Mathematical Models for Decision-Making

Thursday, June 17 at 04:15am (PDT)
Thursday, June 17 at 12:15pm (BST)
Thursday, June 17 08:15pm (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS18" time block.
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Nicholas Barendregt (University of Colorado Boulder, United States), Jonathan Rubin (University of Pittsburgh, United States)


To make effective decisions in real-world settings, an organism must accurately infer the nature of its environment from noisy observations and efficiently commit to a choice. As environments become more complex, so must the internal models and computations that subserve this process. Analyzing the mechanisms underlying decision-making is crucial to understanding individual and collective behaviors and has applications in psychology, economics, and medicine. Decision processes have been investigated from many perspectives, ranging from studies focusing on small groups of neurons to observations of organismal behaviors. In this minisymposium, we highlight these different approaches to modeling decision-making mathematically. The series will focus on connecting theory with empirical observations and will include speakers that specialize in model development, analysis, and validation using experimental data.

Nicholas Barendregt

(University of Colorado Boulder, United States)
"Normative and dynamic decision urgency in unpredictable environments"
Decision-making in uncertain environments often requires adaptive forms of evidence accumulation, but less is known about the decision rules needed to achieve optimal performance. While recent studies of decision models in stochastic and dynamic environments have resulted in several phenomenological models, such as the monotonically collapsing decision threshold of the “urgency-gating model” (UGM), we lack a general, normative description of decision rules and their relation to human decision-making. In this talk, we will develop a normative, Bayes-optimal framework for decision tasks in uncertain and dynamic environments. Using the classic “tokens task” paradigm, we apply Bayesian model fitting and model comparison methods to the normative model, the UGM, and several other heuristic models. Our work demonstrates that the humans using the normative strategy exhibit non-monotonic urgency and identifies regions of parameter space where different types of urgency are optimal. Extending these methods to tasks where the reward for a correct response varies in time, we again find that normative decision rules exhibit rich non-monotonic behavior, providing testable hypotheses for experimentalists to probe in future psychophysics tasks.

Timothy Verstynen

(Carnegie Mellon University, United States)
"Rethinking the computational architecture of cortico-basal ganglia-thalamic pathways"
Humans and other mammals exhibit a high degree of control when selecting actions in noisy contexts, quickly adapting to unexpected outcomes in order to better exploit opportunities arising in the future. This flexible decision-making is mediated, in part, by cortico-basal-ganglia-thalamic (CBGT) circuits that both control action selection and use feedback signals to modify future decisions. In this talk we will highlight how new insights into the circuit-level architecture of CBGT pathways are informing our understanding of the algorithms of decision-making and learning. Specifically we will show how components of the CBGT circuit map to modifiable parameters that balance the speed-accuracy tradeoff during adaptive decision making.

Alex Roxin

(Centre de Recerca Matemàtica, Spain)
"Bump attractor dynamics underlying stimulus integration in perceptual estimation tasks"
Perceptual decision and continuous stimulus estimation tasks involve making judgments based on accumulated sensory evidence. Network models of evidence integration usually rely on competition between neural populations each encoding a discrete categorical choice. By design, these models do not maintain information of the integrated stimulus (e.g. the average stimulus direction in degrees) that is necessary for a continuous perceptual judgement. Here, we show that the continuous ring attractor network can integrate a stimulus feature such as orientation and track the stimulus average in the phase of its activity bump. We reduced the network dynamics of the ring model to a two-dimensional equation for the amplitude and the phase of the bump. Interestingly, these reduced equations are nearly identical to an optimal integration process for computing the running average of the stimulus orientation. They differ only in the intrinsic dynamics of the amplitude, which affects the temporal weighting of the sensory evidence. Whether the network shows early (primacy), uniform or late (recency) weighting depends on the relative strength of sensory stimuli compared to the amplitude of the bump and on the initial state of the network. The specific relation between the internal network dynamics and the sensory inputs can be modulated by changing a single parameter of the model, the global excitatory drive. We show that this can account for the heterogeneity of temporal weighting profiles observed in humans integrating a stream of oriented stimulus frames. Our findings point to continuous attractor dynamics as a plausible mechanism underlying stimulus integration in perceptual estimation tasks.

Wiktor Mlynarski

(Institute of Science and Technology Austria, Austria)
"Attention as efficient and adaptive inference in dynamic environments"
Top-down attention is thought to reflect allocation of limited processing resources to task-relevant computations and representations. According to this hypothesis, attentional processing could be characterized by two fundamental theoretical frameworks: probabilistic inference and efficient coding. Probabilistic inference specifies optimal strategies for learning about relevant properties of the environment from local and ambiguous sensory signals. Efficient coding provides a normative approach to study encoding of natural stimuli in resource-constrained sensory systems. By emphasizing different aspects of information processing they provide complementary approaches to study sensory computations. Here we attempt to bring them together by developing general principles that underlie the tradeoff between energetic cost of sensory coding and accuracy of perceptual inferences. We then apply these general principles to optimize a model of population coding in the visual cortex. The model dynamically adapts a representation of natural images to support maximally accurate perceptual inference at minimal activity cost. The resulting optimality predictions reproduce measured properties of attentional modulation in the visual system and generate novel hypotheses about the functional role of top-down feedback, response variability, and noise correlations. Our results suggest that a range of seemingly disparate attentional phenomena can be derived from a general theory combining probabilistic inference with efficient coding in a dynamic environment.

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