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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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Related in: MedlinePlus

Decision sample in s-MSPRT against mean ISI for range of pdfs and parameter sets.Each bar shows, for the pdf indicated in the legend, the mean decision sample for N = 10 alternatives, averaged over 950 correct out of 1000 total trials. Panel a used parameter sets ΩIV, , , , panel b used ΩFV, , ,  (see Methods). Each group of bars relates to one parameter set with its μ0 indicated on the x − axis (ΩIV, ΩFV have μ0 = 33). For the case of ΩFV and any , the gamma and exponential distributions are identical and so not reported separately.
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pone.0124787.g005: Decision sample in s-MSPRT against mean ISI for range of pdfs and parameter sets.Each bar shows, for the pdf indicated in the legend, the mean decision sample for N = 10 alternatives, averaged over 950 correct out of 1000 total trials. Panel a used parameter sets ΩIV, , , , panel b used ΩFV, , , (see Methods). Each group of bars relates to one parameter set with its μ0 indicated on the x − axis (ΩIV, ΩFV have μ0 = 33). For the case of ΩFV and any , the gamma and exponential distributions are identical and so not reported separately.

Mentions: There is a clear distinction in Fig 4 between the performance of algorithms assuming the different distributions. Is the rank ordering of performance maintained as we vary the distribution statistics? To explore this we repeated the experiments with s-MSPRT corresponding to N = 10 in Fig 4, but with other parameter sets , , μ0 = 49.5,66,82.5 derived from the original sets ΩIV, ΩFV (see Methods). The results are shown in Fig 5, which also show those for ΩIV, ΩFV for comparison (μ0 = 33 ms).


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

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

Decision sample in s-MSPRT against mean ISI for range of pdfs and parameter sets.Each bar shows, for the pdf indicated in the legend, the mean decision sample for N = 10 alternatives, averaged over 950 correct out of 1000 total trials. Panel a used parameter sets ΩIV, , , , panel b used ΩFV, , ,  (see Methods). Each group of bars relates to one parameter set with its μ0 indicated on the x − axis (ΩIV, ΩFV have μ0 = 33). For the case of ΩFV and any , the gamma and exponential distributions are identical and so not reported separately.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0124787.g005: Decision sample in s-MSPRT against mean ISI for range of pdfs and parameter sets.Each bar shows, for the pdf indicated in the legend, the mean decision sample for N = 10 alternatives, averaged over 950 correct out of 1000 total trials. Panel a used parameter sets ΩIV, , , , panel b used ΩFV, , , (see Methods). Each group of bars relates to one parameter set with its μ0 indicated on the x − axis (ΩIV, ΩFV have μ0 = 33). For the case of ΩFV and any , the gamma and exponential distributions are identical and so not reported separately.
Mentions: There is a clear distinction in Fig 4 between the performance of algorithms assuming the different distributions. Is the rank ordering of performance maintained as we vary the distribution statistics? To explore this we repeated the experiments with s-MSPRT corresponding to N = 10 in Fig 4, but with other parameter sets , , μ0 = 49.5,66,82.5 derived from the original sets ΩIV, ΩFV (see Methods). The results are shown in Fig 5, which also show those for ΩIV, ΩFV for comparison (μ0 = 33 ms).

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