David Danks

Erratum to: Synthese DOI 10.1007/s11229-014-0408-3Appendix 1: NotationLet \(X\) represent a sequence of data, and let \(X_B^t\) represent an i.i.d. subsequence of length \(t\) of data generated from distribution \(B\).We conjecture that the i.i.d. assumption could be eliminated by defining probability distributions over sequences of arbitrary length, though this complication would not add conceptual clarity. Let \(\mathbf{F}\) be a framework (in this case, a set of probability distributions or densities).Let any \(P(\,)\) functions be either a probability distribution function or probability density function, as appropriate. Let \(M_\mathbf{F}\) be a method that takes a data sequence \(X\) as input and outputs a distribution

Even if one can experiment on relevant factors, learning the causal structure of a dynamical system can be quite difficult if the relevant measurement processes occur at a much slower sampling rate than the “true” underlying dynamics. This problem is exacerbated if the degree of mismatch is unknown. This paper gives a formal characterization of this learning problem, and then provides two sets of results. First, we prove a set of theorems characterizing how causal structures change under undersampling. Second, we develop an algorithm for inferring aspects of the causal structure at the “true” timescale from the causal structure learned from the undersampled data. Research on causal learning in dynamical contexts has largely ignored the challenges of undersampling, but this paper provides a framework and foundation for learning causal structure from this type of complex time series data

We evaluate the asymptotic performance of boundedly-rational strategies in multi-armed bandit problems, where performance is measured in terms of the tendency (in the limit) to play optimal actions in either (i) isolation or (ii) networks of other learners. We show that, for many strategies commonly employed in economics, psychology, and machine learning, performance in isolation and performance in networks are essentially unrelated. Our results suggest that the appropriateness of various, common boundedly-rational strategies depends crucially upon the social context (if any) in which such strategies are to be employed.

We argue that current discussions of criteria for actual causation are ill-posed in several respects. (1) The methodology of current discussions is by induction from intuitions about an infinitesimal fraction of the possible examples and counterexamples; (2) cases with larger numbers of causes generate novel puzzles; (3) "neuron" and causal Bayes net diagrams are, as deployed in discussions of actual causation, almost always ambiguous; (4) actual causation is (intuitively) relative to an initial system state since state changes are relevant, but most current accounts ignore state changes through time; (5) more generally, there is no reason to think that philosophical judgements about these sorts of cases are normative; but (6) there is a dearth of relevant psychological research that bears on whether various philosophical accounts are descriptive. Our skepticism is not directed towards the possibility of a correct account of actual causation; rather, we argue that standard methods will not lead to such an account. A different approach is required

A pervasive feature of the sciences, particularly the applied sciences, is an experimental focus on a few (often only one) possible causal connections. At the same time, scientists often advance and apply relatively broad models that incorporate many different causal mechanisms. We are naturally led to ask whether there are normative rules for integrating multiple local experimental conclusions into models covering many additional variables. In this paper, we provide a positive answer to this question by developing several inference rules that use local causal models to place constraints on the integrated model, given quite general assumptions. We also demonstrate the practical value of these rules by applying them to a case study from ecology. Experimental scope in applied sciences Fusing the results of experiments A concrete example of the inference rules Application to a case study.

Arguments, claims, and discussions about the “level of description” of a theory are ubiquitous in cognitive science. Such talk is typically expressed more precisely in terms of the granularity of the theory, or in terms of Marr’s three levels. I argue that these ways of understanding levels of description are insufficient to capture the range of different types of theoretical commitments that one can have in cognitive science. When we understand these commitments as points in a multi-dimensional space, we find that we must also reconsider our understanding of intertheoretic relations. In particular, we should understand cognitive theories as constraining one another, rather than reducing to one another