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Detection by neuron populations

Detection by neuron populations. European Mathematical Psychology Group, Graz, September 9 – 11, 2008 Uwe Mortensen University of Münster, Germany. Detection. Probability summation. No probability summation. Models of neural mechanisms. The notion of probability summation:.

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Detection by neuron populations

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  1. Detection by neuron populations European Mathematical Psychology Group, Graz, September 9 – 11, 2008 Uwe Mortensen University of Münster, Germany

  2. Detection Probability summation No probability summation Models of neural mechanisms

  3. The notion of probability summation: Among channels/mechanisms. Detection occurs if the activity in at least one of a number of channels exceeds threshold. Temporal: Detection occurs if the activity at at least one point of time (within some inerval J = [0, T]) exceeds threshold. Spatial: Detection occurs if the activity at at least one point in space (retinal coordinate) exceeds threshold. Usually just one type of PS is assumed in a given experiment

  4. Aim of detection experiments Probability summation Identification of neural mechanisms No probability summation Models/ Noise deterministic stochastic correlated white Inconsistency! Network/popu-lation models Extreme values theory Max mean detection Nonlinear pooling Quick‘s model descriptive! Theoretical status unclear! Can be fitted to most data – meaningful? Test

  5. Quick (1974) Canonical models for PS in visual psychophysics unit respones Equivalent to Weibull-function channels spatial positions c contrast Temporal PS (pooling, Minkowski-Metric) Watson (1979) Tinkering with maxima of Gaussian variables Goal directed ad hoc mathematics Proof/derivation?

  6. Quotes indicating use of Quick‘s approach: ''To allow for the statistical nature of the detection process, the effects of probability summation must be incorporated. … A convenient way to compute the effects of spatial probability summation is based on Quick's (1974) parameterization of the psychometric function. (Wilson 1978, p. 973; similarly Wilson, Philips et al 1979, p. 594, Graham 1989, and many others.) … probability summation […] requires that the noises associated with different stimulations be uncorrelated.'' Gorea, Caetta, Sagi (2005, p.2531) Similar statements by Meese \& Williams (2000), Tversky, Geisler \& Perry (2004) on contour grouping, Monnier (2006), Meese \& Summers (2007), Watson \& Ahumada (2005) take Quick/Minkowski as a basis for a general model of contrast detection – everything is explained (?) Justification: as usual.

  7. Detection and temporal probability summation – correlated noise Assumptions:

  8. Illustration of second spectral moment: Example 1: Example 2:

  9. Temporal probability summation or maximum mean detection? Roufs & Blommaert (1981): Determination of the impulse and step response by means of the perturbation technique Prediction Data:

  10. Detection by a population of matched neurons Hebb‘s rule implies adaptation of neuron – local matched filter Defined by a DOG-function Pre-filter (lens, retina, LGB) Stimulus

  11. Test of matched neuron model: no probability summation of any sort! Response of matched neurons Data and predictions Response of pre-filter Stimulus To be estimated: four free parameters of the pre-filter!

  12. „Channels“ and neuron populations: a stochastic model (based on a model of Gerstner (2000)) Channel = Population of N neurons The meaning of activity

  13. Activity of an individual neuron Threshold (spike generation) Membrane potential of i-th neuron Resting potential

  14. Membrane potential density Membrane potential density Stochastic differential equation for individual trajectory of u:

  15. Diffusion Drift Derivative of Brownian motion = white noise Activity.from stimulus Activity from environment

  16. Response to short pulses and step functions (Response to a 2 ms pulse!) • The amplitude of mean response g is the same in all three cases – the smaller eta, the more pronounced is g • The peaks of the activity (spike rate) are extremely short compared to the mean response to the stimulus – prob. summation is unlikely!

  17. Detection model: The probability of detection depends on how pronounced the (mean) activity generated by the stimulus is with respect to the overall activity. Operationalised: Maximum of mean activity Ground activity: determines probability of false alarm Threshold value Noise (= activity) from environment ( > 0) Yeshurun & Carrasco, 1998, 1999; Treue, 2003; Martinez-Trujillo & Treue, 2004: focussing attention on a position or feature will reduce noise and enhance the response. However: Reynolds & Desimone, 2003: attention increases contrast gain in V4-neurons…

  18. Summary: • Quick‘s (1974) model (white noise) may lead to arbitrary interpretations of data • Correlated activity is the norm, not the exception • More realistic models (correlated noise) of probability summation show that probability summation is not a general mode of detection with max-mean or peak detection a special case • There may be adaptive processes – mechanisms are not necessarily invariant with respect to stimulation • Construct dynamic network or population models, - not diffuse „nonlinear summation“ models

  19. Thank you for your attention!

  20. Probability summation over time - the white noise case: Application of extreme value statistics for independent variables But: Hazard function

  21. Detection by TPS, Gaussian coloured noise Mean response g(t) Psychometric function: Does not approach the expression for white noise if lambda-2 approaches infinity! The form of the psychometric function and its approximation by a Weibull function; different stimulus durations.

  22. Roufs & Blommaert (1981): Direct measurement of impulse and step responses by means of a perturbation technique. Impulse response, transient channel, as determined by perturbation method Impulse response, as derived from MTF: true according to Watson (1981) (although the additional assumption of a minimum phase system has to be made).

  23. Roufs & Blommaert (1981): Direct measurement of impulse and step responses by means of a perturbation technique (assuming maximum-of-mean detection). Impulse response for transient channels: 3- or 2-phasic? Watson (1981): triphasic impulse response is an artifact Quick‘s model with exponent between 2 and 7 yields 3-phasic impulse repsonse. True response is 2-phasic, as derived from MTF. Artifact? Assumption of probability summation? peak detection?

  24. Spatial probability summation: Templates or matched filters for circular discs of different diameters, superimposed on subthreshold Bessel-Jo-patterns for various spatial frequency parameters: neither temporal nor spatial probability summation.

  25. Data and predictions of template/MF-model, based on temporal peak detection There is no „nonlinear Minkowski-summation claimed by Watson & Ahumada (2005) as a necessary element in the detection process!

  26. Determination of line spread function – Hines (1976)

  27. Rentschler & Hilz (1976) – Disinhibition in LSF-measurements? Flanking line about 75% of test line! Disinhibition?

  28. Wilson, Philips et al (1979) – no disinhibition, but spatial probability summation, as modelled by Quick‘s rule

  29. LSF and LSF-estimates – probability summation, correlated noise p(false alarm) = .1

  30. LSF and LSF-estimates – probability summation, correlated noise p(false alarm) = .01

  31. Probability summation: correlated noise (q: luminance proportion of flanking lines, P(fA) = .1) No pseudo-disinhibition for „white noise“! Pseudo-inhibition for higher flanking contrasts, no pseudo-disinhibition! Probability summation does not predict disinhibition, - rather, inhibition!

  32. LSF-prediction by Quick‘s rule; stimulus configuration A

  33. Explore mechanisms Prob. Summation. No Prob. Summation Correlated noise White noise Deterministic models Stochastic models Implies inconsistency Quick (1974) Max Mean response (Canonical model in visual psychophysics) Pooling Equivalent to Weibull-function (Minkowski-Metric) Test

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