one's treatment choice (e.g., which movie to watch) but do not affect the outcome (e.g., assessment of the movie) can be treated as instrumental variables (IVs), we propose a novel Network Instrumental Variable Regression (NetIV) framework exploits IV information from neighborhoods to perform a two-stage regression for treatment effect estimation. Extensive experiments demonstrate that our NetIV method outperforms the state-of-the-art methods for treatment effect estimation in the presence of unmeasured confounders.

Estimating individual treatment effects in networked observational data is a crucial and increasingly recognized problem. One major challenge of this problem is violating the stable unit treatment value assumption (SUTVA), which posits that a unit’s outcome is independent of others’ treatment assignments. However, in network data, a unit’s outcome is influenced not only by its treatment (i.e., direct effect) but also by the treatments of others (i.e., spillover effect) since the presence of interference. Moreover, the interference from other units is always heterogeneous (e.g., friends with similar interests have a different influence than those with different interests). In this article, we focus on the problem of estimating individual treatment effects (including direct effect and spillover effect) under heterogeneous interference in networks. To address this problem, we propose a novel dual weighting regression (DWR) algorithm by simultaneously learning attention weights to capture the heterogeneous interference from neighbors and sample weights to eliminate the complex confounding bias in networks. We formulate the learning process as a bi-level optimization problem. Theoretically, we give a generalization error bound for the expected estimation error of the individual treatment effects. Extensive experiments on four benchmark datasets demonstrate that the proposed DWR algorithm outperforms the state-of-the-art methods in estimating individual treatment effects under heterogeneous network interference.

Domain generalization (DG) aims to learn from multiple source domains a model that can generalize well on unseen target domains. Existing DG methods mainly learn the representations with invariant marginal distribution of the input features, however, the invariance of the conditional distribution of the labels given the input features is more essential for unknown domain prediction. Meanwhile, the existing of unobserved confounders which affect the input features and labels simultaneously cause spurious correlation and hinder the learning of the invariant relationship contained in the conditional distribution. Interestingly, with a causal view on the data generating process, we find that the input features of one domain are valid instrumental variables for other domains. Inspired by this finding, we propose an instrumental variable-driven DG method (IV-DG) by removing the bias of the unobserved confounders with two-stage learning. In the first stage, it learns the conditional distribution of the input features of one domain given input features of another domain. In the second stage, it estimates the relationship by predicting labels with the learned conditional distribution. Theoretical analyses and simulation experiments show that it accurately captures the invariant relationship. Extensive experiments on real-world datasets demonstrate that IV-DG method yields state-of-the-art results.

In this paper, we focus on the problem of stable prediction across unknown test data, where the test distribution might be different from the training one and is always agnostic when model training. In such a case, previous machine learning methods might exploit subtly spurious correlations induced by non-causal variables in training data for prediction. Those spurious correlations are changeable across data, leading to instability of prediction across unknown test data. To address this problem, we propose a conditional independence test based algorithm to screen out part of non-causal features and reduce those spurious correlations for a more stable prediction by leveraging a seed variable. We show, both theoretically and with empirical experiments, that our algorithm can precisely screen out the isolated non-causal variables, which have no causal relationship with other variables, and remove the spurious correlations induced by them, increasing the stability of prediction across unknown test data. Extensive experiments on both synthetic and real-world datasets demonstrate that our algorithm outperforms state-of-the-art methods for stable prediction across unknown test data.

In many important machine learning applications, the training distribution used to learn a probabilistic classifier differs from the distribution on which the classifier will be used to make predictions. Traditional methods correct the distribution shift by reweighting training data with the ratio of the density between test and training data. However, in many applications training takes place without prior knowledge of the testing distribution. Recently, methods have been proposed to address the shift by learning the underlying causal structure, but those methods rely on diversity arising from multiple training data sets, and they further have complexity limitations in high dimensions. In this paper, we propose a novel Deep Global Balancing Regression (DGBR) algorithm to jointly optimize a deep auto-encoder model for feature selection and a global balancing model for stable prediction across unknown environments. The global balancing model constructs balancing weights that facilitate estimation of partial effects of features (holding fixed all other features), a problem that is challenging in high dimensions, and thus helps to identify stable, causal relationships between features and outcomes. The deep auto-encoder model is designed to reduce the dimensionality of the feature space, thus making global balancing easier. We show, both theoretically and with empirical experiments, that our algorithm can make stable predictions across unknown environments. Our experiments on both synthetic and real datasets demonstrate that our algorithm outperforms the state-of-the-art methods for stable prediction across unknown environments.