Randomized Controlled Trials (RCT)s are relied upon to assess new treatments, but suffer from limited power to guide personalized treatment decisions. On the other hand, observational (i.e., non-experimental) studies have large and diverse populations, but are prone to various biases (e.g. residual confounding). To safely leverage the strengths of observational studies, we focus on the problem of falsification, whereby RCTs are used to validate causal effect estimates learned from observational data. In particular, we show that, given data from both an RCT and an observational study, assumptions on internal and external validity have an observable, testable implication in the form of a set of Conditional Moment Restrictions (CMRs). Further, we show that expressing these CMRs with respect to the causal effect, or “causal contrast”, as opposed to individual counterfactual means, provides a more reliable falsification test. In addition to giving guarantees on the asymptotic properties of our test, we demonstrate superior power and type I error of our approach on semi-synthetic and real world datasets. Our approach is interpretable, allowing a practitioner to visualize which subgroups in the population lead to falsification of an observational study.

Randomized Controlled Trials (RCTs) represent a gold standard when developing policy guidelines. However, RCTs are often narrow, and lack data on broader populations of interest. Causal effects in these populations are often estimated using observational datasets, which may suffer from unobserved confounding and selection bias. Given a set of observational estimates (e.g., from multiple studies), we propose a meta-algorithm that attempts to reject observational estimates that are biased. We do so using validation effects, causal effects that can be inferred from both RCT and observational data. After rejecting estimators that do not pass this test, we generate conservative confidence intervals on the extrapolated causal effects for subgroups not observed in the RCT. Under the assumption that at least one observational estimator is asymptotically normal and consistent for both the validation and extrapolated effects, we provide guarantees on the coverage probability of the intervals output by our algorithm. To facilitate hypothesis testing in settings where causal effect transportation across datasets is necessary, we give conditions under which a doubly-robust estimator of group average treatment effects is asymptotically normal, even when flexible machine learning methods are used for estimation of nuisance parameters. We illustrate the properties of our approach on semi-synthetic experiments based on the IHDP dataset, and show that it compares favorably to standard meta-analysis techniques.

In this paper, a robust adaptive fuzzy sliding mode controller is proposed to deal with the tracking control problem for a class of single-input single-output (SISO) perturbed strict-feedback nonlinear systems. It is known that the presence of perturbations is a very common problem in various kinds of engineering systems, and these perturbations involve unmodelled dynamics, external disturbances, and parameter variations. First, the unknown parameter vectors of strict-feedback system is on-line learned to compensate their effects. Besides the parameter variations, the upper bounds of these perturbations are often difficult to be obtained. Therefore, fuzzy logic systems and adaptive laws are applied to approximate the unknown upper bounds of the remained perturbations. In addition, the absolute minimum between the upper bound of perturbation and its learning function is updated to enhance the system performance. By introducing Lyapunov stability theorem as well as the theory of sliding mode control, not only the robust stability of the overall system can be ensured, but also good tracking performance can be obtained. Finally, an example of spring-mass-damper nonlinear system in the presence of perturbations confirms the effectiveness and the feasibility of the proposed control.