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Making decisions with unknown sensory reliability.

Deneve S - Front Neurosci (2012)

Bottom Line: Most of the time, we cannot know this reliability without first observing the decision outcome.We consider here a Bayesian decision model that simultaneously infers the probability of two different choices and at the same time estimates the reliability of the sensory information on which this choice is based.We show that this model can account for recent findings in a motion discrimination task, and can be implemented in a neural architecture using fast Hebbian learning.

View Article: PubMed Central - PubMed

Affiliation: Département d'Etudes Cognitives, Group for Neural Theory, Ecole Normale Supérieure Paris, France.

ABSTRACT
To make fast and accurate behavioral choices, we need to integrate noisy sensory input, take prior knowledge into account, and adjust our decision criteria. It was shown previously that in two-alternative-forced-choice tasks, optimal decision making can be formalized in the framework of a sequential probability ratio test and is then equivalent to a diffusion model. However, this analogy hides a "chicken and egg" problem: to know how quickly we should integrate the sensory input and set the optimal decision threshold, the reliability of the sensory observations must be known in advance. Most of the time, we cannot know this reliability without first observing the decision outcome. We consider here a Bayesian decision model that simultaneously infers the probability of two different choices and at the same time estimates the reliability of the sensory information on which this choice is based. We show that this can be achieved within a single trial, based on the noisy responses of sensory spiking neurons. The resulting model is a non-linear diffusion to bound where the weight of the sensory inputs and the decision threshold are both dynamically changing over time. In difficult decision trials, early sensory inputs have a stronger impact on the decision, and the threshold collapses such that choices are made faster but with low accuracy. The reverse is true in easy trials: the sensory weight and the threshold increase over time, leading to slower decisions but at much higher accuracy. In contrast to standard diffusion models, adaptive sensory weights construct an accurate representation for the probability of each choice. This information can then be combined appropriately with other unreliable cues, such as priors. We show that this model can account for recent findings in a motion discrimination task, and can be implemented in a neural architecture using fast Hebbian learning.

No MeSH data available.


Related in: MedlinePlus

Simplified Bayesian and “diffusion” decision model in the “fixed delay” task. (A) Choice-averaged inputs as a function of time in a zero coherence trial (c = 0). The noisy sensory input (i.e., the input spike train st) was averaged in 10 ms sliding time windows over 20000 trials. Only trials were choice A was made after a 2 s stimulus presentation (i.e., L2000 > 0) were used for this choice-triggered average. Blue line: simplified Bayesian model. Red line: diffusion model. The diffusion model weights all sensory inputs equally while the Bayesian model relies on inputs only early in the trial. (B) Percent of correct choices as a function of the duration of stimulus presentation. Plain blue line: Bayesian model at low coherence (c = 0.1). Dotted blue line: Bayesian model at higher coherence (c = 0.5). Plain red line: diffusion model at low coherence (c = 0.1). Dotted red line: Bayesian model at higher coherence (c = 0.5). In contrast to the diffusion model, the Bayesian model stops integrating early in the trial (i.e., the probability of correct choice saturates whereas it keeps increasing for the diffusion model). (C) Probability of choosing A in zero coherence trial (c = 0), with a prior favoring choice A (Lo = 0.6), as a function of the duration of stimulus presentation. Since the input is pure noise, optimal strategy (if coherence was known) would be to always respond “A” (i.e., probability of choice A should be 1). The Bayesian model saturates to a suboptimal but still high probability of choice A. In the diffusion model, the influence of the prior decays over time.
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Figure 6: Simplified Bayesian and “diffusion” decision model in the “fixed delay” task. (A) Choice-averaged inputs as a function of time in a zero coherence trial (c = 0). The noisy sensory input (i.e., the input spike train st) was averaged in 10 ms sliding time windows over 20000 trials. Only trials were choice A was made after a 2 s stimulus presentation (i.e., L2000 > 0) were used for this choice-triggered average. Blue line: simplified Bayesian model. Red line: diffusion model. The diffusion model weights all sensory inputs equally while the Bayesian model relies on inputs only early in the trial. (B) Percent of correct choices as a function of the duration of stimulus presentation. Plain blue line: Bayesian model at low coherence (c = 0.1). Dotted blue line: Bayesian model at higher coherence (c = 0.5). Plain red line: diffusion model at low coherence (c = 0.1). Dotted red line: Bayesian model at higher coherence (c = 0.5). In contrast to the diffusion model, the Bayesian model stops integrating early in the trial (i.e., the probability of correct choice saturates whereas it keeps increasing for the diffusion model). (C) Probability of choosing A in zero coherence trial (c = 0), with a prior favoring choice A (Lo = 0.6), as a function of the duration of stimulus presentation. Since the input is pure noise, optimal strategy (if coherence was known) would be to always respond “A” (i.e., probability of choice A should be 1). The Bayesian model saturates to a suboptimal but still high probability of choice A. In the diffusion model, the influence of the prior decays over time.

Mentions: In a diffusion model, all sensory inputs are taken equally into account, regardless of whether they occur at the beginning or at the end of stimulus presentation. By contrast, the Bayesian decision model re-weights the sensory evidence as a function of the estimated motion coherence, and thus, sensory inputs do not all contributes equally to the final decision. This is illustrated in Figure 6A where we plotted the average sensory input at different times during stimulus presentation, conditioned on the fact that the final choice was A. Here we consider only trials with zero coherence, i.e., c = 0. In this case the decision is purely driven by random fluctuations in the sensory input. The curves are a result of averaging over 20000 trials. The stimulus was presented for 2000 ms and the decision was made at t = 2000 ms. Only trials resulting in choice A (L2000 > 0) were selected for averaging. For a diffusion model (red), the curve is flat and slightly above zero. This is because positive inputs tend to increase the probability that the final log odds will be positive, and the final choice will be “A.” In a diffusion model, the order of arrival of these inputs does not matter, resulting in a flat curve. In contrast, the Bayesian decision model (blue line) gives more confidence to inputs presented early in the trial. This is because the initial coherence estimate [ĉ(0) = 1] is actually larger that the real motion coherence (c = 0 in this case). This results in the first inputs being taken into account more so than later inputs. As a consequence, the decision-triggered average of the input decays over time.


Making decisions with unknown sensory reliability.

Deneve S - Front Neurosci (2012)

Simplified Bayesian and “diffusion” decision model in the “fixed delay” task. (A) Choice-averaged inputs as a function of time in a zero coherence trial (c = 0). The noisy sensory input (i.e., the input spike train st) was averaged in 10 ms sliding time windows over 20000 trials. Only trials were choice A was made after a 2 s stimulus presentation (i.e., L2000 > 0) were used for this choice-triggered average. Blue line: simplified Bayesian model. Red line: diffusion model. The diffusion model weights all sensory inputs equally while the Bayesian model relies on inputs only early in the trial. (B) Percent of correct choices as a function of the duration of stimulus presentation. Plain blue line: Bayesian model at low coherence (c = 0.1). Dotted blue line: Bayesian model at higher coherence (c = 0.5). Plain red line: diffusion model at low coherence (c = 0.1). Dotted red line: Bayesian model at higher coherence (c = 0.5). In contrast to the diffusion model, the Bayesian model stops integrating early in the trial (i.e., the probability of correct choice saturates whereas it keeps increasing for the diffusion model). (C) Probability of choosing A in zero coherence trial (c = 0), with a prior favoring choice A (Lo = 0.6), as a function of the duration of stimulus presentation. Since the input is pure noise, optimal strategy (if coherence was known) would be to always respond “A” (i.e., probability of choice A should be 1). The Bayesian model saturates to a suboptimal but still high probability of choice A. In the diffusion model, the influence of the prior decays over time.
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Figure 6: Simplified Bayesian and “diffusion” decision model in the “fixed delay” task. (A) Choice-averaged inputs as a function of time in a zero coherence trial (c = 0). The noisy sensory input (i.e., the input spike train st) was averaged in 10 ms sliding time windows over 20000 trials. Only trials were choice A was made after a 2 s stimulus presentation (i.e., L2000 > 0) were used for this choice-triggered average. Blue line: simplified Bayesian model. Red line: diffusion model. The diffusion model weights all sensory inputs equally while the Bayesian model relies on inputs only early in the trial. (B) Percent of correct choices as a function of the duration of stimulus presentation. Plain blue line: Bayesian model at low coherence (c = 0.1). Dotted blue line: Bayesian model at higher coherence (c = 0.5). Plain red line: diffusion model at low coherence (c = 0.1). Dotted red line: Bayesian model at higher coherence (c = 0.5). In contrast to the diffusion model, the Bayesian model stops integrating early in the trial (i.e., the probability of correct choice saturates whereas it keeps increasing for the diffusion model). (C) Probability of choosing A in zero coherence trial (c = 0), with a prior favoring choice A (Lo = 0.6), as a function of the duration of stimulus presentation. Since the input is pure noise, optimal strategy (if coherence was known) would be to always respond “A” (i.e., probability of choice A should be 1). The Bayesian model saturates to a suboptimal but still high probability of choice A. In the diffusion model, the influence of the prior decays over time.
Mentions: In a diffusion model, all sensory inputs are taken equally into account, regardless of whether they occur at the beginning or at the end of stimulus presentation. By contrast, the Bayesian decision model re-weights the sensory evidence as a function of the estimated motion coherence, and thus, sensory inputs do not all contributes equally to the final decision. This is illustrated in Figure 6A where we plotted the average sensory input at different times during stimulus presentation, conditioned on the fact that the final choice was A. Here we consider only trials with zero coherence, i.e., c = 0. In this case the decision is purely driven by random fluctuations in the sensory input. The curves are a result of averaging over 20000 trials. The stimulus was presented for 2000 ms and the decision was made at t = 2000 ms. Only trials resulting in choice A (L2000 > 0) were selected for averaging. For a diffusion model (red), the curve is flat and slightly above zero. This is because positive inputs tend to increase the probability that the final log odds will be positive, and the final choice will be “A.” In a diffusion model, the order of arrival of these inputs does not matter, resulting in a flat curve. In contrast, the Bayesian decision model (blue line) gives more confidence to inputs presented early in the trial. This is because the initial coherence estimate [ĉ(0) = 1] is actually larger that the real motion coherence (c = 0 in this case). This results in the first inputs being taken into account more so than later inputs. As a consequence, the decision-triggered average of the input decays over time.

Bottom Line: Most of the time, we cannot know this reliability without first observing the decision outcome.We consider here a Bayesian decision model that simultaneously infers the probability of two different choices and at the same time estimates the reliability of the sensory information on which this choice is based.We show that this model can account for recent findings in a motion discrimination task, and can be implemented in a neural architecture using fast Hebbian learning.

View Article: PubMed Central - PubMed

Affiliation: Département d'Etudes Cognitives, Group for Neural Theory, Ecole Normale Supérieure Paris, France.

ABSTRACT
To make fast and accurate behavioral choices, we need to integrate noisy sensory input, take prior knowledge into account, and adjust our decision criteria. It was shown previously that in two-alternative-forced-choice tasks, optimal decision making can be formalized in the framework of a sequential probability ratio test and is then equivalent to a diffusion model. However, this analogy hides a "chicken and egg" problem: to know how quickly we should integrate the sensory input and set the optimal decision threshold, the reliability of the sensory observations must be known in advance. Most of the time, we cannot know this reliability without first observing the decision outcome. We consider here a Bayesian decision model that simultaneously infers the probability of two different choices and at the same time estimates the reliability of the sensory information on which this choice is based. We show that this can be achieved within a single trial, based on the noisy responses of sensory spiking neurons. The resulting model is a non-linear diffusion to bound where the weight of the sensory inputs and the decision threshold are both dynamically changing over time. In difficult decision trials, early sensory inputs have a stronger impact on the decision, and the threshold collapses such that choices are made faster but with low accuracy. The reverse is true in easy trials: the sensory weight and the threshold increase over time, leading to slower decisions but at much higher accuracy. In contrast to standard diffusion models, adaptive sensory weights construct an accurate representation for the probability of each choice. This information can then be combined appropriately with other unreliable cues, such as priors. We show that this model can account for recent findings in a motion discrimination task, and can be implemented in a neural architecture using fast Hebbian learning.

No MeSH data available.


Related in: MedlinePlus