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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 decision making with varying levels of motion coherence. (A) Firing rate of the model sensory neuron in response to motion stimuli (start of stimulation marked by upward pointing arrow) for different levels of coherence. Plain lines: stimulus is in the preferred direction. Dashed lines: stimulus is in the anti-preferred direction. The gray scale indicates the strength of motion coherence. (B) Outcome of the “full” Bayesian integrator computing the joint probabilities of all pairs of choices and coherences. Time 0 correspond to the start of the trial. Plain black line: probability of choice A for coherence c = 0.2 (averaged over 20000 trials were A was the correct choice). Plain gray line: probability of choice A for coherence c = 0.05. Dotted black line: expected value for motion coherence ĉ for true coherence c = 0.2. Dotted gray line: expected value for motion coherence ĉ for true coherence c = 0.05.
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Figure 2: Bayesian decision making with varying levels of motion coherence. (A) Firing rate of the model sensory neuron in response to motion stimuli (start of stimulation marked by upward pointing arrow) for different levels of coherence. Plain lines: stimulus is in the preferred direction. Dashed lines: stimulus is in the anti-preferred direction. The gray scale indicates the strength of motion coherence. (B) Outcome of the “full” Bayesian integrator computing the joint probabilities of all pairs of choices and coherences. Time 0 correspond to the start of the trial. Plain black line: probability of choice A for coherence c = 0.2 (averaged over 20000 trials were A was the correct choice). Plain gray line: probability of choice A for coherence c = 0.05. Dotted black line: expected value for motion coherence ĉ for true coherence c = 0.2. Dotted gray line: expected value for motion coherence ĉ for true coherence c = 0.05.

Mentions: For example, let us suppose that the task difficulty in our toy example is varied by controlling the amount of noise in the visual motion stimulus. This can be done by using motion displays composed of moving dots while varying the proportion of dots moving coherently in a single direction, with the rest of the dots moving in random directions (Britten et al., 1992). The proportion of dots moving coherently corresponds to the “motion coherence.” These kind of stimuli have been used intensively to investigate the neural basis of decision making in humans and non-human primates. They induce responses in direction-selective sensory neurons (e.g., in the medio-temporal area MT) that can roughly be described by an increase or decrease of the background firing rate by an amount proportional to motion coherence (Newsome et al., 1989; Britten et al., 1992). Schematically, the firing rate of the sensory neuron is q + cdq for choice A, and q − cdq for choice B, where c is a function of motion coherence (see Figure 2A). The sensory weights and the bounds should be updated accordingly. But how can this happen when trials with high and low coherences are randomly intermixed?


Making decisions with unknown sensory reliability.

Deneve S - Front Neurosci (2012)

Bayesian decision making with varying levels of motion coherence. (A) Firing rate of the model sensory neuron in response to motion stimuli (start of stimulation marked by upward pointing arrow) for different levels of coherence. Plain lines: stimulus is in the preferred direction. Dashed lines: stimulus is in the anti-preferred direction. The gray scale indicates the strength of motion coherence. (B) Outcome of the “full” Bayesian integrator computing the joint probabilities of all pairs of choices and coherences. Time 0 correspond to the start of the trial. Plain black line: probability of choice A for coherence c = 0.2 (averaged over 20000 trials were A was the correct choice). Plain gray line: probability of choice A for coherence c = 0.05. Dotted black line: expected value for motion coherence ĉ for true coherence c = 0.2. Dotted gray line: expected value for motion coherence ĉ for true coherence c = 0.05.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Figure 2: Bayesian decision making with varying levels of motion coherence. (A) Firing rate of the model sensory neuron in response to motion stimuli (start of stimulation marked by upward pointing arrow) for different levels of coherence. Plain lines: stimulus is in the preferred direction. Dashed lines: stimulus is in the anti-preferred direction. The gray scale indicates the strength of motion coherence. (B) Outcome of the “full” Bayesian integrator computing the joint probabilities of all pairs of choices and coherences. Time 0 correspond to the start of the trial. Plain black line: probability of choice A for coherence c = 0.2 (averaged over 20000 trials were A was the correct choice). Plain gray line: probability of choice A for coherence c = 0.05. Dotted black line: expected value for motion coherence ĉ for true coherence c = 0.2. Dotted gray line: expected value for motion coherence ĉ for true coherence c = 0.05.
Mentions: For example, let us suppose that the task difficulty in our toy example is varied by controlling the amount of noise in the visual motion stimulus. This can be done by using motion displays composed of moving dots while varying the proportion of dots moving coherently in a single direction, with the rest of the dots moving in random directions (Britten et al., 1992). The proportion of dots moving coherently corresponds to the “motion coherence.” These kind of stimuli have been used intensively to investigate the neural basis of decision making in humans and non-human primates. They induce responses in direction-selective sensory neurons (e.g., in the medio-temporal area MT) that can roughly be described by an increase or decrease of the background firing rate by an amount proportional to motion coherence (Newsome et al., 1989; Britten et al., 1992). Schematically, the firing rate of the sensory neuron is q + cdq for choice A, and q − cdq for choice B, where c is a function of motion coherence (see Figure 2A). The sensory weights and the bounds should be updated accordingly. But how can this happen when trials with high and low coherences are randomly intermixed?

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