Humans build theories out of the data we observe, and out of those theories arise wonders. The most powerful theories are causal theories, which organise data into actionable structures. Causal theories make explicit claims about the structure of the world: what entities and processes exist in it, which of these relate to one another and in what form those relations consist. We can use causal theories to induce new generalisations about the world (in the form of particular models or other causal theories) and to explain particular occurrences. This allows rapidly disseminating causal information throughout our cognitive communities. Causal theories and the explanations derived from them guide decisions we make, including where and when to look for more data, completing the cycle.
Causal theories play a ubiquitous and potent role in everyday life, in formal pursuit of them in the sciences, and through their applications in medicine, technology and industry. Given this, the rarity of analyses that attempt to characterise causal theories and their uses in general, computational terms is surprising. Only in recent years has there been a substantial refinement of our models of causal induction due to work by computational cognitive scientists — the interdisciplinary tradition out of which which this dissertation originates. And even so, many issues related to causal theories have been left unattended; three features in particular merit much greater attention from a computational perspective: generating and evaluating explanation, the role of simplicity in explanation choice, and continuous-time causal induction. I aim to redress this situation with this dissertation.
In Chapter 0, I introduce the primary paradigms from computational cognitive science – computational level analysis and rational analysis – that govern my research. In Chapter 1, I study formal theories of causal explanation in Bayesian networks by comparing the explanations the generate and evaluate to human judgements about the same systems. No one model of causal explanation captures the pattern of human judgements, though the intuitive hypothesis, that the most probable a posteriori explanation is the best performs worst of the models evaluated. I conclude that the premise of finding model for all of human causal explanation (even in this limited domain) is flawed; the research programme should be refined to consider the features of formal models and how well they capture our explanatory practices as they vary between individuals and circumstances. One feature not expressed in these models explicitly but that has been shown to matter for human explanation is simplicity. Chapter 2 considers the problem of simplicity in human causal explanation choice in a series of four experiments. I study what makes an explanation simple (whether it is the number of causes invoked in or the number of assumptions made by an explanation), how simplicity concerns are traded off against data-fit, which cognitive consequences arise from choosing simpler explanations when the data does not fit, and why people prefer simpler explanations.
In Chapter 3, I change the focus from studying causal explanation to causal induction --- in particular, I develop a framework for continuous time causal theories (ctcts). A ctct defines a generative probabilistic framework for other generative probabilistic models of causal systems, where the data in those systems expressed in terms of continuous time. Chapter 3 is the most interdisciplinary piece of my dissertation, accordingly it begins by reviewing a number of topics: the history of theories of causal induction within philosophy, statistics and medicine; empirical work on causal induction in cognitive science, focusing on issues related to causal induction with temporal data; conceptual issues surrounding the formal definition of time, data, and causal models; and probabilistic graphical models, causal theories, and stochastic processes. I then introduce the desiderata for the ctct framework and how those criteria are met. I then demonstrate the power of ctcts by using them to analyse five sets of experiments (some new and some derived from the literature) on human causal induction with temporal data. Bookending each experiment and the model applied to it is are case from medical history that illustrate a real-world instance of the variety of problem being solved in the section; the opening discussion describes the case and why it fits the problem structure of the model used to analyse the experimental results and the closing discussion illustrates aspects of the case omitted from the initial discussion that complicate the model and fit better with the model introduced in the next section. Then, I discuss ways to incorporate other advances in probabilistic programming, generative theories and stochastic processes into the ctct framework, identify potential applications with specific focus on mechanisms and feedback loops, and conclude by analysing the centrality of temporal information in the study of the mind more generally.
Excepting the supporting appendices and bibliography that end the dissertation, I conclude in two parts. First, in Chapter 4, I analyse issues at the intersection of three of the main themes of my work: namely, (causal) explanation, (causal) induction and time. This proceeds by examining these topics first in pairs and then as a whole. Following that, is Chapter 5, an epilogue that clarifies the interpretations and intended meanings of the “Mind as Theory Engine” metaphor as it applies to human cognition.