Optimal decision bounds for probabilistic population codes and time varying evidence

Abstract

Decision making under time constraints requires the decision maker to trade off between making quick, inaccurate decisions and gathering more evidence for more accurate, but slower decisions. We have previously shown that, under rather general settings, optimal behavior can be described by a time-dependent decision bound on the decision maker’s belief of being correct (Drugowitsch, Moreno-Bote, Pouget, 2009). In cases where the reliability of sensory information remains constant over time, we have shown how to design diffusion models (DMs) with time-changing boundaries that feature such behavior. Such theories can be easily mapped onto simple neural models of decision making with two perfectly anti-correlated neurons, where they predict the existence of a stopping bound on the most active neurons. It is unclear however how the stopping bound would be implemented with more realistic neural population codes, particularly when the reliability of the evidence changes over time.
Here we show that, under certain realistic conditions, we can apply the theory of optimal decision making to the biologically more plausible probabilistic population codes (PPCs; Ma et al. 2006). Our analysis shows that, with population codes, the optimal decision bounds are a function of the neural activity of all neurons in the population, rather than a previously postulated bound on its maximum activity. This theory predicts that the bound on the most active neurons would appear to shift depending on the firing rate of other neurons in the population, a puzzling behavior under the drift diffusion model as it would wrongly suggest that subjects change their stopping rule across conditions. This theory also applies to the case of time varying evidence, a case that cannot be handled by drift diffusion models without unrealistic assumptions