David Danks

Structure learning algorithms for graphical models have focused almost exclusively on stable environments in which the underlying generative process does not change; that is, they assume that the generating model is globally stationary. In real-world environments, however, such changes often occur without warning or signal. Real-world data often come from generating models that are only locally stationary. In this paper, we present LoSST, a novel, heuristic structure learning algorithm that tracks changes in graphical model structure or parameters in a dynamic, real-time manner. We show by simulation that the algorithm performs comparably to batch-mode learning when the generating graphical structure is globally stationary, and significantly better when it is only locally stationary

Many different, seemingly mutually exclusive, theories of categorization have been proposed in recent years. The most notable theories have been those based on prototypes, exemplars, and causal models. This chapter provides “representation theorems” for each of these theories in the framework of probabilistic graphical models. More specifically, it shows for each of these psychological theories that the categorization judgments predicted and explained by the theory can be wholly captured using probabilistic graphical models. In other words, probabilistic graphical models provide a lingua franca for these disparate categorization theories, and so we can quite directly compare the different types of theories. These formal results are used to explain a variety of surprising empirical results, and to propose several novel theories of categorization.

It is “well known” that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of “instrumental variables” sometimes permits an estimation of the influence of one variable on another even when the association between the variables may be confounded by unobserved common causes; (3) the association (or conditional probability distribution of one variable given another) of two variables connected by a path or pair of paths with a single common vertex (a trek) can be computed directly from the parameter values associated with each edge in the trek; (4) the association of two variables produced by multiple treks can be computed from the parameters associated with each trek; and (5) the independence of two variables conditional on a third implies the corresponding independence of the sums of the variables over all units conditional on the sums over all units of each of the original conditioning variables.

Causal structure learning from time series data is a major scientific challenge. Existing algorithms assume that measurements occur sufficiently quickly; more precisely, they assume that the system and measurement timescales are approximately equal. In many scientific domains, however, measurements occur at a significantly slower rate than the underlying system changes. Moreover, the size of the mismatch between timescales is often unknown. This paper provides three distinct causal structure learning algorithms, all of which discover all dynamic graphs that could explain the observed measurement data as arising from undersampling at some rate. That is, these algorithms all learn causal structure without assuming any particular relation between the measurement and system timescales; they are thus rate-agnostic. We apply these algorithms to data from simulations. The results provide insight into the challenge of undersampling

The Rescorla–Wagner model has been a leading theory of animal causal induction for nearly 30 years, and human causal induction for the past 15 years. Recent theories 367) have provided alternative explanations of how people draw causal conclusions from covariational data. However, theoretical attempts to compare the Rescorla–Wagner model with more recent models have been hampered by the fact that the Rescorla–Wagner model is an algorithmic theory, while the more recent theories are all computational. This paper provides a detailed derivation of the long-run behavior of the Rescorla– Wagner model under a wide range of parameters and experimental setups, so that the model can be compared with computational theories. It also shows that the model agrees with competing theories on a wider range of cases than had previously been thought. The paper concludes by showing how recently suggested modifications of the Rescorla–Wagner model impact the long-run behavior of the model

Various causal details of the genetic process of translation have been singled out to account for its privileged status as a ‘code'. We explicate the biological uses of coding talk by characterizing a class of special causal processes in which topological properties are the causally relevant ones. This class contains both the process of translation and communication theoretic coding processes as special cases. We propose a formalism in terms of graphs for expressing our theory of biological codes and discuss its utility in understanding biological systems. *Received May 2007; revised May 2008. †To contact the authors, please write to: Department of Philosophy, Baker Hall 135, Carnegie Mellon University, Pittsburgh, PA 15213; e-mail: [email protected] or [email protected].

It is the height of banality to observe that people, not bullets, fight kinetic wars. The machinery of kinetic warfare is obviously relevant to the conduct of each particular act of warfare, but the reasons for, and meanings of, those acts depend critically on the fact that they are done by humans. Any attempt to understand warfare—its causes, strategies, legitimacy, dynamics, and resolutions—must incorporate humans as an intrinsic part, both descriptively and normatively. Humans from general staff to “boots on the ground” play key roles in all aspects of kinetic warfare, and the literature about it reflects this focus. 2 In contrast, many discussions of cyberwarfare and cyber-conflict focus principally on the technical aspects of machines, systems, and data, 3 and human agents are included only as collateral effects, or as loci of moral responsibility

Causal structure learning algorithms have focused on learning in ”batch-mode”: i.e., when a full dataset is presented. In many domains, however, it is important to learn in an online fashion from sequential or ordered data, whether because of memory storage constraints or because of potential changes in the underlying causal structure over the course of learning. In this paper, we present TDSL, a novel causal structure learning algorithm that processes data sequentially. This algorithm can track changes in the generating causal structure or parameters, and requires significantly less memory in realistic settings. We show by simulation that the algorithm performs comparably to batch-mode learning when the causal structure is stationary, and significantly better in non-stationary environments.

Most learning models assume, either implicitly or explicitly, that the goal of learning is to acquire a complete and veridical representation of the world, but this view assumes away the possibility that pragmatic goals can play a central role in learning. We propose instead that people are relatively frugal learners, acquiring goal-relevant information while ignoring goal-irrelevant features of the environment. Experiment 1 provides evidence that learning is goal-dependent, and that people are relatively frugal when given a specific, practical goal. Experiment 2 investigates possible mechanisms underlying this effect, and finds evidence that people exhibit goal-driven attention allocation, but not goaldriven reasoning. We conclude by examining how frugality can be integrated into Bayesian models of learning

Learning by artificial intelligence systems-what I will typically call machine learning-has a distinguished history, and the field has experienced something of a renaissance in the past twenty years. Machine learning consists principally of a diverse set of algorithms and techniques that have been applied to problems in a wide range of domains. Any overview of the methods and applications will inevitably be incomplete, at least at the level of specific algorithms and techniques. There are many excellent introductions to the formal and statistical details of machine learning algorithms and techniques available elsewhere. The present chapter focuses on machine learning as a general way of “thinking about the world,” and provides a high-level characterization of the major goals of machine learning. There are a number of philosophical concerns that have been raised about machine learning, but upon closer examination, it is not always clear whether the objections really speak against machine learning specifically. Many seem rather to be directed towards machine learning as a particular instantiation of some more general phenomenon or process. One of the general morals of this chapter is that machine learning is, in many ways, less unusual or peculiar than is sometimes thought

In the latter half of the twentieth century, philosophers of science have argued (implicitly and explicitly) that epistemically rational individuals might compose epistemically irrational groups and that, conversely, epistemically rational groups might be composed of epistemically irrational individuals. We call the conjunction of these two claims the Independence Thesis, as they together imply that methodological prescriptions for scientific communities and those for individual scientists might be logically independent of one another. We develop a formal model of scientific inquiry, define four criteria for individual and group epistemic rationality, and then prove that the four definitions diverge, in the sense that individuals will be judged rational when groups are not and vice versa. We conclude by explaining implications of the inconsistency thesis for (i) descriptive history and sociology of science and (ii) normative prescriptions for scientific communities.

Bayesian models of human learning are becoming increasingly popular in cognitive science. We argue that their purported confirmation largely relies on a methodology that depends on premises that are inconsistent with the claim that people are Bayesian about learning and inference. Bayesian models in cognitive science derive their appeal from their normative claim that the modeled inference is in some sense rational. Standard accounts of the rationality of Bayesian inference imply predictions that an agent selects the option that maximizes the posterior expected utility. Experimental confirmation of the models, however, has been claimed because of groups of agents that probability match the posterior. Probability matching only constitutes support for the Bayesian claim if additional unobvious and untested (but testable) assumptions are invoked. The alternative strategy of weakening the underlying notion of rationality no longer distinguishes the Bayesian model uniquely. A new account of rationality—either for inference or for decision-making—is required to successfully confirm Bayesian models in cognitive science.

In many people, caffeine causes slight muscle tremors, particularly in their hands. In general, the Caffeine → Muscle Tremors causal connection is a noisy one: someone can drink coffee and experience no hand shaking, and there are many other factors that can lead to muscle tremors. Now suppose that Jane drinks several cups of coffee and then notices that her hands are trembling; an obvious question is: did this instance of coffee drinking cause this instance of hand-trembling? Structurally similar questions arise throughout everyday life: Did this pressing of the ‘k’ key cause this change in the pixels on the computer monitor? Did these episodes of smoking cause this lung cancer? Did this studying cause this test score? And so on. These questions all ask about singular causation in a particular situation, in contrast with general causation across multiple cases. They are thus particularly salient in situations in which we care about that specific case, as in many legal contexts, social interactions, physical explanations of anomalous events, and more

There is now substantial agreement about the representational component of a normative theory of causal reasoning: Causal Bayes Nets. There is less agreement about a normative theory of causal discovery from data, either computationally or cognitively, and almost no work investigating how teaching the Causal Bayes Nets representational apparatus might help individuals faced with a causal learning task. Psychologists working to describe how naïve participants represent and learn causal structure from data have focused primarily on learning from single trials under a variety of conditions. In contrast, one component of the normative theory focuses on learning from a sample drawn from a population under some experimental or observational study regime. Through a virtual Causality Lab that embodies the normative theory of causal reasoning and which allows us to record student behavior, we have begun to systematically explore how best to teach the normative theory. In this paper we explain the overall project and report on pilot studies which suggest that students can quickly be taught to (appear to) be quite rational

Our concept of actual causation plays a deep, ever-present role in our experiences. I first argue that traditional philosophical methods for understanding this concept are unlikely to be successful. I contend that we should instead use functional analyses and an understanding of the cognitive bases of causal cognition to gain insight into the concept of actual causation. I additionally provide initial, programmatic steps towards carrying out such analyses. The characterization of the concept of actual causation that results is quite different from many standard views: it is graded, context-sensitive, and extrinsic

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