Lee M. Gunderson

David S. Watson, Jordan Penn, Lee M. Gunderson et al.

Instrumental variables (IVs) are a popular and powerful tool for estimating causal effects in the presence of unobserved confounding. However, classical approaches rely on strong assumptions such as the $\textit{exclusion criterion}$, which states that instrumental effects must be entirely mediated by treatments. This assumption often fails in practice. When IV methods are improperly applied to data that do not meet the exclusion criterion, estimated causal effects may be badly biased. In this work, we propose a novel solution that provides $\textit{partial}$ identification in linear systems given a set of $\textit{leaky instruments}$, which are allowed to violate the exclusion criterion to some limited degree. We derive a convex optimization objective that provides provably sharp bounds on the average treatment effect under some common forms of information leakage, and implement inference procedures to quantify the uncertainty of resulting estimates. We demonstrate our method in a set of experiments with simulated data, where it performs favorably against the state of the art. An accompanying $\texttt{R}$ package, $\texttt{leakyIV}$, is available from $\texttt{CRAN}$.

Gecia Bravo-Hermsdorff, Robert Busa-Fekete, Lee M. Gunderson et al.

Data anonymization is an approach to privacy-preserving data release aimed at preventing participants reidentification, and it is an important alternative to differential privacy in applications that cannot tolerate noisy data. Existing algorithms for enforcing $k$-anonymity in the released data assume that the curator performing the anonymization has complete access to the original data. Reasons for limiting this access range from undesirability to complete infeasibility. This paper explores ideas -- objectives, metrics, protocols, and extensions -- for reducing the trust that must be placed in the curator, while still maintaining a statistical notion of $k$-anonymity. We suggest trust (amount of information provided to the curator) and privacy (anonymity of the participants) as the primary objectives of such a framework. We describe a class of protocols aimed at achieving these goals, proposing new metrics of privacy in the process, and proving related bounds. We conclude by discussing a natural extension of this work that completely removes the need for a central curator.