Tom Griffiths

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

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).

Humans can learn complex functional relationships between variables from small amounts of data. In doing so, they draw on prior expectations about the form of these relationships. In three experiments, we show that people learn to adjust these expectations through experience, learning about the likely forms of the functions they will encounter. Previous work has used Gaussian processes—a statistical framework that extends Bayesian nonparametric approaches to regression—to model human function learning. We build on this work, modeling the process of learning to learn functions as a form of hierarchical Bayesian inference about the Gaussian process hyperparameters.

Convolutional neural networks (CNNs) are increasingly widely used in psychology and neuroscience to predict how human minds and brains respond to visual images. Typically, CNNs represent these images using thousands of features that are learned through extensive training on image datasets. This raises a question: How many of these features are really needed to model human behavior? Here, we attempt to estimate the number of dimensions in CNN representations that are required to capture human psychological representations in two ways: (1) directly, using human similarity judgments and (2) indirectly, in the context of categorization. In both cases, we find that low-dimensional projections of CNN representations are sufficient to predict human behavior. We show that these low-dimensional representations can be easily interpreted, providing further insight into how people represent visual information. A series of control studies indicate that these findings are not due to the size of the dataset we used and may be due to a high level of redundancy in the features appearing in CNN representations.

Language research has come to rely heavily on large‐scale, web‐based datasets. These datasets can present significant methodological challenges, requiring researchers to make a number of decisions about how they are collected, represented, and analyzed. These decisions often concern long‐standing challenges in corpus‐based language research, including determining what counts as a word, deciding which words should be analyzed, and matching sets of words across languages. We illustrate these challenges by revisiting “Word lengths are optimized for efficient communication” (Piantadosi, Tily, & Gibson, 2011), which found that word lengths in 11 languages are more strongly correlated with their average predictability (or average information content) than their frequency. Using what we argue to be best practices for large‐scale corpus analyses, we find significantly attenuated support for this result and demonstrate that a stronger relationship obtains between word frequency and length for a majority of the languages in the sample. We consider the implications of the results for language research more broadly and provide several recommendations to researchers regarding best practices.

Spoken communication occurs in a “noisy channel” characterized by high levels of environmental noise, variability within and between speakers, and lexical and syntactic ambiguity. Given these properties of the received linguistic input, robust spoken word recognition—and language processing more generally—relies heavily on listeners' prior knowledge to evaluate whether candidate interpretations of that input are more or less likely. Here we compare several broad-coverage probabilistic generative language models in their ability to capture human linguistic expectations. Serial reproduction, an experimental paradigm where spoken utterances are reproduced by successive participants similar to the children's game of “Telephone,” is used to elicit a sample that reflects the linguistic expectations of English-speaking adults. When we evaluate a suite of probabilistic generative language models against the yielded chains of utterances, we find that those models that make use of abstract representations of preceding linguistic context (i.e., phrase structure) best predict the changes made by people in the course of serial reproduction. A logistic regression model predicting which words in an utterance are most likely to be lost or changed in the course of spoken transmission corroborates this result. We interpret these findings in light of research highlighting the interaction of memory-based constraints and representations in language processing.

Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how to solve the equation and the ways in which they might answer incorrectly offers the opportunity to obtain a more nuanced perspective of their algebra skills. To automatically make sense of step‐by‐step solutions, we propose a Bayesian inverse planning model for equation solving that computes an assessment of a learner's skills based on her pattern of errors in individual steps and her choices about what sequence of problem‐solving steps to take. Bayesian inverse planning builds on existing machine learning tools to create a generative model relating (mis)‐understandings to equation solving choices. Two behavioral experiments demonstrate that the model can interpret people's equation solving and that its assessments are consistent with those of experienced teachers. A third experiment uses this model to tailor guidance for learners based on individual differences in misunderstandings, closing the loop between assessing understanding, and using that assessment within an educational technology. Finally, because the bottleneck in applying inverse planning to a new domain is in creating the model of possible student misunderstandings, we show how to combine inverse planning with an existing production rule model to make inferences about student misunderstandings of fraction arithmetic.