STA and the encoding and decoding problems. NEU 466M Instructor: Professor Ila R. Fiete Spring 2016
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1 STA and the encoding and decoding problems NEU 466M Instructor: Professor Ila R. Fiete Spring 2016
2 Last Gme: sgmulus, spike cross- correlagon 16 x single H1 neuron in lobula plate per hemisphere When sgmulus goes up (more posigve velocity), response increases (more spikes): posigve peak. C(stim, rho) Response lags sgmulus (peak to right of zero- shiv) sample number (500 Hz) x 10 5 Cross- correlagon uncovers relagonships between Gme- series. What specifically does it mean about sgmulus à spike response?
3 Back to original goal: Modeling WHAT DOES IT MEAN TO BUILD A MODEL OF OBSERVATIONS OF A STIMULUS AND RESPONSE?
4 Modeling spike train data Model: Simple, predicgve descripgon. But what is it we want to describe/predict? OpGon 1) Given sgmulus, predict spikes? OpGon 2) Given spikes, predict sgmulus?
5 Modeling spike train data Model: Simple, predicgve descripgon. But what is it we want to describe/predict? OpGon 1): Given sgmulus, predict spikes? Encoding model OpGon 2): Given spikes, predict sgmulus?
6 Modeling spike train data Model: Simple, predicgve descripgon. But what is it we want to describe/predict? OpGon 1): Given sgmulus, predict spikes? OpGon 2): Given spikes, predict sgmulus? Encoding model Decoding model
7 Modeling spike train data Model: Simple, predicgve descripgon. But what is it we want to describe/predict? OpGon 1): Given sgmulus, predict spikes? Encoding model OpGon 2): Given spikes, predict sgmulus? Decoding model Both are good and closely related modeling goals!
8 Decoding problem Given a spike, what was the sgmulus?
9 The spike- triggered average from Spikes, Rieke et al. Given a spike, what was the mean sgmulus that led up to it?
10 The spike- triggered average from Spikes, Rieke et al. STA: (average) sgmulus feature to which cell responds
11 The spike- triggered average stimulus s(t) N spikes at times t i (i =1 N) STA( ) = 1 N NX i=1 s(t i )
12 The spike- triggered average as a correlagon STA( ) = 1 N = 1 N NX i=1 X t s(t i ) (t)s(t ) is the spike vector of 0 0 s, 1 0 s = 1 N C s( ) STA = CorrelaGon between spike- train, sgmulus at negagve (earlier) Gmes Reverse correlagon
13 STA and reverse correlagon STA implies that the response is a binary spike- train. Reverse correlagon: the response can be any Gme- varying signal. Also called white noise analysis (we will see why later).
14 STA and the decoding problem Decoding problem: Infer sgmulus given spike train. Mindreading : read spike output and infer what the brain saw. STA: Given that cell fired spike, STA returns average of preceding sgmulus.
15 Decoding problem Volterra series expansion: stimulus s(t) N spikes at times t i (i =1 N) s est (t) = X i F 1 (t t i )+ X i,j F 2 (t t i,t t j )+ each spike an independent event, and contributes independently to sgmulus reconstrucgon spike pairs in specific configuragon carry informagon about sgmulus, beyond that contained in their individual occurrences. spike pair a separate event contribugng to reconstrucgon.
16 Decoding problem Volterra series expansion: s est (t) = X i F 1 (t t i )+ X i,j F 2 (t t i,t t j )+ each spike an independent event given sgmulus, and contributes independently to sgmulus reconstrucgon STA spike pairs in specific configuragon carry informagon about sgmulus, beyond that contained in their individual occurrences. spike pair an independent event contribugng to reconstrucgon.
17 Geometric view length- T sgmulus vector preceding Gme point t: {s(t T ) s(t 2)s(t 1)} t 2 s(t 1) s(t 2) t T t 1 s(t T ) sgmulus space
18 Geometric view length- T sgmulus vector preceding Gme point t: {s(t T ) s(t 2)s(t 1)} t 2 s(t 1) s(t 2) t T t 1 s(t T ) Any possible sgmulus Gme- series is one point in sgmulus space
19 Geometric view of STA presented sgmuli s(t 1) s(t 2) s(t T )
20 Geometric view of STA s(t 1) s(t 2) s(t T ) presented sgmuli effecgve sgmuli (evoked spike)
21 Geometric view of STA s(t 1) STA s(t 2) s(t T ) presented sgmuli effecgve sgmuli (evoked spike) STA picks single direcgon in sgmulus space
22 Geometric view of STA STA STA
23 Geometric view of STA: when does it fail? STA STA points in direcgon where sgmuli were actually ineffecgve in producing spikes.
24 Geometric view of STA: when does it fail? Same caugon as correlagon: measure of linear relagonship between sgmulus, response. If response is specific nonlinear funcgon of sgmulus, then STA may not be informagve. STA = 0 Example: mogon energy model for complex cells in V1.
25 Summary: STA Simple/compact descripgon of data. ExtracGng single feature of data. Linear feature; first term in Volterra expansion. Test: PredicGon of response (encoding). Homework.
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