Tom Griffiths

We study human performance in two classical NP‐hard optimization problems: Set Cover and Maximum Coverage. We suggest that Set Cover and Max Coverage are related to means selection problems that arise in human problem‐solving and in pursuing multiple goals: The relationship between goals and means is expressed as a bipartite graph where edges between means and goals indicate which means can be used to achieve which goals. While these problems are believed to be computationally intractable in general, they become more tractable when the structure of the network resembles a tree. Thus, our main prediction is that people should perform better with goal systems that are more tree‐like. We report three behavioral experiments which confirm this prediction. Our results suggest that combinatorial parameters that are instrumental to algorithm design can also be useful for understanding when and why people struggle to choose between multiple means to achieve multiple goals.

Social learning has been shown to be an evolutionarily adaptive strategy, but it can be implemented via many different cognitive mechanisms. The adaptive advantage of social learning depends crucially on the ability of each learner to obtain relevant and accurate information from informants. The source of informants’ knowledge is a particularly important cue for evaluating advice from multiple informants; if the informants share the source of their information or have obtained their information from each other, then their testimony is statistically dependent and may be less reliable than testimony from informants who do not share information. In this study, we use a Bayesian model to determine how rational learners should incorporate the effects of shared information when learning from other people, conducting three experiments that examine whether human learners behave similarly. We find that people are sensitive to a number of different patterns of dependency, supporting the use of a sophisticated strategy for social learning that goes beyond copying the majority, and broadening the situations in which social learning is likely to be an adaptive strategy.

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

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.

Analyzing the rate at which languages change can clarify whether similarities across languages are solely the result of cognitive biases or might be partially due to descent from a common ancestor. To demonstrate this approach, we use a simple model of language evolution to mathematically determine how long it should take for the distribution over languages to lose the influence of a common ancestor and converge to a form that is determined by constraints on language learning. We show that modeling language learning as Bayesian inference ofnbinary parameters or the ordering ofnconstraints results in convergence in a number of generations that is on the order ofn log n. We relax some of the simplifying assumptions of this model to explore how different assumptions about language evolution affect predictions about the time to convergence; in general, convergence time increases as the model becomes more realistic. This allows us to characterize the assumptions about language learning (given the models that we consider) that are sufficient for convergence to have taken place on a timescale that is consistent with the origin of human languages. These results clearly identify the consequences of a set of simple models of language evolution and show how analysis of convergence rates provides a tool that can be used to explore questions about the relationship between accounts of language learning and the origins of similarities across languages.

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.

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.”

Most cognitive psychology experiments evaluate models of human cognition using a relatively small, well-controlled set of stimuli. This approach stands in contrast to current work in neuroscience, perception, and computer vision, which have begun to focus on using large databases of natural images. We argue that natural images provide a powerful tool for characterizing the statistical environment in which people operate, for better evaluating psychological theories, and for bringing the insights of cognitive science closer to real applications. We discuss how some of the challenges of using natural images as stimuli in experiments can be addressed through increased sample sizes, using representations from computer vision, and developing new experimental methods. Finally, we illustrate these points by summarizing recent work using large image databases to explore questions about human cognition in four different domains: modeling subjective randomness, defining a quantitative measure of representativeness, identifying prior knowledge used in word learning, and determining the structure of natural categories.

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

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

When someone hosts a party, when governments choose an aid program, or when assistive robots decide what meal to serve to a family, decision‐makers must determine how to help even when their recipients have very different preferences. Which combination of people’s desires should a decision‐maker serve? To provide a potential answer, we turned to psychology: What do people think is best when multiple people have different utilities over options? We developed a quantitative model of what people consider desirable behavior, characterizing participants’ preferences by inferring which combination of “metrics” (maximax, maxsum, maximin, or inequality aversion [IA]) best explained participants’ decisions in a drink‐choosing task. We found that participants’ behavior was best described by the maximin metric, describing the desire to maximize the happiness of the worst‐off person, though participant behavior was also consistent with maximizing group utility (the maxsum metric) and the IA metric to a lesser extent. Participant behavior was consistent across variation in the agents involved and tended to become more maxsum‐oriented when participants were told they were players in the task (Experiment 1). In later experiments, participants maintained maximin behavior across multi‐step tasks rather than shortsightedly focusing on the individual steps therein (Experiment 2, Experiment 3). By repeatedly asking participants what choices they would hope for in an optimal, just decision‐maker, and carefully disambiguating which quantitative metrics describe these nuanced choices, we help constrain the space of what behavior we desire in leaders, artificial intelligence systems helping decision‐makers, and the assistive robots and decision‐makers of the future.

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.

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

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