Causality and Generalizability: Identifiability and Learning Methods

by   Martin Emil Jakobsen, et al.

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.


Structure Learning for Directed Trees

Knowing the causal structure of a system is of fundamental interest in m...

Distributional Robustness of K-class Estimators and the PULSE

In causal settings, such as instrumental variable settings, it is well k...

Inference for Individual Mediation Effects and Interventional Effects in Sparse High-Dimensional Causal Graphical Models

We consider the problem of identifying intermediate variables (or mediat...

Causality-oriented robustness: exploiting general additive interventions

Since distribution shifts are common in real-world applications, there i...

The Difficult Task of Distribution Generalization in Nonlinear Models

We consider the problem of predicting a response from a set of covariate...

The Causal Learning of Retail Delinquency

This paper focuses on the expected difference in borrower's repayment wh...

Please sign up or login with your details

Forgot password? Click here to reset