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We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…

Estimation of individual treatment effects is commonly used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, it is often sufficient for the decision maker to have estimates of…

Modern causal decision-making increasingly demands individualized treatment-effect estimation in networks where interventions are high-dimensional, combinatorial vectors. While network interference, effect heterogeneity, and…

The problem of individualization is recognized as crucial in almost every field. Identifying causes of effects in specific events is likewise essential for accurate decision making. However, such estimates invoke counterfactual…

Semiparametric efficient estimation of various multi-valued causal effects, including quantile treatment effects, is important in economic, biomedical, and other social sciences. Under the unconfoundedness condition, adjustment for…

Under interference, the treatment of one unit may affect the outcomes of other units. Such interference patterns between units are typically represented by a network. Correctly specifying this network requires identifying which units can…

A common concern when a policymaker draws causal inferences from and makes decisions based on observational data is that the measured covariates are insufficiently rich to account for all sources of confounding, i.e., the standard no…

The explainability of Graph Neural Networks (GNNs) is critical to various GNN applications, yet it remains a significant challenge. A convincing explanation should be both necessary and sufficient simultaneously. However, existing GNN…

This paper deals with the problem of estimating the probabilities of causation when treatment and effect are not binary. Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency (PNS), the probability of…

Neural networks are universal approximators and are studied for their use in solving differential equations. However, a major criticism is the lack of error bounds for obtained solutions. This paper proposes a technique to rigorously…

In contrast to problems of interference in (exogenous) treatments, models of interference in unit-specific (endogenous) outcomes do not usually produce a reduced-form representation where outcomes depend on other units' treatment status…

Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

There is intense interest in applying machine learning to problems of causal inference in fields such as healthcare, economics and education. In particular, individual-level causal inference has important applications such as precision…

In observational studies, confounding variables affect both treatment and outcome. Moreover, instrumental variables also influence the treatment assignment mechanism. This situation sets the study apart from a standard randomized controlled…

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for…

Practitioners in diverse fields such as healthcare, economics and education are eager to apply machine learning to improve decision making. The cost and impracticality of performing experiments and a recent monumental increase in electronic…

Bounding causal effects analytically, rather than numerically, is appealing for its interpretability and conceptual clarity. Existing sharp methods rely on optimization-based approaches such as the Balke-Pearl framework, whose computational…

Estimating treatment effects in networks is challenging, as each potential outcome depends on the treatments of all other nodes in the network. To overcome this difficulty, existing methods typically impose an exposure mapping that…

The neural process (NP) is a family of computationally efficient models for learning distributions over functions. However, it suffers from under-fitting and shows suboptimal performance in practice. Researchers have primarily focused on…