Many of the problems studied in cognitive science are inductive problems, requiring people to evaluate hypotheses in the light of data. The key to solving these problems successfully is having the right inductive biases—assumptions about the world that make it possible to choose between hypotheses that are equally consistent with the observed data. This article explores a novel experimental method for identifying the biases that guide human inductive inferences. The idea behind this method is simple: This article uses the responses (...) produced by a participant on one trial to generate the stimuli that either they or another participant will see on the next. A formal analysis of this “iterated learning” procedure, based on the assumption that the learners are Bayesian agents, predicts that it should reveal the inductive biases of these learners, as expressed in a prior probability distribution over hypotheses. This article presents a series of experiments using stimuli based on a well-studied set of category structures, demonstrating that iterated learning can be used to reveal the inductive biases of human learners. (shrink)

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute a posterior distribution over languages by combining a prior (representing their inductive biases) with the evidence provided by linguistic data. We show that when learners sample languages from this posterior (...) distribution, iterated learning converges to a distribution over languages that is determined entirely by the prior. Under these conditions, iterated learning is a form of Gibbs sampling, a widely-used Markov chain Monte Carlo algorithm. The consequences of iterated learning are more complicated when learners choose the language with maximum posterior probability, being affected by both the prior of the learners and the amount of information transmitted between generations. We show that in this case, iterated learning corresponds to another statistical inference algorithm, a variant of the expectation-maximization (EM) algorithm. These results clarify the role of iterated learning in explanations of linguistic universals and provide a formal connection between constraints on language acquisition and the languages that come to be spoken, suggesting that information transmitted via iterated learning will ultimately come to mirror the minds of the learners. (shrink)

Inductive generalization, where people go beyond the data provided, is a basic cognitive capability, and it underpins theoretical accounts of learning, categorization, and decision making. To complete the inductive leap needed for generalization, people must make a key ‘‘sampling’’ assumption about how the available data were generated. Previous models have considered two extreme possibilities, known as strong and weak sampling. In strong sampling, data are assumed to have been deliberately generated as positive examples of a concept, whereas in weak sampling, (...) data are assumed to have been generated without any restrictions. We develop a more general account of sampling that allows for an intermediate mixture of these two extremes, and we test its usefulness. In two experiments, we show that most people complete simple one-dimensional generalization tasks in a way that is consistent with their believing in some mixture of strong and weak sampling, but that there are large individual differences in the relative emphasis different people give to each type of sampling. We also show experimentally that the relative emphasis of the mixture is influenced by the structure of the available information. We discuss the psychological meaning of mixing strong and weak sampling, and possible extensions of our modeling approach to richer problems of inductive generalization. (shrink)

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in which (...) participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults’ judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children’s judgments (Experiments 3 and 5) agreed qualitatively with this account. (shrink)

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. (shrink)

The tendency to test outcomes that are predicted by our current theory (the confirmation bias) is one of the best-known biases of human decision making. We prove that the confirmation bias is an optimal strategy for testing hypotheses when those hypotheses are deterministic, each making a single prediction about the next event in a sequence. Our proof applies for two normative standards commonly used for evaluating hypothesis testing: maximizing expected information gain and maximizing the probability of falsifying the current hypothesis. (...) This analysis rests on two assumptions: (a) that people predict the next event in a sequence in a way that is consistent with Bayesian inference; and (b) when testing hypotheses, people test the hypothesis to which they assign highest posterior probability. We present four behavioral experiments that support these assumptions, showing that a simple Bayesian model can capture people's predictions about numerical sequences (Experiments 1 and 2), and that we can alter the hypotheses that people choose to test by manipulating the prior probability of those hypotheses (Experiments 3 and 4). (shrink)

We criticise Shepard's notions of “invariance” and “universality,” and the incorporation of Shepard's work on inference into the general framework of his paper. We then criticise Tenenbaum and Griffiths' account of Shepard (1987b), including the attributed likelihood function, and the assumption of “weak sampling.” Finally, we endorse Barlow's suggestion that minimum message length (MML) theory has useful things to say about the Bayesian inference problems discussed by Shepard and Tenenbaum and Griffiths. [Barlow; Shepard; Tenenbaum & Griffiths].

We argue that confusability between items should be distinguished from generalization between items. Shepard's data concern confusability, but the theories proposed by Shepard and by Tenenbaum & Griffiths concern generalization, indicating a gap between theory and data. We consider the empirical and theoretical work involved in bridging this gap. [Shepard; Tenenbaum & Griffiths].

Tenenbaum and Griffiths (Behavioral and Brain Sciences 24(4):629–640, 2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (Science 237(4820): 1317–1323, 1987) and Tversky’s (Psychological Review 84(4): 327–352, 1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that (...) generalisation as a Bayesian inference should be seen as a complement to, instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

Tenenbaum and Griffiths (2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (1987) and Tversky’s (1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that generalisation as a Bayesian inference should be seen as a complement to, (...) instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

Shepard’s (1987) universal law of generalisation (ULG) illustrates that an invariant gradient of generalisation across species and across stimuli conditions can be obtained by mapping the probability of a generalisation response onto the representations of similarity between individual stimuli. Tenenbaum and Griffiths (2001) Bayesian account of generalisation expands ULG towards generalisation from multiple examples. Though the Bayesian model starts from Shepard’s account it refrains from any commitment to the notion of psychological similarity to explain categorisation. This chapter presents the conceptual (...) spaces theory (Gärdenfors 2000, 2014) as a mediator between Shepard’s and Tenenbaum & Griffiths’ conflicting views on the role of psychological similarity for a successful model of categorisation. It suggests that the conceptual spaces theory can help to improve the Bayesian model while finding an explanatory role for psychological similarity. (shrink)

Artificial intelligence (AI) research enjoyed an initial period of enthusiasm in the 1970s and 80s. But this enthusiasm was tempered by a long interlude of frustration when genuinely useful AI applications failed to be forthcoming. Today, we are experiencing once again a period of enthusiasm, fired above all by the successes of the technology of deep neural networks or deep machine learning. In this paper we draw attention to what we take to be serious problems underlying current views of artificial (...) intelligence encouraged by these successes, especially in the domain of language processing. We then show an alternative approach to language-centric AI, in which we identify a role for philosophy. (shrink)

Rule-like behaviour is found throughout human language, provoking a number of apparently conflicting explanations. This paper frames the topic in terms of Tinbergen’s four questions and works within the context of rule-like behaviour seen both in nature and the non-linguistic domain in humans. I argue for a minimal account of linguistic rules which relies on powerful domain-general cognition, has a communicative function allowing for multiple engineering solutions, and evolves mainly culturally, while leaving the door open for some genetic adaptation in (...) the form of learning biases. (shrink)

People draw subtle distinctions in the normative domain. But it remains unclear exactly what gives rise to such distinctions. On one prominent approach, emotion systems trigger non-utilitarian judgments. The main alternative, inspired by Chomskyan linguistics, suggests that moral distinctions derive from an innate moral grammar. In this article, we draw on Bayesian learning theory to develop a rational learning account. We argue that the ‘size principle’, which is implicated in word learning, can also explain how children would use scant and (...) equivocal evidence to interpret candidate rules as applying more narrowly than utilitarian rules. (shrink)

Human and automated tutors attempt to choose pedagogical activities that will maximize student learning, informed by their estimates of the student's current knowledge. There has been substantial research on tracking and modeling student learning, but significantly less attention on how to plan teaching actions and how the assumed student model impacts the resulting plans. We frame the problem of optimally selecting teaching actions using a decision-theoretic approach and show how to formulate teaching as a partially observable Markov decision process planning (...) problem. This framework makes it possible to explore how different assumptions about student learning and behavior should affect the selection of teaching actions. We consider how to apply this framework to concept learning problems, and we present approximate methods for finding optimal teaching actions, given the large state and action spaces that arise in teaching. Through simulations and behavioral experiments, we explore the consequences of choosing teacher actions under different assumed student models. In two concept-learning tasks, we show that this technique can accelerate learning relative to baseline performance. (shrink)

We consider approaches to explanation within the cognitive sciences that begin with Marr's computational level or Marr's implementational level and argue that each is subject to fundamental limitations which impair their ability to provide adequate explanations of cognitive phenomena. For this reason, it is argued, explanation cannot proceed at either level without tight coupling to the algorithmic and representation level. Even at this level, however, we argue that additional constraints relating to the decomposition of the cognitive system into a set (...) of interacting subfunctions are required. Integrated cognitive architectures that permit abstract specification of the functions of components and that make contact with the neural level provide a powerful bridge for linking the algorithmic and representational level to both the computational level and the implementational level. (shrink)

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. Through (...) these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

People feel they understand complex phenomena with far greater precision, coherence, and depth than they really do; they are subject to an illusion—an illusion of explanatory depth. The illusion is far stronger for explanatory knowledge than many other kinds of knowledge, such as that for facts, procedures or narratives. The illusion for explanatory knowledge is most robust where the environment supports real‐time explanations with visible mechanisms. We demonstrate the illusion of depth with explanatory knowledge in Studies 1–6. Then we show (...) differences in overconfidence about knowledge across different knowledge domains in Studies 7–10. Finally, we explore the mechanisms behind the initial confidence and behind overconfidence in Studies 11 and 12, and discuss the implications of our findings for the roles of intuitive theories in concepts and cognition. (shrink)

More than 50 years ago, Bongard introduced 100 visual concept learning problems as a challenge for artificial vision systems. These problems are now known as Bongard problems. Although they are well known in cognitive science and artificial intelligence, only very little progress has been made toward building systems that can solve a substantial subset of them. In the system presented here, visual features are extracted through image processing and then translated into a symbolic visual vocabulary. We introduce a formal language (...) that allows representing compositional visual concepts based on this vocabulary. Using this language and Bayesian inference, concepts can be induced from the examples that are provided in each problem. We find a reasonable agreement between the concepts with high posterior probability and the solutions formulated by Bongard himself for a subset of 35 problems. While this approach is far from solving Bongard problems like humans, it does considerably better than previous approaches. We discuss the issues we encountered while developing this system and their continuing relevance for understanding visual cognition. For instance, contrary to other concept learning problems, the examples are not random in Bongard problems; instead they are carefully chosen to ensure that the concept can be induced, and we found it helpful to take the resulting pragmatic constraints into account. (shrink)

Generalization is a fundamental problem solved by every cognitive system in essentially every domain. Although it is known that how people generalize varies in complex ways depending on the context or domain, it is an open question how people learn the appropriate way to generalize for a new context. To understand this capability, we cast the problem of learning how to generalize as a problem of learning the appropriate hypothesis space for generalization. We propose a normative mathematical framework for learning (...) how to generalize by learning inductive biases for which properties are relevant for generalization in a domain from the statistical structure of features and concepts observed in that domain. More formally, the framework predicts that an ideal learner should learn to generalize by either taking the weighted average of the results of generalizing according to each hypothesis space, with weights given by how well each hypothesis space fits the previously observed concepts, or by using the most likely hypothesis space. We compare the predictions of this framework to human generalization behavior with three experiments in one perceptual (rectangles) and two conceptual (animals and numbers) domains. Across all three studies we find support for the framework's predictions, including individual‐level support for averaging in the third study. (shrink)

Do you know you are not being massively deceived by an evil demon? That is a familiar skeptical challenge. Less familiar is this question: How do you have a conception of knowledge on which the evil demon constitutes a prima facie challenge? Recently several philosophers have suggested that our responses to skeptical scenarios can be explained in terms of heuristics and biases. We offer an alternative explanation, based in learning theory. We argue that, given the evidence available to the learner, (...) it would be rational for the learner to infer an infallibilist conception of knowledge. (shrink)

Occam's razor—the idea that all else being equal, we should pick the simpler hypothesis—plays a prominent role in ordinary and scientific inference. But why are simpler hypotheses better? One attractive hypothesis known as Bayesian Occam's razor is that more complex hypotheses tend to be more flexible—they can accommodate a wider range of possible data—and that flexibility is automatically penalized by Bayesian inference. In two experiments, we provide evidence that people's intuitive probabilistic and explanatory judgments follow the prescriptions of BOR. In (...) particular, people's judgments are consistent with the two most distinctive characteristics of BOR: They penalize hypotheses as a function not only of their numbers of free parameters but also as a function of the size of the parameter space, and they penalize those hypotheses even when their parameters can be “tuned” to fit the data better than comparatively simpler hypotheses. (shrink)

An expression-induction model was used to simulate the evolution of basic color terms to test Berlin and Kay's (1969) hypothesis that the typological patterns observed in basic color term systems are produced by a process of cultural evolution under the influence of biases resulting from the special properties of universal focal colors. Ten agents were simulated, each of which could learn color term denotations by generalizing from examples using Bayesian inference, and for which universal focal red, yellow, green, and blue (...) were especially salient, but unevenly spaced in the perceptual color space. Conversations between these agents, in which agents would learn from one another, were simulated over several generations, and the languages emerging at the end of each simulation were investigated. The proportion of color terms of each type correlated closely with the equivalent frequencies found in the World Color Survey, and most of the emergent languages could be placed on one of the evolutionary trajectories proposed by Kay and Maffi (1999). The simulation therefore demonstrates how typological patterns can emerge as a result of learning biases acting over a period of time. (shrink)

This article reviews a number of different areas in the foundations of formal learning theory. After outlining the general framework for formal models of learning, the Bayesian approach to learning is summarized. This leads to a discussion of Solomonoff's Universal Prior Distribution for Bayesian learning. Gold's model of identification in the limit is also outlined. We next discuss a number of aspects of learning theory raised in contributed papers, related to both computational and representational complexity. The article concludes with a (...) description of how semi-supervised learning can be applied to the study of cognitive learning models. Throughout this overview, the specific points raised by our contributing authors are connected to the models and methods under review. (shrink)

Surprise—operationalized as looking time—has a long history in developmental research, providing a window into the perception and cognition of infants. Recently, however, a number of developmental researchers have considered infants’ and children's surprise in its own right. This article reviews empirical evidence and computational models of complex statistical inferences underlying surprise, and discusses how these findings relate to the role that surprise appears to play as a catalyst for learning.

Examples from Archimedes, Galileo, Newton, Einstein, and others suggest that fundamental laws of physics were—or, at least, could have been—discovered by experiments performed not in the physical world but only in the mind. Although problematic for a strict empiricist, the evolutionary emergence in humans of deeply internalized implicit knowledge of abstract principles of transformation and symmetry may have been crucial for humankind's step to rationality—including the discovery of universal principles of mathematics, physics, ethics, and an account of free will that (...) is compatible with determinism. (shrink)

Identifying patterns in the world requires noticing not only unusual occurrences, but also unusual absences. We examined how people learn from absences, manipulating the extent to which an absence is expected. People can make two types of inferences from the absence of an event: either the event is possible but has not yet occurred, or the event never occurs. A rational analysis using Bayesian inference predicts that inferences from absent data should depend on how much the absence is expected to (...) occur, with less probable absences being more salient. We tested this prediction in two experiments in which we elicited people's judgments about patterns in the data as a function of absence salience. We found that people were able to decide that absences either were mere coincidences or were indicative of a significant pattern in the data in a manner that was consistent with predictions of a simple Bayesian model. (shrink)

Normal children learn tens of thousands of words, and do so quickly and efficiently, often in highly impoverished environments. In How Children Learn the Meanings of Words, I argue that word learning is the product of certain cognitive and linguistic abilities that include the ability to acquire concepts, an appreciation of syntactic cues to meaning, and a rich understanding of the mental states of other people. These capacities are powerful, early emerging, and to some extent uniquely human, but they are (...) not special to word learning. This proposal is an alternative to the view that word learning is the result of simple associative learning mechanisms, and it rejects as well the notion that children possess constraints, either innate or learned, that are specifically earmarked for word learning. This theory is extended to account for how children learn names for objects, substances, and abstract entities, pronouns and proper names, verbs, determiners, prepositions, and number words. Several related topics are also discussed, including naïve essentialism, children's understanding of representational art, the nature of numerical and spatial reasoning, and the role of words in the shaping of mental life. Key Words: cognitive development; concepts; meaning; semantics; social cognition; syntax; theory of mind; word learning. (shrink)