PhD Defense: Causal Programming

Joshua Brulé

Abstract

Causality is central to scientific inquiry. There is broad agreement on the meaning of causal statements, such as ``Smoking causes cancer'', or, ``Applying pesticides affects crop yields''. However, formalizing the intuition underlying such statements and conducting rigorous inference is difficult in practice. Accordingly, the overall goal of this dissertation is to reduce the difficulty of, and ambiguity in, causal modeling and inference. In other words, the goal is to make it easy for researchers to state precise causal assumptions, understand what they represent, understand why they are necessary, and to yield precise causal conclusions with minimal difficulty.

Using the framework of structural causal models, I introduce a causation coefficient as an analogue of the correlation coefficient, analyze its properties, and create a taxonomy of correlation/causation relationships. Analyzing these relationships provides insight into why correlation and causation are often conflated in practice, as well as a principled argument as to why formal causal analysis is necessary. Next, I introduce a theory of causal programming that unifies a large number of previously separate problems in causal modeling and inference. I describe the use and implementation of a causal programming language as an embedded, domain-specific language called `Whittemore'. Whittemore permits rigorously identifying and estimating interventional queries without requiring the user to understand the details of the underlying inference algorithms. Finally, I analyze the computational complexity in determining the equilibrium distribution of cyclic causal models. I show this is uncomputable in the general case, under mild assumptions about the distributions of the model's variables, suggesting that the structural causal model focus on acyclic causal models is a `natural' limitation. Further extensions of the concept will have to give up either completeness or require the user to make additional --- likely parametric --- model assumptions.

Together, this work supports the thesis that rigorous causal modeling and inference can be effectively abstracted over, giving a researcher access to all of the relevant details of causal modeling while encapsulating and automating the irrelevant details of inference.

Using the framework of structural causal models, I introduce a causation coefficient as an analogue of the correlation coefficient, analyze its properties, and create a taxonomy of correlation/causation relationships. Analyzing these relationships provides insight into why correlation and causation are often conflated in practice, as well as a principled argument as to why formal causal analysis is necessary. Next, I introduce a theory of causal programming that unifies a large number of previously separate problems in causal modeling and inference. I describe the use and implementation of a causal programming language as an embedded, domain-specific language called `Whittemore'. Whittemore permits rigorously identifying and estimating interventional queries without requiring the user to understand the details of the underlying inference algorithms. Finally, I analyze the computational complexity in determining the equilibrium distribution of cyclic causal models. I show this is uncomputable in the general case, under mild assumptions about the distributions of the model's variables, suggesting that the structural causal model focus on acyclic causal models is a `natural' limitation. Further extensions of the concept will have to give up either completeness or require the user to make additional --- likely parametric --- model assumptions.

Together, this work supports the thesis that rigorous causal modeling and inference can be effectively abstracted over, giving a researcher access to all of the relevant details of causal modeling while encapsulating and automating the irrelevant details of inference.

Examining Committee:

Chair: Dr. James Reggia

Dean's rep: Dr. Derek Paley

Members: Dr. Dana Nau

Dr. Mihai Pop

Dr. William Gasarch

Dean's rep: Dr. Derek Paley

Members: Dr. Dana Nau

Dr. Mihai Pop

Dr. William Gasarch

This talk is organized by Tom Hurst