Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams

We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also prove some necessary and some sufficient conditions for distributional equivalence of BAPs which are used in an algorithmic ap- proach to compute (nearly) equivalent model structures. This allows us to infer lower bounds of causal effects. We also present applications to real and simulated datasets using our publicly available R-package

Assessing bias in the estimation of causal effects: Rosenbaum bounds on matching estimators and instrumental variables estimation with imperfect instruments

Propensity score matching provides an estimate of the effect of a treatment variable on an outcome variable that is largely free of bias arising from an association between treatment status and observable variables. However, matching methods are not robust against hidden bias arising from unobserved variables that simultaneously affect assignment to treatment and the outcome variable. One strategy for addressing this problem is the Rosenbaum bounds approach, which allows the analyst to determine how strongly an unmeasured confounding variable must affect selection into treatment in order to undermine the conclusions about causal effects from a matching analysis. Instrumental variables (IV) estimation provides an alternative strategy for the estimation of causal effects, but the method typically reduces the precision of the estimate and has an additional source of uncertainty that derives from the untestable nature of the assumptions of the IV approach. A method of assessing this additional uncertainty is proposed so that the total uncertainty of the IV approach can be compared with the Rosenbaum bounds approach to uncertainty using matching methods. Because the approaches rely on different information and different assumptions, they provide complementary information about causal relationships. The approach is illustrated via an analysis of the impact of unemployment insurance on the timing of reemployment, the postunemployment wage, and the probability of relocation, using data from several panels of the Survey of Income and Program Participation (SIPP). -- Propensity score matching ermöglicht die verzerrungsfreie Abschätzung der Kausalwirkung einer treatment-Variable auf eine Ergebnisvariable sofern Verzerrungen allein aus dem Zusammenhang zwischen Kausalfaktor und beobachteten Kovariaten resultieren. Matchingverfahren sind allerdings anfällig für Schätzverzerrungen aufgrund von hidden bias durch unbeobachtete Variablen, die sowohl die Zuweisung des Kausalfaktors als auch die Ergebnisvariable bestimmen. Im letzteren Fall besteht eine mögliche Strategie darin, mit Hilfe der Methode der sogenannten Rosenbaumschranken abzuschätzen, wie stark der Einfluss unbeobachteter Kovariaten auf die Zuweisung des Kausalstatus sein müsste, um die beabsichtigten Schlussfolgerungen im Hinblick auf den interessierenden kausalen Effekt qualitativ zu verändern. Instrumentalvariablenschätzer (IV) wären ein zweites Verfahren, um in dieser Situation kausale Effekte abschätzen zu können, allerdings führt das Verfahren in der Regel zu wenig präzisen Schätzungen und beinhaltet in der Anwendung zusätzliche Unsicherheiten aufgrund der empirisch nicht testbaren Annahmen des IV-Ansatzes. In diesem Aufsatz wird eine Methode zur Abschätzung dieser Unsicherheiten vorgeschlagen, wodurch die potentiellen Verzerrungen innerhalb einer IV-Schätzung mit den durch die Rosenbaumschranken abgeschätzten Verzerrungen innerhalb eines entsprechenden Matchingansatzes verglichen werden können. Da diesen Verfahren jeweils unterschiedliche Informationsgrundlage sowie unterschiedliche Annahmen zugrunde liegen, erbringen sie komplementäre Informationen über den Gehalt kausaler Beziehungen. Wir illustrieren die vorgeschlagene Vorgehensweise anhand einer Analyse des kausalen Effekts der Arbeitslosenversicherung auf die Dauer der Arbeitslosigkeit, den Lohn bei Wiederbeschäftigung sowie der Wahrscheinlichkeit geographischer Mobilität auf der Basis von Daten des amerikanischen Survey of Income and Program Participation (SIPP).

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

Learning stable and predictive structures in kinetic systems: Benefits of a causal approach

Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called CausalKinetiX, that identifies structure from discrete time, noisy observations, generated from heterogeneous experiments. The algorithm assumes the existence of an underlying, invariant kinetic model, a key criterion for reproducible research. Results on both simulated and real-world examples suggest that learning the structure of kinetic systems benefits from a causal perspective. The identified variables and models allow for a concise description of the dynamics across multiple experimental settings and can be used for prediction in unseen experiments. We observe significant improvements compared to well established approaches focusing solely on predictive performance, especially for out-of-sample generalization

Active inference and oculomotor pursuit: the dynamic causal modelling of eye movements.

This paper introduces a new paradigm that allows one to quantify the Bayesian beliefs evidenced by subjects during oculomotor pursuit. Subjects' eye tracking responses to a partially occluded sinusoidal target were recorded non-invasively and averaged. These response averages were then analysed using dynamic causal modelling (DCM). In DCM, observed responses are modelled using biologically plausible generative or forward models - usually biophysical models of neuronal activity

Graphical models for mediation analysis

Mediation analysis seeks to infer how much of the effect of an exposure on an outcome can be attributed to specific pathways via intermediate variables or mediators. This requires identification of so-called path-specific effects. These express how a change in exposure affects those intermediate variables (along certain pathways), and how the resulting changes in those variables in turn affect the outcome (along subsequent pathways). However, unlike identification of total effects, adjustment for confounding is insufficient for identification of path-specific effects because their magnitude is also determined by the extent to which individuals who experience large exposure effects on the mediator, tend to experience relatively small or large mediator effects on the outcome. This chapter therefore provides an accessible review of identification strategies under general nonparametric structural equation models (with possibly unmeasured variables), which rule out certain such dependencies. In particular, it is shown which path-specific effects can be identified under such models, and how this can be done