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The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. A standard approach reduces the problem to a finite…

The recent availability of huge, many-dimensional data sets, like those arising from genome-wide association studies (GWAS), provides many opportunities for strengthening causal inference. One popular approach is to utilize these…

Instrumental variable methods are often used for parameter estimation in the presence of confounding. They can also be applied in stochastic processes. Instrumental variable analysis exploits moment equations to obtain estimators for causal…

Since Pearson [Philosophical Transactions of the Royal Society of London. A, 185 (1894), pp. 71-110] first applied the method of moments (MM) for modeling data as a mixture of one-dimensional Gaussians, moment-based estimation methods have…

A major limitation of machine learning (ML) prediction models is that they recover associational, rather than causal, predictive relationships between variables. In high-stakes automation applications of ML this is problematic, as the model…

Instrumental variable methods are fundamental to causal inference when treatment assignment is confounded by unobserved variables. In this article, we develop a general nonparametric causal framework for identification and learning with…

The instrumental variable method is widely used in the health and social sciences for identification and estimation of causal effects in the presence of potentially unmeasured confounding. In order to improve efficiency, multiple…

Instrumental variable (IV) methods are used to estimate causal effects in settings with unobserved confounding, where we cannot directly experiment on the treatment variable. Instruments are variables which only affect the outcome…

Instrumental variables are a popular tool to infer causal effects under unobserved confounding, but choosing suitable instruments is challenging in practice. We propose gIVBMA, a Bayesian model averaging procedure that addresses this…

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypic variation, there is increasing…

Moment-based estimation is a theoretically attractive approach to parametric inference, especially when likelihood-based estimation is unavailable, misspecified, or computationally inconvenient. However, the moment equations involve sample…

Recent works have proposed regression models which are invariant across data collection environments. These estimators often have a causal interpretation under conditions on the environments and type of invariance imposed. One recent…

Causal inference is the process of using assumptions, study designs, and estimation strategies to draw conclusions about the causal relationships between variables based on data. This allows researchers to better understand the underlying…

Weak identification arises in many statistical problems when key variables exhibit weak correlations-for example, when instrumental variables correlate weakly with treatment, or when proxy variables correlate weakly with unmeasured…

A common issue in learning decision-making policies in data-rich settings is spurious correlations in the offline dataset, which can be caused by hidden confounders. Instrumental variable (IV) regression, which utilises a key unconfounded…

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular…

We are in the middle of a remarkable rise in the use and capability of artificial intelligence. Much of this growth has been fueled by the success of deep learning architectures: models that map from observables to outputs via multiple…

We study estimation and inference using data collected by reinforcement learning (RL) algorithms. These algorithms adaptively experiment by interacting with individual units over multiple stages, updating their strategies based on past…

The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical…