arXiv subjects

Tobias Freidling

Publications and source records attributed to Tobias Freidling.

5 recordsLinked to original sources

arXiv2026

Counterfactual Optimization of Policy Interventions: Lexical Ordering and Leapfrogging

Most data-driven policy learning methods maximize average outcomes, overlooking the possibility that a policy beneficial on average may still harm a substantial fraction of individuals. Motivated by the ethical principle of "first do no harm", we study how to design a change from a baseline policy that improves overall welfare while keeping the worst-case probability or expectation of individual harm below a specified limit. We establish sufficient conditions under which an optimal policy transition has a lexical leapfrogging structure: groups defined by covariates and current treatment are ranked by a priority score, and any treatment change moves them directly to the conditionally optimal treatment. We derive this score under several models for the dependence among potential outcomes. We demonstrate this harm-aware policy optimization approach in a reanalysis of the I-SPY2 breast cancer platform trial and show how the consideration of counterfactual harm may lead to different conclusions about which treatment-subgroup pairs may warrant deprioritization in further clinical evaluation.

stat.ME↗

arXiv2026

Selective Randomization Inference for Adaptive Experiments

Adaptive experiments use preliminary analyses of the data to inform further course of action and are commonly used in many disciplines including medical and social sciences. Because the null hypothesis and experimental design are data-dependent, it has long been recognized that statistical inference for adaptive experiments is not straightforward. Most existing methods only apply to specific adaptive designs and rely on strong assumptions. In this work, we propose selective randomization inference as a general framework for analysing adaptive experiments. In a nutshell, our approach applies conditional post-selection inference to randomization tests. By using directed acyclic graphs to describe the data generating process, we derive a selective randomization p-value that controls the selective type-I error. As inference only relies on the randomness in the treatment assignment, no modelling assumptions or independent and identically distributed data are needed. We elaborate on conditions that render the proposed p-value computable and provide rejection sampling and MCMC algorithms to find a Monte Carlo approximation. Moreover, this article shows how to estimate and construct confidence intervals for a homogeneous treatment effect. Lastly, we demonstrate our method and compare it with other randomization tests using synthetic and real-world data.

stat.ME↗

arXiv2025

Optimization-based Sensitivity Analysis for Unmeasured Confounding using Partial Correlations

Causal inference necessarily relies upon untestable assumptions; hence, it is crucial to assess the robustness of obtained results to violations of identification assumptions. However, such sensitivity analysis is only occasionally undertaken in practice, as many existing methods require analytically tractable solutions and their results are often difficult to interpret. We take a more flexible approach to sensitivity analysis and view it as a constrained stochastic optimization problem. This work focuses on sensitivity analysis for a linear causal effect when an unmeasured confounder and a potential instrument are present. We show how the bias of the OLS and TSLS estimands can be expressed in terms of partial correlations. Leveraging the algebraic rules that relate different partial correlations, practitioners can specify intuitive sensitivity models which bound the bias. We further show that the heuristic "plug-in" sensitivity interval may not have any confidence guarantees; instead, we propose a bootstrap approach to construct sensitivity intervals which performs well in numerical simulations. We illustrate the proposed methods with a real study on the causal effect of education on earnings and provide user-friendly visualization tools.

stat.ME↗

arXiv2021

Post-selection inference with HSIC-Lasso

Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection inference. Indeed, the selected features can be significantly flawed when the selection procedure is not accounted for. We propose a selective inference procedure using the so-called model-free "HSIC-Lasso" based on the framework of truncated Gaussians combined with the polyhedral lemma. We then develop an algorithm, which allows for low computational costs and provides a selection of the regularisation parameter. The performance of our method is illustrated by both artificial and real-world data based experiments, which emphasise a tight control of the type-I error, even for small sample sizes.

math.ST↗

arXiv2021

Confidence in Causal Discovery with Linear Causal Models

Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which other variables it causally depends upon. Under a number of different model assumptions, it has been shown that this causal graph and, thus also, causal effects are identifiable from mere observational data. For these models, practical algorithms have been devised to learn the graph. Moreover, when the graph is known, standard techniques may be used to give estimates and confidence intervals for causal effects. We argue, however, that a two-step method that first learns a graph and then treats the graph as known yields confidence intervals that are overly optimistic and can drastically fail to account for the uncertain causal structure. To address this issue we lay out a framework based on test inversion that allows us to give confidence regions for total causal effects that capture both sources of uncertainty: causal structure and numerical size of nonzero effects. Our ideas are developed in the context of bivariate linear causal models with homoscedastic errors, but as we exemplify they are generalizable to larger systems as well as other settings such as, in particular, linear non-Gaussian models.

math.ST↗