SPIKE TRIGGERED APPROACHES. Odelia Schwartz Computational Neuroscience Course 2017
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1 SPIKE TRIGGERED APPROACHES Odelia Schwartz Computational Neuroscience Course 2017
2 LINEAR NONLINEAR MODELS Linear Nonlinear o Often constrain to some form of Linear, Nonlinear computations, e.g. visual receptive fields or filters, followed by nonlinear interactions
3 LINEAR NONLINEAR MODELS What type of nonlinearities?
4 DESCRIPTIVE MODELS: DIVISIVE NORMALIZATION o Canonical computation (Carandini, Heeger, 2013) o Has been applied to primary visual cortex (V1) o More broadly, to other systems and modalities, multimodal processing, value encoding, etc
5 DESCRIPTIVE MODELS: COMPLEX CELLS AND INVARIANCE o after Adelson & Bergen, 1985
6 FITTING DESCRIPTIVE MODELS TO DATA Linear Nonlinear Poisson
7 ROADMAP o Simple cell traditional approach o Simple cell (STA) o When STA fails o Complex cell (STC) o Another example (STC) o More generic model with multiple filters
8 REMINDER: RECEPTIVE FIELD Hubel and Wiesel, 1959 Stimuli Spikes
9 Primary Visual Cortex (V1) REMINDER: RECEPTIVE FIELD
10 RECEPTIVE FIELD o Response of a filter = inner/dot product/projection of filter with stimulus
11 ROADMAP o Simple cell traditional approach o Simple cell (STA) o When STA fails o Complex cell (STC) o Another example (STC) o More generic model with multiple filters
12
13 SPIKE-TRIGGERED AVERAGE
14 SPIKE-TRIGGERED AVERAGE
15 SPIKE-TRIGGERED AVERAGE
16 STA SPIKE-TRIGGERED AVERAGE
17 EFFECT OF NONLINEARITY IN MODEL?
18 EFFECT OF NONLINEARITY IN MODEL?
19 EFFECT OF NONLINEARITY IN MODEL? o Nonlinearity sets negative filter responses to zero (firing rates are positive)
20 SPIKE-TRIGGERED AVERAGE (STA) o Stimuli that are more similar to filter are more likely to elicit a spike
21 Model: SPIKE-TRIGGERED AVERAGE (STA)
22 SPIKE-TRIGGERED AVERAGE (STA) STA response Random filter response
23 Geometrical view: change in the mean Large filter response likely to elicit spike SPIKE-TRIGGERED AVERAGE (STA) Spike stimuli Raw stimuli STA response Random filter response
24 SPIKE-TRIGGERED AVERAGE (STA) STA We can also recover the nonlinearity
25 SPIKE-TRIGGERED AVERAGE (STA) We can also recover the nonlinearity
26 STEPS 1.Assume a model (filter/s, nonlinearity) (we assumed one filter and asymmetric nonlinearity) 2. Estimate model components (filter/s, nonlinearity) (we looked for changes in mean: STA)
27 ROADMAP o Simple cell traditional approach o Simple cell (STA) o When STA fails o Complex cell (STC) o Another example (STC) o More generic model with multiple filters
28 BUT STA DOES NOT ALWAYS WORK STA filter??
29 BUT STA DOES NOT ALWAYS WORK STA filter!
30 WHAT HAPPENED?? Nonlinearity sets negative filter responses to positive (firing rates are positive)
31 WHAT HAPPENED?? Spike stimuli Raw stimuli Model filter STA filter! Random filter response Large or small filter response likely to elicit spike Mean stimuli eliciting spikes = 0
32 CHANGE IN THE VARIANCE Spike stimuli Raw stimuli Positive 0 Model filter Negative STA filter! Large or small filter response likely to elicit spike Random filter response
33 SPIKE-TRIGGERED COVARIANCE (STC) Spike stimuli Raw stimuli Positive 0 Model filter Negative Standard algebra techniques (eigenvector analysis) recovers changes in variance Random filter response
34 SPIKE-TRIGGERED COVARIANCE (STC) Model filter Random filter response We can also recover the nonlinearity
35 STEPS 1.Assume a model (filter/s, nonlinearity) (we assumed one filter and symmetric nonlinearity) 2. Estimate model components (filter/s, nonlinearity) (STA failed) (we looked for changes in variance: STC)
36 SPIKE-TRIGGERED COVARIANCE (STC) o Figure from Schwartz et al. 2006; see also Rust et al. 2005, de Ruyter & Bialek 1988 o Approach estimates linear subspace and nonlinearity
37 ROADMAP o Simple cell traditional approach o Simple cell (STA) o When STA fails o Complex cell (STC) o Another example (STC) o More generic model with multiple filters
38 SPIKE-TRIGGERED COVARIANCE (STC)
39 CHANGE IN VARIANCE (STC) Spike stimuli Raw stimuli
40 CHANGE IN VARIANCE (STC) STA filter!
41 CHANGE IN VARIANCE (STC)
42 STEPS 1.Assume a model (filter/s, nonlinearity) (we assumed more than one filter and symmetric nonlinearity) 2. Estimate model components (filter/s, nonlinearity) (STA failed) (we looked for changes in variance: STC)
43 ROADMAP o Simple cell traditional approach o Simple cell (STA) o When STA fails o Complex cell (STC) o Another example (STC) o More generic model with multiple filters
44 SECOND FILTER SUPPRESSIVE (E.G., DIVISIVE)
45 SECOND FILTER SUPPRESSIVE (E.G., DIVISIVE) Second filter brings about reduction in variance! Spike stimuli Raw stimuli
46 SECOND FILTER SUPPRESSIVE (E.G., DIVISIVE) Second filter brings about reduction in variance!
47 STEPS 1.Assume a model (filter/s, nonlinearity) (we assumed more than one filter and symmetric nonlinearity) 2. Estimate model components (filter/s, nonlinearity) (we looked for changes in variance, this time reduced variance: STC)
48 SPIKE TRIGGERED APPROACES Change in the mean (STA) Complex cell Divisive normalization Changes in the variance (STC)
49 ROADMAP o Simple cell traditional approach o Simple cell (STA) o When STA fails o Complex cell (STC) o Another example (STC) o More generic model with multiple filters
50 MORE GENERAL CLASS OF MODEL Look for changes in both the mean and the variance
51 APPLICATION: V1 EXPERIMENT
52 V1 NEURAL DATA: SPIKE-TRIGGERED COVARIANCE o Example V1 neuron estimated filters from Rust et al. 2005
53 V1 NEURAL DATA: RECALL THE STANDARD MODELS But Data show multiple filters (excitatory and suppressive) for both. Are these really two different classes of neurons, or is there a continuum??
54 STC ISSUES: HOW MANY SPIKES? Filter estimate depends on: Spatial and time dimensionality of input stimulus (smaller = better estimate) Number of spikes (more = better estimate)
55 STC CAVEATS Analysis forces filters that are 90 degrees apart! Filters should not be taken literally as physiological mechanisms
56 STC CAVEATS But true filters are linear combinations of original ( span the same subspace )
57 STC CAVEATS Analysis forces filters that are 90 degrees apart! Filters should not be taken literally as physiological mechanisms Spiking in neuron may be non Poisson (bursts;; refractory period;; etc.) Filters should not be taken literally as physiological mechanisms There might be more filters affecting neural response than what analysis finds STC guaranteed to work only for Gaussian stimuli There might be changes that are not in the mean or variance (other approaches;; e.g., info theory)
58 EXAMPLE: FITTING LN-LN MODEL o o o Figure from Pagan et al describing retina and V1 with subunits (see Rust et al. 2005; Vintch et al. 2015) In Pagan et al addressing higher level brain areas See also Rowekamp et al addressing area V2
59 EXAMPLE: GENERALIZED LINEAR MODEL Stimulus filter Stochastic Nonlinearity spiking e x Post-spike filter Neuron 1 Coupling filters Neuron 2 o Figure from Pillow et al., 2008, describing retina
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