Bayesian just-so stories in psychology and neuroscience

According to Bayesian theories in psychology and neuroscience, minds and brains are (near) optimal in solving a wide range of tasks. We challenge this view and argue that more traditional, non-Bayesian approaches are more promising. We make 3 main arguments. First, we show that the empirical evidence for Bayesian theories in psychology is weak. This weakness relates to the many arbitrary ways that priors, likelihoods, and utility functions can be altered in order to account for the data that are obtained, making the models unfalsifiable. It further relates to the fact that Bayesian theories are rarely better at predicting data compared with alternative (and simpler) non-Bayesian theories. Second, we show that the empirical evidence for Bayesian theories in neuroscience is weaker still. There are impressive mathematical analyses showing how populations of neurons could compute in a Bayesian manner but little or no evidence that they do. Third, we challenge the general scientific approach that characterizes Bayesian theorizing in cognitive science. A common premise is that theories in psychology should largely be constrained by a rational analysis of what the mind ought to do. We question this claim and argue that many of the important constraints come from biological, evolutionary, and processing (algorithmic) considerations that have no adaptive relevance to the problem per se. In our view, these factors have contributed to the development of many Bayesian "just so" stories in psychology and neuroscience; that is, mathematical analyses of cognition that can be used to explain almost any behavior as optimal.     

Sensitivity to sampling in Bayesian word learning

We report a new study testing our proposal that word learning may be best explained as an approximate form of Bayesian inference (Xu & Tenenbaum, in press). Children are capable of learning word meanings across a wide range of communicative contexts. In different contexts, learners may encounter different sampling processes generating the examples of word-object pairings they observe. An ideal Bayesian word learner could take into account these differences in the sampling process and adjust his/her inferences about word meaning accordingly. We tested how children and adults learned words for novel object kinds in two sampling contexts, in which the objects to be labeled were sampled either by a knowledgeable teacher or by the learners themselves. Both adults and children generalized more conservatively in the former context; that is, they restricted the label to just those objects most similar to the labeled examples when the exemplars were chosen by a knowledgeable teacher, but not when chosen by the learners themselves. We discuss how this result follows naturally from a Bayesian analysis, but not from other statistical approaches such as associative word-learning models.     

Word learning as Bayesian inference

The authors present a Bayesian framework for understanding how adults and children learn the meanings of words. The theory explains how learners can generalize meaningfully from just one or a few positive examples of a novel word's referents, by making rational inductive inferences that integrate prior knowledge about plausible word meanings with the statistical structure of the observed examples. The theory addresses shortcomings of the two best known approaches to modeling word learning, based on deductive hypothesis elimination and associative learning. Three experiments with adults and children test the Bayesian account's predictions in the context of learning words for object categories at multiple levels of a taxonomic hierarchy. Results provide strong support for the Bayesian account over competing accounts, in terms of both quantitative model fits and the ability to explain important qualitative phenomena. Several extensions of the basic theory are discussed, illustrating the broader potential for Bayesian models of word learning.     

LEARNING THEORY APPROACHES TO PERSUASION

This review synthesizes relevant research dealing with the processes of learning and suggests its applications to compliance gaining. The two major issues addressed are: (1) to what degree can learning theories explain the acquisition of new attitudes and behaviors, and (2) to what degree are attitudinal and behavioral changes governed by learning theory principles? The learning theories discussed are grouped into three categories: stimulus-response or connectionist approaches; cognitive approaches; and stochastic, mathematical, and cybernetic approaches. The stimulus-response models, which encompass most of the research examined in this paper, are further broken down into four types: (1) classical conditioning, (2) contiguity models, (3) instrumental (or operant) conditioning and (4) models including drive and drive reduction. Principles and major research evidence from numerous learning theories are reviewed and analyzed, and suggestions are made as to how this evidence may aid in the construction of more complete theories of persuasion and attitude change.     

Probabilistic models in human sensorimotor control

Sensory and motor uncertainty form a fundamental constraint on human sensorimotor control. Bayesian decision theory (BDT) has emerged as a unifying framework to understand how the central nervous system performs optimal estimation and control in the face of such uncertainty. BDT has two components: Bayesian statistics and decision theory. Here we review Bayesian statistics and show how it applies to estimating the state of the world and our own body. Recent results suggest that when learning novel tasks we are able to learn the statistical properties of both the world and our own sensory apparatus so as to perform estimation using Bayesian statistics. We review studies which suggest that humans can combine multiple sources of information to form maximum likelihood estimates, can incorporate prior beliefs about possible states of the world so as to generate maximum a posteriori estimates and can use Kalman filter-based processes to estimate time-varying states. Finally, we review Bayesian decision theory in motor control and how the central nervous system processes errors to determine loss functions and select optimal actions. We review results that suggest we plan movements based on statistics of our actions that result from signal-dependent noise on our motor outputs. Taken together these studies provide a statistical framework for how the motor system performs in the presence of uncertainty.     

Directed Convergence in Stable Percept Acquisition

We view a perceptual capacity as a nondeductive inference, represented as a function from a set of premises to a set of conclusions. The application of the function to a single premise to produce a single conclusion is called a "percept" or "instantaneous percept." We define a stable percept as a convergent sequence of instantaneous percepts. Assuming that the sets of premises and conclusions are metric spaces, we introduce a strategy for acquiring stable percepts, called directed convergence. We consider probabilistic inferences, where the premise and conclusion sets are spaces of probability measures, and in this context we study Bayesian probabilistic/recursive inference. In this type of Bayesian inference the premises are probability measures, and the prior as well as the posterior is updated nontrivially at each iteration. This type of Bayesian inference is distinguished from classical Bayesian statistical inference where the prior remains fixed, and the posterior evolves by conditioning on successively more punctual premises. We indicate how the directed convergence procedure may be implemented in the context of Bayesian probabilistic/recursive inference. We discuss how the L(infinity) metric can be used to give numerical control of this type of Bayesian directed convergence. Copyright 2001 Academic Press.     

Contextual inference in learning and memory

Context is widely regarded as a major determinant of learning and memory across numerous domains, including classical and instrumental conditioning, episodic memory, economic decision-making, and motor learning. However, studies across these domains remain disconnected due to the lack of a unifying framework formalizing the concept of context and its role in learning. Here, we develop a unified vernacular allowing direct comparisons between different domains of contextual learning. This leads to a Bayesian model positing that context is unobserved and needs to be inferred. Contextual inference then controls the creation, expression, and updating of memories. This theoretical approach reveals two distinct components that underlie adaptation, proper and apparent learning, respectively referring to the creation and updating of memories versus time-varying adjustments in their expression. We review a number of extensions of the basic Bayesian model that allow it to account for increasingly complex forms of contextual learning.     

Theory-based Bayesian models of inductive learning and reasoning

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.     

Neuroscience and learning: lessons from studying the involvement of a region of cerebellar cortex in eyeblink classical conditioning

How the nervous system encodes learning and memory processes has interested researchers for 100 years. Over this span of time, a number of basic neuroscience methods has been developed to explore the relationship between learning and the brain, including brain lesion, stimulation, pharmacology, anatomy, imaging, and recording techniques. In this paper, we summarize how different research approaches can be employed to generate converging data that speak to how structures and systems in the brain are involved in simple associative learning. To accomplish this, we review data regarding the involvement of a particular region of cerebellar cortex (Larsell's lobule HVI) in the widely used paradigm of classical eyeblink conditioning. We also present new data on the role of lobule HVI in eyeblink conditioning generated by combining temporary brain inactivation and single-cell recording methods, an approach that looks promising for further advancing our understanding of relationships between brain and behavior.     

One and Done? Optimal Decisions From Very Few Samples

In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling‐based approximations are a common way to implement Bayesian inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst‐case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling‐based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource‐constrained cognition.     

Modeling Statistical Insensitivity: Sources of Suboptimal Behavior

Children acquiring languages with noun classes (grammatical gender) have ample statistical information available that characterizes the distribution of nouns into these classes, but their use of this information to classify novel nouns differs from the predictions made by an optimal Bayesian classifier. We use rational analysis to investigate the hypothesis that children are classifying nouns optimally with respect to a distribution that does not match the surface distribution of statistical features in their input. We propose three ways in which children's apparent statistical insensitivity might arise, and find that all three provide ways to account for the difference between children's behavior and the optimal classifier. A fourth model combines two of these proposals and finds that children's insensitivity is best modeled as a bias to ignore certain features during classification, rather than an inability to encode those features during learning. These results provide insight into children's developing knowledge of noun classes and highlight the complex ways in which statistical information from the input interacts with children's learning processes.     

Hierarchical Bayes Models for Response Time Data

Human response time (RT) data are widely used in experimental psychology to evaluate theories of mental processing. Typically, the data constitute the times taken by a subject to react to a succession of stimuli under varying experimental conditions. Because of the sequential nature of the experiments there are trends (due to learning, fatigue, fluctuations in attentional state, etc.) and serial dependencies in the data. The data also exhibit extreme observations that can be attributed to lapses, intrusions from outside the experiment, and errors occurring during the experiment. Any adequate analysis should account for these features and quantify them accurately. Recognizing that Bayesian hierarchical models are an excellent modeling tool, we focus on the elaboration of a realistic likelihood for the data and on a careful assessment of the quality of fit that it provides. We judge quality of fit in terms of the predictive performance of the model. We demonstrate how simple Bayesian hierarchical models can be built for several RT sequences, differentiating between subject-specific and condition-specific effects.     

Modeling behavior in a clinically diagnostic sequential risk-taking task

This article models the cognitive processes underlying learning and sequential choice in a risk-taking task for the purposes of understanding how they occur in this moderately complex environment and how behavior in it relates to self-reported real-world risk taking. The best stochastic model assumes that participants incorrectly treat outcome probabilities as stationary, update probabilities in a Bayesian fashion, evaluate choice policies prior to rather than during responding, and maintain constant response sensitivity. The model parameter associated with subjective value of gains correlates well with external risk taking. Both the overall approach, which can be expanded as the basic paradigm is varied, and the specific results provide direction for theories of risky choice and for understanding risk taking as a public health problem.     

Confirmation and reduction: a Bayesian account

Various scientific theories stand in a reductive relation to each other. In a recent article, we have argued that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, we present a Bayesian analysis of how GNS impacts on confirmation. We formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. We then ask when a purported reduction should be accepted on epistemic grounds. To do so, we compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence.     

The role of partial knowledge in statistical word learning

A critical question about the nature of human learning is whether it is an all-or-none or a gradual, accumulative process. Associative and statistical theories of word learning rely critically on the later assumption: that the process of learning a word’s meaning unfolds over time. That is, learning the correct referent for a word involves the accumulation of partial knowledge across multiple instances. Some theories also make an even stronger claim: Partial knowledge of one word–object mapping can speed up the acquisition of other word–object mappings. We present three experiments that test and verify these claims by exposing learners to two consecutive blocks of cross-situational learning, in which half of the words and objects in the second block were those that participants failed to learn in Block 1. In line with an accumulative account, Re-exposure to these mis-mapped items accelerated the acquisition of both previously experienced mappings and wholly new word–object mappings. But how does partial knowledge of some words speed the acquisition of others? We consider two hypotheses. First, partial knowledge of a word could reduce the amount of information required for it to reach threshold, and the supra-threshold mapping could subsequently aid in the acquisition of new mappings. Alternatively, partial knowledge of a word’s meaning could be useful for disambiguating the meanings of other words even before the threshold of learning is reached. We construct and compare computational models embodying each of these hypotheses and show that the latter provides a better explanation of the empirical data.     

Generalization and similarity in exemplar models of categorization: Insights from machine learning

Exemplar theories of categorization depend on similarity for explaining subjects’ ability to generalize to new stimuli. A major criticism of exemplar theories concerns their lack of abstraction mechanisms and thus, seemingly, of generalization ability. Here, we use insights from machine learning to demonstrate that exemplar models can actually generalize very well. Kernel methods in machine learning are akin to exemplar models and are very successful in real-world applications. Their generalization performance depends crucially on the chosen similarity measure. Although similarity plays an important role in describing generalization behavior, it is not the only factor that controls generalization performance. In machine learning, kernel methods are often combined with regularization techniques in order to ensure good generalization. These same techniques are easily incorporated in exemplar models. We show that the generalized context model (Nosofsky, 1986) and ALCOVE (Kruschke, 1992) are closely related to a statistical model called kernel logistic regression. We argue that generalization is central to the enterprise of understanding categorization behavior, and we suggest some ways in which insights from machine learning can offer guidance.     

Cerebellar Substrates for Error Correction in Motor Conditioning

The authors evaluate a mapping of Rescorla and Wagner's (1972) behavioral model of classical conditioning onto the cerebellar substrates for motor reflex learning and illustrate how the limitations of the Rescorla-Wagner model are just as useful as its successes for guiding the development of new psychobiological theories of learning. They postulate that the inhibitory pathway that returns conditioned response information from the cerebellar interpositus nucleus back to the inferior olive is the neural basis for the error correction learning proposed by Rescorla and Wagner (Gluck, Myers, & Thompson, 1994; Thompson, 1986). The authors' cerebellar model expects that behavioral processes described by the Rescorla-Wagner model will be localized within the cerebellum and related brain stem structures, whereas behavioral processes beyond the scope of the Rescorla-Wagner model will depend on extracerebellar structures such as the hippocampus and related cortical regions. Simulations presented here support both implications. Several novel implications of the authors' cerebellar error-correcting model are described including a recent empirical study by Kim, Krupa, and Thompson (1998), who verified that suppressing the putative error correction pathway should interfere with the Kamin (1969) blocking effect, a behavioral manifestation of error correction learning. The authors also discuss the model's implications for understanding the limits of cerebellar contributions to associative learning and how this informs our understanding of hippocampal function in conditioning. This leads to a more integrative view of the neural substrates of conditioning in which the authors' real-time circuit-level model of the cerebellum can be viewed as a generalization of the long-term memory module of Gluck and Myers' (1993) trial-level theory of cerebellar-hippocampal interaction in motor conditioning.