Rickard K. A. Karlsson

Rickard K. A. Karlsson, Jesse H. Krijthe

A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms underlying the data-generating process, we demonstrate a way to detect unobserved confounders when having multiple observational datasets coming from different environments. We present a theory for testable conditional independencies that are only absent when there is hidden confounding and examine cases where we violate its assumptions: degenerate & dependent mechanisms, and faithfulness violations. Additionally, we propose a procedure to test these independencies and study its empirical finite-sample behavior using simulation studies and semi-synthetic data based on a real-world dataset. In most cases, the proposed procedure correctly predicts the presence of hidden confounding, particularly when the confounding bias is large.

Rickard K. A. Karlsson, Jesse H. Krijthe

A major challenge in estimating treatment effects in observational studies is the reliance on untestable conditions such as the assumption of no unmeasured confounding. In this work, we propose an algorithm that can falsify the assumption of no unmeasured confounding in a setting with observational data from multiple heterogeneous sources, which we refer to as environments. Our proposed falsification strategy leverages a key observation that unmeasured confounding can cause observed causal mechanisms to appear dependent. Building on this observation, we develop a novel two-stage procedure that detects these dependencies with high statistical power while controlling false positives. The algorithm does not require access to randomized data and, in contrast to other falsification approaches, functions even under transportability violations when the environment has a direct effect on the outcome of interest. To showcase the practical relevance of our approach, we show that our method is able to efficiently detect confounding on both simulated and semi-synthetic data.

Rickard K. A. Karlsson, Martin Willbo, Zeshan Hussain et al.

We study prediction of future outcomes with supervised models that use privileged information during learning. The privileged information comprises samples of time series observed between the baseline time of prediction and the future outcome; this information is only available at training time which differs from the traditional supervised learning. Our question is when using this privileged data leads to more sample-efficient learning of models that use only baseline data for predictions at test time. We give an algorithm for this setting and prove that when the time series are drawn from a non-stationary Gaussian-linear dynamical system of fixed horizon, learning with privileged information is more efficient than learning without it. On synthetic data, we test the limits of our algorithm and theory, both when our assumptions hold and when they are violated. On three diverse real-world datasets, we show that our approach is generally preferable to classical learning, particularly when data is scarce. Finally, we relate our estimator to a distillation approach both theoretically and empirically.