Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model that incorporates varying degrees of prior belief in class-conditional independence, learns whether or not independence holds, (...) and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments—designed using optimal experimental design principles—were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-conditional independence, before adapting to the true environmental structure. Class-conditional independence may be a strong and useful default assumption in category learning tasks. (shrink)

We offer a review of some of the most influential views on the status of Reichenbach’s Principle of the Common Cause (RPCC) for genuinely indeterministic systems. We first argue that the RPCC is properly a conjunction of two distinct claims, one metaphysical and another methodological. Both claims can and have been contested in the literature, but here we simply assume that the metaphysical claim is correct, in order to focus our analysis on the status of the methodological claim. We briefly (...) review the most entrenched or classical positions, including Salmon’s ‘interactive forks’, van Fraassen’s scepticism, and Cartwright’s generalisation of the fork criterion. We then go on to review the results of the ‘Budapest school’ on the existence of formally defined screening­ off events for any correlation —by means of the ideas of probability space extensibility and (Reichenbachian common cause) completability. We distinguish the Budapest doctrine clearly from any of the classical conceptions, and thus present an overall framework for discussions of causal inference in quantum mechanics. We argue that this review is preliminary essential work for a thorough assessment of the conditions under which RCCP may be a reliable tool for causal inference in a genuinely probabilistic (indeterministic) context. (shrink)

“Probabilistic Causation” designates a group of theories that aim to characterize the relationship between cause and effect using the tools of probability theory. The central idea behind these theories is that causes change the probabilities of their effects. This article traces developments in probabilistic causation, including recent developments in causal modeling. A variety of issues within, and objections to, probabilistic theories of causation will also be discussed.

This essay explains what the Causal Markov Condition says and defends the condition from the many criticisms that have been launched against it. Although we are skeptical about some of the applications of the Causal Markov Condition, we argue that it is implicit in the view that causes can be used to manipulate their effects and that it cannot be surrendered without surrendering this view of causation.

It is still a matter of controversy whether the Principle of the Common Cause (PCC) can be used as a basis for sound causal inference. It is thus to be expected that its application to quantum mechanics should be a correspondingly controversial issue. Indeed the early 90’s saw a flurry of papers addressing just this issue in connection with the EPR correlations. Yet, that debate does not seem to have caught up with the most recent literature on causal inference generally, (...) which has moved on to consider the virtues of a generalised PCC-inspired condition, the so-called Causal Markov Condition (CMC). In this paper we argue that the CMC is an appropriate benchmark for debating possible causal explanations of the EPR correlations. But we go on to take issue with some pronouncements on EPR by defenders of the CMC. (shrink)

It is still a matter of controversy whether the Principle of the Common Cause can be used as a basis for sound causal inference. It is thus to be expected that its application to quantum mechanics should be a correspondingly controversial issue. Indeed the early 90’s saw a flurry of papers addressing just this issue in connection with the EPR correlations. Yet, that debate does not seem to have caught up with the most recent literature on causal inference generally, which (...) has moved on to consider the virtues of a generalised PCC inspired condition, the so called Causal Markov Condition. In this paper we argue that the CMC is an appropriate benchmark for debating possible causal explanations of the EPR correlations. But we go on to take issue with some pronouncements on EPR by defenders of the CMC. (shrink)

We argue against the common view that it is impossible to give a causal account of the distant correlations that are revealed in EPR-type experiments. We take a realistic attitude about quantum mechanics which implies a willingness to modify our familiar concepts according to its teachings. We object to the argument that the violation of factorizability in EPR rules out causal accounts, since such an argument is at best based on the desire to retain a classical description of nature that (...) consists of processes that are continuous in space and time. We also do not think special relativity prohibits the superluminal propagation of causes in EPR, for the phenomenon of quantum measurement may very well fall outside the domain of application of special relativity. It is possible to give causal accounts of EPR as long as we are willing to take quantum mechanics seriously, and we offer two such accounts. (shrink)

The most serious candidates for common causes that fail to screen off and thus violate the causal Markov condition refer to quantum phenomena. In her seminal debate with Hausman and Woodward, Cartwright early on focussed on unfortunate non-quantum examples. Especially, Hausman and Woodward’s redescriptions of quantum cases saving the CMC remain unchallenged. This paper takes up this lose end of the discussion and aims to resolve the debate in favour of Cartwright’s position. It systematically considers redescriptions of ICC structures, including (...) those by Hausman and Woodward, and explains why these are inappropriate, when quantum mechanics is true. It first shows that all cases of purported quantum ICCs are cases of entanglement and then, using the tools of causal modelling, it provides an analysis of the quantum mechanical formalism for the case that the collapse of entangled systems is best described as a causal model with an ICC. (shrink)

We assess Cartwright's models for probabilistic causality and, in particular, her models for EPR-like experiments of quantum mechanics. Our first objection is that, contrary to econometric linear models, her quasi-linear models do not allow for the unique estimation of parameters. We next argue that although, as Cartwright proves, Reichenbach's screening-off condition has only limited validity, her generalized condition is not empirically applicable. Finally, we show that her models for the EPR are mathematically incorrect and physically implausible.

Modern empirical macroeconomic models, known as structural autoregressions (SVARs) are dynamic models that typically claim to represent a causal order among contemporaneously valued variables and to merely represent non-structural (reduced-form) co-occurence between lagged variables and contemporaneous variables. The strategy is held to meet the minimal requirements for identifying the residual errors in particular equations in the model with independent, though otherwise not directly observable, exogenous causes (“shocks”) that ultimately account for change in the model. In nonstationary models, such shocks accumulate (...) so that variables have discernible trends. Econometricians have conceived of variables that trend in sympathy with each other (so-called “cointegrated variables”) as sharing one or more of these unobserved trends as a common cause. It is possible for estimates of the values of both the otherwise unobservable individual shocks and the otherwise unobservable common trends to be backed-out of cointegrated systems of equations. The issue addressed in this paper is whether and in what circumstances these values can be regarded as observations of real entities rather than merely artifacts of the representation of variables in the model. The issue is related, on the one hand, to practical methodological problems in the use of SVARs for policy analysis—e.g., does it make sense to estimate of shocks or trends in one model and then use them as measures of variables in a conceptually distinct model? The issue is also related to debates in the philosophical analysis of causation—particularly, whether we are entitled, as assumed by the developers of Bayes-net approaches, to rely on the causal Markov condition (a generalization of Reichenbach’s common-cause condition) or whether cointegration generates a practical example of Nancy Cartwright’s “byproducts” objection to the causal Markov condition. (shrink)