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Probabilistic Decision Making with Spikes: From ISI Distributions to Behaviour via Information Gain.

Caballero JA, Lepora NF, Gurney KN - PLoS ONE (2015)

Bottom Line: Computational theories of decision making in the brain usually assume that sensory 'evidence' is accumulated supporting a number of hypotheses, and that the first accumulator to reach threshold triggers a decision in favour of its associated hypothesis.Thus, we find the mean information needed for a decision is constant, thereby offering an account of Hick's law (relating decision time to the number of choices).These results show the foundations for a research programme in which spike train analysis can be made the basis for predictions about behavior in multi-alternative choice tasks.

View Article: PubMed Central - PubMed

Affiliation: Dept of Psychology, University of Sheffield, Sheffield, UK; Faculty of Life Sciences, University of Manchester, Manchester, UK.

ABSTRACT
Computational theories of decision making in the brain usually assume that sensory 'evidence' is accumulated supporting a number of hypotheses, and that the first accumulator to reach threshold triggers a decision in favour of its associated hypothesis. However, the evidence is often assumed to occur as a continuous process whose origins are somewhat abstract, with no direct link to the neural signals - action potentials or 'spikes' - that must ultimately form the substrate for decision making in the brain. Here we introduce a new variant of the well-known multi-hypothesis sequential probability ratio test (MSPRT) for decision making whose evidence observations consist of the basic unit of neural signalling - the inter-spike interval (ISI) - and which is based on a new form of the likelihood function. We dub this mechanism s-MSPRT and show its precise form for a range of realistic ISI distributions with positive support. In this way we show that, at the level of spikes, the refractory period may actually facilitate shorter decision times, and that the mechanism is robust against poor choice of the hypothesized data distribution. We show that s-MSPRT performance is related to the Kullback-Leibler divergence (KLD) or information gain between ISI distributions, through which we are able to link neural signalling to psychophysical observation at the behavioural level. Thus, we find the mean information needed for a decision is constant, thereby offering an account of Hick's law (relating decision time to the number of choices). Further, the mean decision time of s-MSPRT shows a power law dependence on the KLD offering an account of Piéron's law (relating reaction time to stimulus intensity). These results show the foundations for a research programme in which spike train analysis can be made the basis for predictions about behavior in multi-alternative choice tasks.

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Mean decision samples against number of choices for a range of pdfs, parameter sets, and mechanisms.Each panel shows mean decision sample as a function of the number of choices for a range of pdfs (see legend) and for the two alternative mechanisms: s-MSPRT (solid lines) and u-MSPRT (solid circles). Panels a and b are for the parameter sets ΩIV and ΩFV respectively (see Methods). In the case of ΩFV, the gamma and exponential distributions are identical and so not reported separately. All data points are the mean of 950 correct, out of 1000 total trials (see text for inverse gamma based s-MSPRT). Error bars are omitted for clarity and are small; the standard error of the mean is typically 2% of the mean.
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pone.0124787.g004: Mean decision samples against number of choices for a range of pdfs, parameter sets, and mechanisms.Each panel shows mean decision sample as a function of the number of choices for a range of pdfs (see legend) and for the two alternative mechanisms: s-MSPRT (solid lines) and u-MSPRT (solid circles). Panels a and b are for the parameter sets ΩIV and ΩFV respectively (see Methods). In the case of ΩFV, the gamma and exponential distributions are identical and so not reported separately. All data points are the mean of 950 correct, out of 1000 total trials (see text for inverse gamma based s-MSPRT). Error bars are omitted for clarity and are small; the standard error of the mean is typically 2% of the mean.

Mentions: We ran simulations of s-MSPRT as a function of the number of choices or hypotheses, N, for a range of pdfs, and the two parameter sets ΩIV, ΩFV (see Methods). All the simulation results use trials with an error rate of 5% obtained by iteratively seeking a threshold that satisfied this criterion. Every data point for a particular number of alternatives is the mean over 950 correct, out of 1000 total trials (982 correct for the inverse gamma based s-MSPRT at N = 2 with ΩFV in Fig 4 which is at an error rate of 1.8% as it was not possible to reliably achieve a 5% error here; this decision task would appear to be too easy to be compromised to this extent). The large trial numbers ensure that estimation of the error rate during threshold determination is sufficiently accurate. For the simulations in this section, the ISIs are drawn from the distributions, f* for the preferred channel, and f0 for the channels.


Probabilistic Decision Making with Spikes: From ISI Distributions to Behaviour via Information Gain.

Caballero JA, Lepora NF, Gurney KN - PLoS ONE (2015)

Mean decision samples against number of choices for a range of pdfs, parameter sets, and mechanisms.Each panel shows mean decision sample as a function of the number of choices for a range of pdfs (see legend) and for the two alternative mechanisms: s-MSPRT (solid lines) and u-MSPRT (solid circles). Panels a and b are for the parameter sets ΩIV and ΩFV respectively (see Methods). In the case of ΩFV, the gamma and exponential distributions are identical and so not reported separately. All data points are the mean of 950 correct, out of 1000 total trials (see text for inverse gamma based s-MSPRT). Error bars are omitted for clarity and are small; the standard error of the mean is typically 2% of the mean.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4414410&req=5

pone.0124787.g004: Mean decision samples against number of choices for a range of pdfs, parameter sets, and mechanisms.Each panel shows mean decision sample as a function of the number of choices for a range of pdfs (see legend) and for the two alternative mechanisms: s-MSPRT (solid lines) and u-MSPRT (solid circles). Panels a and b are for the parameter sets ΩIV and ΩFV respectively (see Methods). In the case of ΩFV, the gamma and exponential distributions are identical and so not reported separately. All data points are the mean of 950 correct, out of 1000 total trials (see text for inverse gamma based s-MSPRT). Error bars are omitted for clarity and are small; the standard error of the mean is typically 2% of the mean.
Mentions: We ran simulations of s-MSPRT as a function of the number of choices or hypotheses, N, for a range of pdfs, and the two parameter sets ΩIV, ΩFV (see Methods). All the simulation results use trials with an error rate of 5% obtained by iteratively seeking a threshold that satisfied this criterion. Every data point for a particular number of alternatives is the mean over 950 correct, out of 1000 total trials (982 correct for the inverse gamma based s-MSPRT at N = 2 with ΩFV in Fig 4 which is at an error rate of 1.8% as it was not possible to reliably achieve a 5% error here; this decision task would appear to be too easy to be compromised to this extent). The large trial numbers ensure that estimation of the error rate during threshold determination is sufficiently accurate. For the simulations in this section, the ISIs are drawn from the distributions, f* for the preferred channel, and f0 for the channels.

Bottom Line: Computational theories of decision making in the brain usually assume that sensory 'evidence' is accumulated supporting a number of hypotheses, and that the first accumulator to reach threshold triggers a decision in favour of its associated hypothesis.Thus, we find the mean information needed for a decision is constant, thereby offering an account of Hick's law (relating decision time to the number of choices).These results show the foundations for a research programme in which spike train analysis can be made the basis for predictions about behavior in multi-alternative choice tasks.

View Article: PubMed Central - PubMed

Affiliation: Dept of Psychology, University of Sheffield, Sheffield, UK; Faculty of Life Sciences, University of Manchester, Manchester, UK.

ABSTRACT
Computational theories of decision making in the brain usually assume that sensory 'evidence' is accumulated supporting a number of hypotheses, and that the first accumulator to reach threshold triggers a decision in favour of its associated hypothesis. However, the evidence is often assumed to occur as a continuous process whose origins are somewhat abstract, with no direct link to the neural signals - action potentials or 'spikes' - that must ultimately form the substrate for decision making in the brain. Here we introduce a new variant of the well-known multi-hypothesis sequential probability ratio test (MSPRT) for decision making whose evidence observations consist of the basic unit of neural signalling - the inter-spike interval (ISI) - and which is based on a new form of the likelihood function. We dub this mechanism s-MSPRT and show its precise form for a range of realistic ISI distributions with positive support. In this way we show that, at the level of spikes, the refractory period may actually facilitate shorter decision times, and that the mechanism is robust against poor choice of the hypothesized data distribution. We show that s-MSPRT performance is related to the Kullback-Leibler divergence (KLD) or information gain between ISI distributions, through which we are able to link neural signalling to psychophysical observation at the behavioural level. Thus, we find the mean information needed for a decision is constant, thereby offering an account of Hick's law (relating decision time to the number of choices). Further, the mean decision time of s-MSPRT shows a power law dependence on the KLD offering an account of Piéron's law (relating reaction time to stimulus intensity). These results show the foundations for a research programme in which spike train analysis can be made the basis for predictions about behavior in multi-alternative choice tasks.

Show MeSH
Related in: MedlinePlus