Bayesian models are often criticized for postulating computations that are computationally intractable (e.g., NP-hard) and therefore implausibly performed by our resource-bounded minds/brains. Our letter is motivated by the observation that Bayesian modelers have been claiming that they can counter this charge of “intractability” by proposing that Bayesian computations can be tractably approximated. We would like to make the cognitive science community aware of the problematic nature of such claims. We cite mathematical proofs from the computer science literature that show intractable (...) Bayesian computations, such as postulated in existing Bayesian models, cannot be tractably approximated. This does not mean that human brains do not (or cannot) implement the type of algorithms that Bayesian modelers are advancing, but it does mean that proposing that they do by itself does nothing to parry the charge of intractability, because the postulated algorithms are as intractable (i.e., require exponential time) as the computations they try to approximate. Besides our negative message for the community, our letter also makes a positive contribution by referring to a methodology that Bayesian modelers can use to try and parry the charge of intractability in a mathematically sound way. (shrink)

Inspired by, and in close relation with, the contributions of this special issue, Kuperberg elegantly links event comprehension, production, and learning. She proposes an overarching hierarchical generative framework of processing events enabling us to make sense of the world around us and to interact with it in a competent manner.

Mathematical developments in probabilistic inference have led to optimism over the prospects for Bayesian models of cognition. Our target article calls for better differentiation of these technical developments from theoretical contributions. It distinguishes between Bayesian Fundamentalism, which is theoretically limited because of its neglect of psychological mechanism, and Bayesian Enlightenment, which integrates rational and mechanistic considerations and is thus better positioned to advance psychological theory. The commentaries almost uniformly agree that mechanistic grounding is critical to the success of the Bayesian (...) program. Some commentaries raise additional challenges, which we address here. Other commentaries claim that all Bayesian models are mechanistically grounded, while at the same time holding that they should be evaluated only on a computational level. We argue this contradictory stance makes it difficult to evaluate a model's scientific contribution, and that the psychological commitments of Bayesian models need to be made more explicit. (shrink)

Conviction Narrative Theory (CNT) is a theory of choice underradical uncertainty– situations where outcomes cannot be enumerated and probabilities cannot be assigned. Whereas most theories of choice assume that people rely on (potentially biased) probabilistic judgments, such theories cannot account for adaptive decision-making when probabilities cannot be assigned. CNT proposes that people usenarratives– structured representations of causal, temporal, analogical, and valence relationships – rather than probabilities, as the currency of thought that unifies our sense-making and decision-making faculties. According to CNT, (...) narratives arise from the interplay between individual cognition and the social environment, with reasoners adopting a narrative that feels “right” to explain the available data; using that narrative to imagine plausible futures; and affectively evaluating those imagined futures to make a choice. Evidence from many areas of the cognitive, behavioral, and social sciences supports this basic model, including lab experiments, interview studies, and econometric analyses. We identify 12 propositions to explain how the mental representations (narratives) interact with four inter-related processes (explanation, simulation, affective evaluation, and communication), examining the theoretical and empirical basis for each. We conclude by discussing how CNT can provide a common vocabulary for researchers studying everyday choices across areas of the decision sciences. (shrink)

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)

Utility maximization is a key element of a number of theoretical approaches to explaining human behavior. Among these approaches are rational analysis, ideal observer theory, and signal detection theory. While some examples of these approaches define the utility maximization problem with little reference to the bounds imposed by the organism, others start with, and emphasize approaches in which bounds imposed by the information processing architecture are considered as an explicit part of the utility maximization problem. These latter approaches are the (...) topic of this issue of the journal. (shrink)

Bayesian accounts are currently popular in the field of inductive reasoning. This commentary briefly reviews the limitations of one such account, the Rational Model (Anderson 1991b), in explaining how inferences are made about objects whose category membership is uncertain. These shortcomings are symptomatic of what Jones & Love (J&L) refer to as Bayesian approaches.

It is often claimed that the greatest value of the Bayesian framework in cognitive science consists in its unifying power. Several Bayesian cognitive scientists assume that unification is obviously linked to explanatory power. But this link is not obvious, as unification in science is a heterogeneous notion, which may have little to do with explanation. While a crucial feature of most adequate explanations in cognitive science is that they reveal aspects of the causal mechanism that produces the phenomenon to be (...) explained, the kind of unification afforded by the Bayesian framework to cognitive science does not necessarily reveal aspects of a mechanism. Bayesian unification, nonetheless, can place fruitful constraints on causal–mechanical explanation. 1 Introduction2 What a Great Many Phenomena Bayesian Decision Theory Can Model3 The Case of Information Integration4 How Do Bayesian Models Unify?5 Bayesian Unification: What Constraints Are There on Mechanistic Explanation?5.1 Unification constrains mechanism discovery5.2 Unification constrains the identification of relevant mechanistic factors5.3 Unification constrains confirmation of competitive mechanistic models6 ConclusionAppendix. (shrink)

Marr's levels of analysis—computational, algorithmic, and implementation—have served cognitive science well over the last 30 years. But the recent increase in the popularity of the computational level raises a new challenge: How do we begin to relate models at different levels of analysis? We propose that it is possible to define levels of analysis that lie between the computational and the algorithmic, providing a way to build a bridge between computational- and algorithmic-level models. The key idea is to push the (...) notion of rationality, often used in defining computational-level models, deeper toward the algorithmic level. We offer a simple recipe for reverse-engineering the mind's cognitive strategies by deriving optimal algorithms for a series of increasingly more realistic abstract computational architectures, which we call “resource-rational analysis.”. (shrink)

The success of models of human behavior based on Bayesian inference over logical formulas or programs is taken as evidence that people employ a “language-of-thought” that has similarly discrete and compositional structure. We argue that this conclusion problematically crosses levels of analysis, identifying representations at the algorithmic level based on inductive biases at the computational level.

We routinely observe others’ choices and use them to guide our own. Whose choices influence us more, and why? Prior work has focused on the effect of perceived similarity between two individuals, such as the degree of overlap in past choices or explicitly recognizable group affiliations. In the real world, however, any dyadic relationship is part of a more complex social structure involving multiple social groups that are not directly observable. Here we suggest that human learners go beyond dyadic similarities (...) in choice behaviors or explicit group memberships; they infer the structure of social influence by grouping individuals based on choices, and they use these groups to decide whose choices to follow. We propose a computational model that formalizes this idea, and we test the model predictions in a series of behavioral experiments. In Experiment 1, we reproduce a well-established finding that people's choices are more likely to be influenced by someone whose past choices are more similar to their own past choices, as predicted by our model as well as dyadic similarity models. In Experiments 2–5, we test a set of unique predictions of our model by looking at cases where the degree of choice overlap between individuals is equated, but their choices indicate a latent group structure. We then apply our model to prior empirical results on infants’ understanding of others’ preferences, presenting an alternative account of developmental changes. Finally, we discuss how our model relates to classical findings in the social influence literature and the theoretical implications of our model. Taken together, our findings demonstrate that structure learning is a powerful framework for explaining the influence of social information on decision making in a variety of contexts. (shrink)

In recent years quantum probability models have been used to explain many aspects of human decision making, and as such quantum models have been considered a viable alternative to Bayesian models based on classical probability. One criticism that is often leveled at both kinds of models is that they lack a clear interpretation in terms of psychological mechanisms. In this paper we discuss the mechanistic underpinnings of a quantum walk model of human decision making and response time. The quantum walk (...) model is compared to standard sequential sampling models, and the architectural assumptions of both are considered. In particular, we show that the quantum model has a natural interpretation in terms of a cognitive architecture that is both massively parallel and involves both co-operative and competitive interactions between units. Additionally, we introduce a family of models that includes aspects of the classical and quantum walk models. (shrink)

Models of category learning have been extensively studied in cognitive science and primarily tested on perceptual abstractions or artificial stimuli. In this paper, we focus on categories acquired from natural language stimuli, that is, words. We present a Bayesian model that, unlike previous work, learns both categories and their features in a single process. We model category induction as two interrelated subproblems: the acquisition of features that discriminate among categories, and the grouping of concepts into categories based on those features. (...) Our model learns categories incrementally using particle filters, a sequential Monte Carlo method commonly used for approximate probabilistic inference that sequentially integrates newly observed data and can be viewed as a plausible mechanism for human learning. Experimental results show that our incremental learner obtains meaningful categories which yield a closer fit to behavioral data compared to related models while at the same time acquiring features which characterize the learned categories. (shrink)

How do human infants learn the causal dependencies between events? Evidence suggests that this remarkable feat can be achieved by observation of only a handful of examples. Many computational models have been produced to explain how infants perform causal inference without explicit teaching about statistics or the scientific method. Here, we propose a spiking neuronal network implementation that can be entrained to form a dynamical model of the temporal and causal relationships between events that it observes. The network uses spike-time (...) dependent plasticity, long-term depression, and heterosynaptic competition rules to implement Rescorla–Wagner-like learning. Transmission delays between neurons allow the network to learn a forward model of the temporal relationships between events. Within this framework, biologically realistic synaptic plasticity rules account for well-known behavioral data regarding cognitive causal assumptions such as backwards blocking and screening-off. These models can then be run as emulators for state inference. Furthermore, this mechanism is capable of copying synaptic connectivity patterns between neuronal networks by observing the spontaneous spike activity from the neuronal circuit that is to be copied, and it thereby provides a powerful method for transmission of circuit functionality between brain regions. (shrink)

Theories of rational decision making often abstract away from computational and other resource limitations faced by real agents. An alternative approach known as resource rationality puts such matters front and center, grounding choice and decision in the rational use of finite resources. Anticipated by earlier work in economics and in computer science, this approach has recently seen rapid development and application in the cognitive sciences. Here, the theory of rationality plays a dual role, both as a framework for normative assessment (...) and as a source of scientific hypotheses about how mental processes in fact work. The latter project, often called rational analysis, depends for its success on a fine-grained characterization of the computational problem facing a decision maker, which may in turn depend on realistic assumptions about what the relevant agent is like. As a consequence, resource rationality involves a delicate, but often fruitful interplay between the normative and the descriptive. (shrink)

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools (...) adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning. (shrink)

Resource rationality may explain suboptimal patterns of reasoning; but what of “anti-Bayesian” effects where the mind updates in a direction opposite the one it should? We present two phenomena — belief polarization and the size-weight illusion — that are not obviously explained by performance- or resource-based constraints, nor by the authors’ brief discussion of reference repulsion. Can resource rationality accommodate them?

At least two distinct modeling frameworks contribute to the view that mind and brain are Bayesian: Bayesian Rational Analysis (BRA) and Hierarchical Predictive Coding (HPC). What is the relative contribution of each, and how exactly do they relate? In order to answer this question, we compare the way in which these two modeling frameworks address different levels of analysis within Marr’s tripartite conception of explanation in cognitive science. Whereas BRA answers questions at the computational level only, many HPC-theorists answer questions (...) at the computational, algorithmic, and implementational levels simultaneously. Given that all three levels of analysis need to be addressed in order to explain a behavioral or cognitive phenomenon, HPC seems to deliver more complete explanations. Nevertheless, BRA is well-suited for providing a solution to the dark room problem, a major theoretical obstacle for HPC. A combination of the two approaches also combines the benefits of an embodied-externalistic approach to resolving the dark room problem with the idea of a persisting evidentiary border beyond which matters are out of cognitive reach. For this reason, the development of explanations spanning all three Marrian levels within the general Bayesian approach may require combining the BRA and HPC modeling frameworks. (shrink)