17 research outputs found
Robust causal structure learning with some hidden variables
We introduce a new method to estimate the Markov equivalence class of a
directed acyclic graph (DAG) in the presence of hidden variables, in settings
where the underlying DAG among the observed variables is sparse, and there are
a few hidden variables that have a direct effect on many of the observed ones.
Building on the so-called low rank plus sparse framework, we suggest a
two-stage approach which first removes the effect of the hidden variables, and
then estimates the Markov equivalence class of the underlying DAG under the
assumption that there are no remaining hidden variables. This approach is
consistent in certain high-dimensional regimes and performs favourably when
compared to the state of the art, both in terms of graphical structure recovery
and total causal effect estimation
Estimating the effect of joint interventions from observational data in sparse high-dimensional settings
We consider the estimation of joint causal effects from observational data.
In particular, we propose new methods to estimate the effect of multiple
simultaneous interventions (e.g., multiple gene knockouts), under the
assumption that the observational data come from an unknown linear structural
equation model with independent errors. We derive asymptotic variances of our
estimators when the underlying causal structure is partly known, as well as
high-dimensional consistency when the causal structure is fully unknown and the
joint distribution is multivariate Gaussian. We also propose a generalization
of our methodology to the class of nonparanormal distributions. We evaluate the
estimators in simulation studies and also illustrate them on data from the
DREAM4 challenge.Comment: 30 pages, 3 figures, 45 pages supplemen
Detection and Mitigation of Algorithmic Bias via Predictive Rate Parity
Recently, numerous studies have demonstrated the presence of bias in machine
learning powered decision-making systems. Although most definitions of
algorithmic bias have solid mathematical foundations, the corresponding bias
detection techniques often lack statistical rigor, especially for non-iid data.
We fill this gap in the literature by presenting a rigorous non-parametric
testing procedure for bias according to Predictive Rate Parity, a commonly
considered notion of algorithmic bias. We adapt traditional asymptotic results
for non-parametric estimators to test for bias in the presence of dependence
commonly seen in user-level data generated by technology industry applications
and illustrate how these approaches can be leveraged for mitigation. We further
propose modifications of this methodology to address bias measured through
marginal outcome disparities in classification settings and extend notions of
predictive rate parity to multi-objective models. Experimental results on real
data show the efficacy of the proposed detection and mitigation methods