Tom Griffiths

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).

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

Information changes as it is passed from person to person, with this process of cultural transmission allowing the minds of individuals to shape the information that they transmit. We present mathematical models of cultural transmission which predict that the amount of information passed from person to person should affect the rate at which that information changes. We tested this prediction using a function-learning task, in which people learn a functional relationship between two variables by observing the values of those variables. We varied the total number of observations and the number of those observations that take unique values. We found an effect of the number of observations, with functions transmitted using fewer observations changing form more quickly. We did not find an effect of the number of unique observations, suggesting that noise in perception or memory may have affected learning

Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models. Key Words: additive clustering; Bayesian inference; categorization; concept learning; contrast model; features; generalization; psychological space; similarity.

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.”

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

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

If Bayesian Fundamentalism existed, Jones & Love's (J&L's) arguments would provide a necessary corrective. But it does not. Bayesian cognitive science is deeply concerned with characterizing algorithms and representations, and, ultimately, implementations in neural circuits; it pays close attention to environmental structure and the constraints of behavioral data, when available; and it rigorously compares multiple models, both within and across papers. J&L's recommendation of Bayesian Enlightenment corresponds to past, present, and, we hope, future practice in Bayesian cognitive science

Decades of psychological research have been aimed at modeling how people learn features and categories. The empirical validation of these theories is often based on artificial stimuli with simple representations. Recently, deep neural networks have reached or surpassed human accuracy on tasks such as identifying objects in natural images. These networks learn representations of real‐world stimuli that can potentially be leveraged to capture psychological representations. We find that state‐of‐the‐art object classification networks provide surprisingly accurate predictions of human similarity judgments for natural images, but they fail to capture some of the structure represented by people. We show that a simple transformation that corrects these discrepancies can be obtained through convex optimization. We use the resulting representations to predict the difficulty of learning novel categories of natural images. Our results extend the scope of psychological experiments and computational modeling by enabling tractable use of large natural stimulus sets.

Exploring how people represent natural categories is a key step toward developing a better understanding of how people learn, form memories, and make decisions. Much research on categorization has focused on artificial categories that are created in the laboratory, since studying natural categories defined on high-dimensional stimuli such as images is methodologically challenging. Recent work has produced methods for identifying these representations from observed behavior, such as reverse correlation (RC). We compare RC against an alternative method for inferring the structure of natural categories called Markov chain Monte Carlo with People (MCMCP). Based on an algorithm used in computer science and statistics, MCMCP provides a way to sample from the set of stimuli associated with a natural category. We apply MCMCP and RC to the problem of recovering natural categories that correspond to two kinds of facial affect (happy and sad) from realistic images of faces. Our results show that MCMCP requires fewer trials to obtain a higher quality estimate of people’s mental representations of these two categories

Determining the knowledge that guides human judgments is fundamental to understanding how people reason, make decisions, and form predictions. We use an experimental procedure called ‘‘iterated learning,’’ in which the responses that people give on one trial are used to generate the data they see on the next, to pinpoint the knowledge that informs people's predictions about everyday events (e.g., predicting the total box office gross of a movie from its current take). In particular, we use this method to discriminate between two models of human judgments: a simple Bayesian model (Griffiths & Tenenbaum, 2006) and a recently proposed alternative model that assumes people store only a few instances of each type of event in memory (MinK; Mozer, Pashler, & Homaei, 2008). Although testing these models using standard experimental procedures is difficult due to differences in the number of free parameters and the need to make assumptions about the knowledge of individual learners, we show that the two models make very different predictions about the outcome of iterated learning. The results of an experiment using this methodology provide a rich picture of how much people know about the distributions of everyday quantities, and they are inconsistent with the predictions of the MinK model. The results suggest that accurate predictions about everyday events reflect relatively sophisticated knowledge on the part of individuals.

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.