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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

“Bayesian” diffusion model. (A) Log odd ratios Lt as a function of time in the trial (t = 0: start of sensory stimulation) on three different trials. Dashed lines correspond to the decision thresholds. Red plain line: a correct trial where “choice A” was made (i.e., the upward threshold was reached first), and choice “A” was indeed the correct choice. Blue plain line: another correct trial where choice B was made (the lower decision threshold was reached first) and B was indeed the correct choice. Dotted blue line: an error trial where choice “A” was made while choice “B” would have been the correct choice. (B) Optimal decision thresholds as a function of the strength of the modulation of input firing rate by motion direction (dq).
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Figure 1: “Bayesian” diffusion model. (A) Log odd ratios Lt as a function of time in the trial (t = 0: start of sensory stimulation) on three different trials. Dashed lines correspond to the decision thresholds. Red plain line: a correct trial where “choice A” was made (i.e., the upward threshold was reached first), and choice “A” was indeed the correct choice. Blue plain line: another correct trial where choice B was made (the lower decision threshold was reached first) and B was indeed the correct choice. Dotted blue line: an error trial where choice “A” was made while choice “B” would have been the correct choice. (B) Optimal decision thresholds as a function of the strength of the modulation of input firing rate by motion direction (dq).

Mentions: where st − q corresponds to the sensory evidence at time t and the sensory weight is set by the input signal-over-noise ratio (SNR) w = 2dq/q. The log odds Lt represent the current confidence in choice A relative to choice B. It increases on average if the input firing rate is above baseline, and decreases on average if the input firing rate is below baseline. However, this accumulation is noisy due to the Poisson variability of the sensory spike train. Three example trials are plotted in Figure 1A.


Making decisions with unknown sensory reliability.

Deneve S - Front Neurosci (2012)

“Bayesian” diffusion model. (A) Log odd ratios Lt as a function of time in the trial (t = 0: start of sensory stimulation) on three different trials. Dashed lines correspond to the decision thresholds. Red plain line: a correct trial where “choice A” was made (i.e., the upward threshold was reached first), and choice “A” was indeed the correct choice. Blue plain line: another correct trial where choice B was made (the lower decision threshold was reached first) and B was indeed the correct choice. Dotted blue line: an error trial where choice “A” was made while choice “B” would have been the correct choice. (B) Optimal decision thresholds as a function of the strength of the modulation of input firing rate by motion direction (dq).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3367295&req=5

Figure 1: “Bayesian” diffusion model. (A) Log odd ratios Lt as a function of time in the trial (t = 0: start of sensory stimulation) on three different trials. Dashed lines correspond to the decision thresholds. Red plain line: a correct trial where “choice A” was made (i.e., the upward threshold was reached first), and choice “A” was indeed the correct choice. Blue plain line: another correct trial where choice B was made (the lower decision threshold was reached first) and B was indeed the correct choice. Dotted blue line: an error trial where choice “A” was made while choice “B” would have been the correct choice. (B) Optimal decision thresholds as a function of the strength of the modulation of input firing rate by motion direction (dq).
Mentions: where st − q corresponds to the sensory evidence at time t and the sensory weight is set by the input signal-over-noise ratio (SNR) w = 2dq/q. The log odds Lt represent the current confidence in choice A relative to choice B. It increases on average if the input firing rate is above baseline, and decreases on average if the input firing rate is below baseline. However, this accumulation is noisy due to the Poisson variability of the sensory spike train. Three example trials are plotted in Figure 1A.

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