Fast and Accurate Learning When Making Discrete Numerical Estimates

The role of episodic memory sampling in evaluation

Many models of choice assume that people retrieve memories of past experiences and use them to guide evaluation and choice. In this paper, we examine whether samples of recalled past experiences do indeed underpin our evaluations of options. We showed participants sequences of numerical values and asked them to recall as many of those values as possible and also to state how much they would be willing to pay for another draw from the sequence. Using Bayesian mixed effects modeling, we predicted participants' evaluation of the sequences at the group level from either the average of the values they recalled or the average of the values they saw. Contrary to the predictions of recall-based models, people's evaluations appear to be sensitive to information beyond what was actually recalled. Moreover, we did not find consistent evidence that memory for specific items is sufficient to predict evaluation of sequences. We discuss the implications for sampling models of memory and decision-making and alternative explanations.

The autocorrelated Bayesian sampler: A rational process for probability judgments, estimates, confidence intervals, choices, confidence judgments, and response times

Normative models of decision-making that optimally transform noisy (sensory) information into categorical decisions qualitatively mismatch human behavior. Indeed, leading computational models have only achieved high empirical corroboration by adding task-specific assumptions that deviate from normative principles. In response, we offer a Bayesian approach that implicitly produces a posterior distribution of possible answers (hypotheses) in response to sensory information. But we assume that the brain has no direct access to this posterior, but can only sample hypotheses according to their posterior probabilities. Accordingly, we argue that the primary problem of normative concern in decision-making is integrating stochastic hypotheses, rather than stochastic sensory information, to make categorical decisions. This implies that human response variability arises mainly from posterior sampling rather than sensory noise. Because human hypothesis generation is serially correlated, hypothesis samples will be autocorrelated. Guided by this new problem formulation, we develop a new process, the Autocorrelated Bayesian Sampler (ABS), which grounds autocorrelated hypothesis generation in a sophisticated sampling algorithm. The ABS provides a single mechanism that qualitatively explains many empirical effects of probability judgments, estimates, confidence intervals, choice, confidence judgments, response times, and their relationships. Our analysis demonstrates the unifying power of a perspective shift in the exploration of normative models. It also exemplifies the proposal that the "Bayesian brain" operates using samples not probabilities, and that variability in human behavior may primarily reflect computational rather than sensory noise. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Temporal integration of feature probability distributions

Humans are surprisingly good at learning the statistical characteristics of their visual environment. Recent studies have revealed that not only can the visual system learn repeated features of visual search distractors, but also their actual probability distributions. Search times were determined by the frequency of distractor features over consecutive search trials. The search displays applied in these studies involved many exemplars of distractors on each trial and while there is clear evidence that feature distributions can be learned from large distractor sets, it is less clear if distributions are well learned for single targets presented on each trial. Here, we investigated potential learning of probability distributions of single targets during visual search. Over blocks of trials, observers searched for an oddly colored target that was drawn from either a Gaussian or a uniform distribution. Search times for the different target colors were clearly influenced by the probability of that feature within trial blocks. The same search targets, coming from the extremes of the two distributions were found significantly slower during the blocks where the targets were drawn from a Gaussian distribution than from a uniform distribution indicating that observers were sensitive to the target probability determined by the distribution shape. In Experiment 2, we replicated the effect using binned distributions and revealed the limitations of encoding complex target distributions. Our results demonstrate detailed internal representations of target feature distributions and that the visual system integrates probability distributions of target colors over surprisingly long trial sequences.

Biased confabulation in risky choice

When people make risky decisions based on past experience, they must rely on memory. The nature of the memory representations that support these decisions is not yet well understood. A key question concerns the extent to which people recall specific past episodes or whether they have learned a more abstract rule from their past experience. To address this question, we examined the precision of the memories used in risky decisions-from-experience. In three pre-registered experiments, we presented people with risky options, where the outcomes were drawn from continuous ranges (e.g., 100-190 or 500-590), and then assessed their memories for the outcomes experienced. In two preferential tasks, people were more risk seeking for high-value than low-value options, choosing as though they overweighted the outcomes from more extreme ranges. Moreover, in two preferential tasks and a parallel evaluation task, people were very poor at recalling the exact outcomes encountered, but rather confabulated outcomes that were consistent with the outcomes they had seen and were biased towards the more extreme ranges encountered. This common pattern suggests that the observed decision bias in the preferential task reflects a basic cognitive process to overweight extreme outcomes in memory. These results highlight the importance of the edges of the distribution in providing the encoding context for memory recall. They also suggest that episodic memory influences decision-making through gist memory and not through direct recall of specific instances.

Using Occam's razor and Bayesian modelling to compare discrete and continuous representations in numerosity judgements

Previous research has established that numeric estimates are based not just on perceptual data but also past experience, and so may be influenced by the form of this stored information. It remains unclear, however, how such experience is represented: numerical data can be processed by either a continuous analogue number system or a discrete symbolic number system, with each predicting different generalisation effects. The present paper therefore contrasts discrete and continuous prior formats within the domain of numerical estimation using both direct comparisons of computational models of this process using these representations, as well as empirical contrasts exploiting different predicted reactions of these formats to uncertainty via Occam's razor. Both computational and empirical results indicate that numeric estimates commonly rely on a continuous prior format, mirroring the analogue approximate number system, or 'number sense'. This implies a general preference for the use of continuous numerical representations even where both stimuli and responses are discrete, with learners seemingly relying on innate number systems rather than the symbolic forms acquired in later life. There is however remaining uncertainty in these results regarding individual differences in the use of these systems, which we address in recommendations for future work.

A dilution effect without dilution: When missing evidence, not non-diagnostic evidence, is judged inaccurately

When asked to combine two pieces of evidence, one diagnostic and one non-diagnostic, people show a dilution effect: the addition of non-diagnostic evidence dilutes the overall strength of the evidence. This non-normative effect has been found in a variety of tasks and has been taken as evidence that people inappropriately combine information. In a series of five experiments, we found the dilution effect, but surprisingly it was not due to the inaccurate combination of diagnostic and non-diagnostic information. Because we have objectively correct answers for our task, we could see that participants were relatively accurate in judging diagnostic evidence combined with non-diagnostic evidence, but overestimated the strength of diagnostic evidence alone. This meant that the dilution effect - the gap between diagnostic evidence alone and diagnostic evidence combined with non-diagnostic evidence - was not caused by dilution. We hypothesized that participants were filling in "missing" evidence in a biased fashion when presented with diagnostic evidence alone. This hypothesis best explained the experimental results.

What does the mind learn? A comparison of human and machine learning representations

We present a brief review of modern machine learning techniques and their use in models of human mental representations, detailing three notable branches: spatial methods, logical methods and artificial neural networks. Each of these branches contains an extensive set of systems, and demonstrate accurate emulations of human learning of categories, concepts and language, despite substantial differences in operation. We suggest that continued applications will allow cognitive researchers the ability to model the complex real-world problems where machine learning has recently been successful, providing more complete behavioural descriptions. This will, however, also require careful consideration of appropriate algorithmic constraints alongside these methods in order to find a combination which captures both the strengths and weaknesses of human cognition.

Bayesian adaptive stimulus selection for dissociating models of psychophysical data

Comparing models facilitates testing different hypotheses regarding the computational basis of perception and action. Effective model comparison requires stimuli for which models make different predictions. Typically, experiments use a predetermined set of stimuli or sample stimuli randomly. Both methods have limitations; a predetermined set may not contain stimuli that dissociate the models, whereas random sampling may be inefficient. To overcome these limitations, we expanded the psi-algorithm (Kontsevich & Tyler, 1999) from estimating the parameters of a psychometric curve to distinguishing models. To test our algorithm, we applied it to two distinct problems. First, we investigated dissociating sensory noise models. We simulated ideal observers with different noise models performing a two-alternative forced-choice task. Stimuli were selected randomly or using our algorithm. We found using our algorithm improved the accuracy of model comparison. We also validated the algorithm in subjects by inferring which noise model underlies speed perception. Our algorithm converged quickly to the model previously proposed (Stocker & Simoncelli, 2006), whereas if stimuli were selected randomly, model probabilities separated slower and sometimes supported alternative models. Second, we applied our algorithm to a different problem-comparing models of target selection under body acceleration. Previous work found target choice preference is modulated by whole body acceleration (Rincon-Gonzalez et al., 2016). However, the effect is subtle, making model comparison difficult. We show that selecting stimuli adaptively could have led to stronger conclusions in model comparison. We conclude that our technique is more efficient and more reliable than current methods of stimulus selection for dissociating models.

How effective is incidental learning of the shape of probability distributions?

The idea that people learn detailed probabilistic generative models of the environments they interact with is intuitively appealing, and has received support from recent studies of implicit knowledge acquired in daily life. The goal of this study was to see whether people efficiently induce a probability distribution based upon incidental exposure to an unknown generative process. Subjects played a 'whack-a-mole' game in which they attempted to click on objects appearing briefly, one at a time on the screen. Horizontal positions of the objects were generated from a bimodal distribution. After 180 plays of the game, subjects were unexpectedly asked to generate another 180 target positions of their own from the same distribution. Their responses did not even show a bimodal distribution, much less an accurate one (Experiment 1). The same was true for a pre-announced test (Experiment 2). On the other hand, a more extreme bimodality with zero density in a middle region did produce some distributional learning (Experiment 3), perhaps reflecting conscious hypothesis testing. We discuss the challenge this poses to the idea of efficient accurate distributional learning.

Generalization of prior information for rapid Bayesian time estimation

To enable effective interaction with the environment, the brain combines noisy sensory information with expectations based on prior experience. There is ample evidence showing that humans can learn statistical regularities in sensory input and exploit this knowledge to improve perceptual decisions and actions. However, fundamental questions remain regarding how priors are learned and how they generalize to different sensory and behavioral contexts. In principle, maintaining a large set of highly specific priors may be inefficient and restrict the speed at which expectations can be formed and updated in response to changes in the environment. However, priors formed by generalizing across varying contexts may not be accurate. Here, we exploit rapidly induced contextual biases in duration reproduction to reveal how these competing demands are resolved during the early stages of prior acquisition. We show that observers initially form a single prior by generalizing across duration distributions coupled with distinct sensory signals. In contrast, they form multiple priors if distributions are coupled with distinct motor outputs. Together, our findings suggest that rapid prior acquisition is facilitated by generalization across experiences of different sensory inputs but organized according to how that sensory information is acted on.