Efficient sampling and noisy decisions

Efficient numerosity estimation under limited time

The ability to rapidly estimate non-symbolic numerical quantities is a well-conserved sense across species with clear evolutionary advantages. However, despite its importance, this sense is surprisingly imprecise and biased, and a formal explanation for this seemingly irrational behavior remains unclear. We develop a unified normative theory of numerosity estimation that parsimoniously incorporates in a single framework information processing constraints alongside (i) Brownian diffusion noise to capture the effects of time exposure of sensory information, (ii) logarithmic encoding of numerosity representations, and (iii) optimal inference via Bayesian decoding. We show that for a given allowable biological capacity constraint our model naturally endogenizes time perception during noisy efficient encoding to predict the complete posterior distribution of numerosity estimates. This model accurately predicts many features of human numerosity estimation as a function of temporal exposure, indicating that humans can rapidly and efficiently sample numerosity information over time. Additionally, we demonstrate how our model fundamentally differs from a thermodynamically-inspired formalization of bounded rationality, where information processing is modeled as acting to shift away from default states. The mechanism we propose is the likely origin of a variety of numerical cognition patterns observed in humans and other animals.

Exploring the bounded rationality in human decision anomalies through an assemblable computational framework

Some seemingly irrational decision behaviors (anomalies), once seen as flaws in human cognition, have recently received explanations from a rational perspective. The basic idea is that the brain has limited cognitive resources to process the quantities (e.g., value, probability, time, etc.) required for decision making, with specific biases arising as byproducts of the resource allocation that is optimized for the environment. While appealing for providing normative accounts, the existing resource-rational models have limitations such as inconsistent assumptions across models, a focus on optimization for one specific aspect of the environment, and limited coverage of decision anomalies. One challenging anomaly is the peanuts effect, a pervasive phenomenon in decision-making under risk that implies an interdependence between the processing of value and probability. To extend the resource rationality approach to explain the peanuts effect, here we develop a computational framework-the Assemblable Resource-Rational Modules (ARRM)-that integrates ideas from different lines of boundedly-rational decision models as freely assembled modules. The framework can accommodate the joint functioning of multiple environmental factors, and allow new models to be built and tested along with the existing ones, potentially opening a wider range of decision phenomena to bounded rationality modeling. For one new and three published datasets that cover two different task paradigms and both the gain and loss domains, our boundedly-rational models reproduce two characteristic features of the peanuts effect and outperform previous models in fitting human decision behaviors.

Metacognition of perceptual resolution across and around the visual field

Do people have accurate metacognition of non-uniformities in perceptual resolution across (i.e., eccentricity) and around (i.e., polar angle) the visual field? Despite its theoretical and practical importance, this question has not yet been empirically tested. This study investigated metacognition of perceptual resolution by guessing patterns during a degradation (i.e., loss of high spatial frequencies) localization task. Participants localized the degraded face among the nine faces that simultaneously appeared throughout the visual field: fovea (fixation at the center of the screen), parafovea (left, right, above, and below fixation at 4° eccentricity), and periphery (left, right, above, and below fixation at 10° eccentricity). We presumed that if participants had accurate metacognition, in the absence of a degraded face, they would exhibit compensatory guessing patterns based on counterfactual reasoning ("The degraded face must have been presented at locations with lower perceptual resolution, because if it were presented at locations with higher perceptual resolution, I would have easily detected it."), meaning that we would expect more guess responses for locations with lower perceptual resolution. In two experiments, we observed guessing patterns that suggest that people can monitor non-uniformities in perceptual resolution across, but not around, the visual field during tasks, indicating partial in-the-moment metacognition. Additionally, we found that global explicit knowledge of perceptual resolution is not sufficient to guide in-the-moment metacognition during tasks, which suggests a dissociation between local and global metacognition.

Neurobehavioral meaning of pupil size

Pupil size is a widely used metric of brain state. It is one of the few signals originating from the brain that can be readily monitored with low-cost devices in basic science, clinical, and home settings. It is, therefore, important to investigate and generate well-defined theories related to specific interpretations of this metric. What exactly does it tell us about the brain? Pupils constrict in response to light and dilate during darkness, but the brain also controls pupil size irrespective of luminosity. Pupil size fluctuations resulting from ongoing "brain states" are used as a metric of arousal, but what is pupil-linked arousal and how should it be interpreted in neural, cognitive, and computational terms? Here, we discuss some recent findings related to these issues. We identify open questions and propose how to answer them through a combination of well-defined tasks, neurocomputational models, and neurophysiological probing of the interconnected loops of causes and consequences of pupil size.

Beyond discrete-choice options

While decision theories have evolved over the past five decades, their focus has largely been on choices among a limited number of discrete options, even though many real-world situations have a continuous-option space. Recently, theories have attempted to address decisions with continuous-option spaces, and several computational models have been proposed within the sequential sampling framework to explain how we make a decision in continuous-option space. This article aims to review the main attempts to understand decisions on continuous-option spaces, give an overview of applications of these types of decisions, and present puzzles to be addressed by future developments.

Rationality, preferences, and emotions with biological constraints: it all starts from our senses

Is the role of our sensory systems to represent the physical world as accurately as possible? If so, are our preferences and emotions, often deemed irrational, decoupled from these 'ground-truth' sensory experiences? We show why the answer to both questions is 'no'. Brain function is metabolically costly, and the brain loses some fraction of the information that it encodes and transmits. Therefore, if brains maximize objective functions that increase the fitness of their species, they should adapt to the objective-maximizing rules of the environment at the earliest stages of sensory processing. Consequently, observed 'irrationalities', preferences, and emotions stem from the necessity for our early sensory systems to adapt and process information while considering the metabolic costs and internal states of the organism.

The parieto-occipital cortex is a candidate neural substrate for the human ability to approximate Bayesian inference

Adaptive decision-making often requires one to infer unobservable states based on incomplete information. Bayesian logic prescribes that individuals should do so by estimating the posterior probability by integrating the prior probability with new information, but the neural basis of this integration is incompletely understood. We record fMRI during a task in which participants infer the posterior probability of a hidden state while we independently modulate the prior probability and likelihood of evidence regarding the state; the task incentivizes participants to make accurate inferences and dissociates expected value from posterior probability. Here we show that activation in a region of left parieto-occipital cortex independently tracks the subjective posterior probability, combining its subcomponents of prior probability and evidence likelihood, and reflecting the individual participants' systematic deviations from objective probabilities. The parieto-occipital cortex is thus a candidate neural substrate for humans' ability to approximate Bayesian inference by integrating prior beliefs with new information.

Individual risk attitudes arise from noise in neurocognitive magnitude representations

Humans are generally risk averse, preferring smaller certain over larger uncertain outcomes. Economic theories usually explain this by assuming concave utility functions. Here, we provide evidence that risk aversion can also arise from relative underestimation of larger monetary payoffs, a perceptual bias rooted in the noisy logarithmic coding of numerical magnitudes. We confirmed this with psychophysics and functional magnetic resonance imaging, by measuring behavioural and neural acuity of magnitude representations during a magnitude perception task and relating these measures to risk attitudes during separate risky financial decisions. Computational modelling indicated that participants use similar mental magnitude representations in both tasks, with correlated precision across perceptual and risky choices. Participants with more precise magnitude representations in parietal cortex showed less variable behaviour and less risk aversion. Our results highlight that at least some individual characteristics of economic behaviour can reflect capacity limitations in perceptual processing rather than processes that assign subjective values to monetary outcomes.

Sensory perception relies on fitness-maximizing codes

Sensory information encoded by humans and other organisms is generally presumed to be as accurate as their biological limitations allow. However, perhaps counterintuitively, accurate sensory representations may not necessarily maximize the organism's chances of survival. To test this hypothesis, we developed a unified normative framework for fitness-maximizing encoding by combining theoretical insights from neuroscience, computer science, and economics. Behavioural experiments in humans revealed that sensory encoding strategies are flexibly adapted to promote fitness maximization, a result confirmed by deep neural networks with information capacity constraints trained to solve the same task as humans. Moreover, human functional MRI data revealed that novel behavioural goals that rely on object perception induce efficient stimulus representations in early sensory structures. These results suggest that fitness-maximizing rules imposed by the environment are applied at early stages of sensory processing in humans and machines.

The effects of base rate neglect on sequential belief updating and real-world beliefs

Base-rate neglect is a pervasive bias in judgment that is conceptualized as underweighting of prior information and can have serious consequences in real-world scenarios. This bias is thought to reflect variability in inferential processes but empirical support for a cohesive theory of base-rate neglect with sufficient explanatory power to account for longer-term and real-world beliefs is lacking. A Bayesian formalization of base-rate neglect in the context of sequential belief updating predicts that belief trajectories should exhibit dynamic patterns of dependence on the order in which evidence is presented and its consistency with prior beliefs. To test this, we developed a novel 'urn-and-beads' task that systematically manipulated the order of colored bead sequences and elicited beliefs via an incentive-compatible procedure. Our results in two independent online studies confirmed the predictions of the sequential base-rate neglect model: people exhibited beliefs that are more influenced by recent evidence and by evidence inconsistent with prior beliefs. We further found support for a noisy-sampling inference model whereby base-rate neglect results from rational discounting of noisy internal representations of prior beliefs. Finally, we found that model-derived indices of base-rate neglect-including noisier prior representation-correlated with propensity for unusual beliefs outside the laboratory. Our work supports the relevance of Bayesian accounts of sequential base-rate neglect to real-world beliefs and hints at strategies to minimize deleterious consequences of this pervasive bias.

Rethinking delusions: A selective review of delusion research through a computational lens

Delusions are rigid beliefs held with high certainty despite contradictory evidence. Notwithstanding decades of research, we still have a limited understanding of the computational and neurobiological alterations giving rise to delusions. In this review, we highlight a selection of recent work in computational psychiatry aimed at developing quantitative models of inference and its alterations, with the goal of providing an explanatory account for the form of delusional beliefs in psychosis. First, we assess and evaluate the experimental paradigms most often used to study inferential alterations in delusions. Based on our review of the literature and theoretical considerations, we contend that classic draws-to-decision paradigms are not well-suited to isolate inferential processes, further arguing that the commonly cited 'jumping-to-conclusion' bias may reflect neither delusion-specific nor inferential alterations. Second, we discuss several enhancements to standard paradigms that show promise in more effectively isolating inferential processes and delusion-related alterations therein. We further draw on our recent work to build an argument for a specific failure mode for delusions consisting of prior overweighting in high-level causal inferences about partially observable hidden states. Finally, we assess plausible neurobiological implementations for this candidate failure mode of delusional beliefs and outline promising future directions in this area.

Efficiently irrational: deciphering the riddle of human choice

For the past half-century, cognitive and social scientists have struggled with the irrationalities of human choice behavior; people consistently make choices that are logically inconsistent. Is human choice behavior evolutionarily adaptive or is it an inefficient patchwork of competing mechanisms? In this review, I present an interdisciplinary synthesis arguing for a novel interpretation: choice is efficiently irrational. Connecting findings across disciplines suggests that observed choice behavior reflects a precise optimization of the trade-off between the costs of increasing the precision of the choice mechanism and the declining benefits that come as precision increases. Under these constraints, a rationally imprecise strategy emerges that works toward optimal efficiency rather than toward optimal rationality. This approach rationalizes many of the puzzling inconsistencies of human choice behavior, explaining why these inconsistencies arise as an optimizing solution in biological choosers.

Rational inattention in mice

Behavior exhibited by humans and other organisms is generally inconsistent and biased and, thus, is often labeled irrational. However, the origins of this seemingly suboptimal behavior remain elusive. We developed a behavioral task and normative framework to reveal how organisms should allocate their limited processing resources such that sensory precision and its related metabolic investment are balanced to guarantee maximal utility. We found that mice act as rational inattentive agents by adaptively allocating their sensory resources in a way that maximizes reward consumption in previously unexperienced stimulus-reward association environments. Unexpectedly, perception of commonly occurring stimuli was relatively imprecise; however, this apparent statistical fallacy implies "awareness" and efficient adaptation to their neurocognitive limitations. Arousal systems carry reward distribution information of sensory signals, and distributional reinforcement learning mechanisms regulate sensory precision via top-down normalization. These findings reveal how organisms efficiently perceive and adapt to previously unexperienced environmental contexts within the constraints imposed by neurobiology.

Sources of confidence in value-based choice

Confidence, the subjective estimate of decision quality, is a cognitive process necessary for learning from mistakes and guiding future actions. The origins of confidence judgments resulting from economic decisions remain unclear. We devise a task and computational framework that allowed us to formally tease apart the impact of various sources of confidence in value-based decisions, such as uncertainty emerging from encoding and decoding operations, as well as the interplay between gaze-shift dynamics and attentional effort. In line with canonical decision theories, trial-to-trial fluctuations in the precision of value encoding impact economic choice consistency. However, this uncertainty has no influence on confidence reports. Instead, confidence is associated with endogenous attentional effort towards choice alternatives and down-stream noise in the comparison process. These findings provide an explanation for confidence (miss)attributions in value-guided behaviour, suggesting mechanistic influences of endogenous attentional states for guiding decisions and metacognitive awareness of choice certainty.

Normative Principles for Decision-Making in Natural Environments

The decisions we make are shaped by a lifetime of learning. Past experience guides the way that we encode information in neural systems for perception and valuation, and determines the information we retrieve when making decisions. Distinct literatures have discussed how lifelong learning and local context shape decisions made about sensory signals, propositional information, or economic prospects. Here, we build bridges between these literatures, arguing for common principles of adaptive rationality in perception, cognition, and economic choice. We discuss how a single common framework, based on normative principles of efficient coding and Bayesian inference, can help us understand a myriad of human decision biases, including sensory illusions, adaptive aftereffects, choice history biases, central tendency effects, anchoring effects, contrast effects, framing effects, congruency effects, reference-dependent valuation, nonlinear utility functions, and discretization heuristics. We describe a simple computational framework for explaining these phenomena. Expected final online publication date for the Annual Review of Psychology, Volume 73 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Variance misperception under skewed empirical noise statistics explains overconfidence in the visual periphery

Perceptual confidence typically corresponds to accuracy. However, observers can be overconfident relative to accuracy, termed "subjective inflation." Inflation is stronger in the visual periphery relative to central vision, especially under conditions of peripheral inattention. Previous literature suggests inflation stems from errors in estimating noise (i.e., "variance misperception"). However, despite previous Bayesian hypotheses about metacognitive noise estimation, no work has systematically explored how noise estimation may critically depend on empirical noise statistics, which may differ across the visual field, with central noise distributed symmetrically but peripheral noise positively skewed. Here, we examined central and peripheral vision predictions from five Bayesian-inspired noise-estimation algorithms under varying usage of noise priors, including effects of attention. Models that failed to optimally estimate noise exhibited peripheral inflation, but only models that explicitly used peripheral noise priors-but used them incorrectly-showed increasing peripheral inflation under increasing peripheral inattention. Further, only one model successfully captured previous empirical results, which showed a selective increase in confidence in incorrect responses under performance reductions due to inattention accompanied by no change in confidence in correct responses; this was the model that implemented Bayesian estimation of peripheral noise, but using an (incorrect) symmetric rather than the correct positively skewed peripheral noise prior. Our findings explain peripheral inflation, especially under inattention, and suggest future experiments that might reveal the noise expectations used by the visual metacognitive system.

Optimal utility and probability functions for agents with finite computational precision

When making economic choices, such as those between goods or gambles, humans act as if their internal representation of the value and probability of a prospect is distorted away from its true value. These distortions give rise to decisions which apparently fail to maximize reward, and preferences that reverse without reason. Why would humans have evolved to encode value and probability in a distorted fashion, in the face of selective pressure for reward-maximizing choices? Here, we show that under the simple assumption that humans make decisions with finite computational precision--in other words, that decisions are irreducibly corrupted by noise--the distortions of value and probability displayed by humans are approximately optimal in that they maximize reward and minimize uncertainty. In two empirical studies, we manipulate factors that change the reward-maximizing form of distortion, and find that in each case, humans adapt optimally to the manipulation. This work suggests an answer to the longstanding question of why humans make "irrational" economic choices.

Efficient sampling and noisy decisions

Human decisions are based on finite information, which makes them inherently imprecise. But what determines the degree of such imprecision? Here, we develop an efficient coding framework for higher-level cognitive processes in which information is represented by a finite number of discrete samples. We characterize the sampling process that maximizes perceptual accuracy or fitness under the often-adopted assumption that full adaptation to an environmental distribution is possible, and show how the optimal process differs when detailed information about the current contextual distribution is costly. We tested this theory on a numerosity discrimination task, and found that humans efficiently adapt to contextual distributions, but in the way predicted by the model in which people must economize on environmental information. Thus, understanding decision behavior requires that we account for biological restrictions on information coding, challenging the often-adopted assumption of precise prior knowledge in higher-level decision systems.