Inferring the learning rule from spike train data with particle Metropolis-Hastings

Abstract

Hjernen vår består av nerveceller som kommuniserer med hverandre ved å sende elektriske impulser gjennom bindinger. Forskning har vist at disse bindingene kan utvikle seg over tid, og at måten disse utvikler seg på ser ut til å følge noen underliggende regler, som vi referer til som «læringsregler». Disse er essensielle for læring og hukommelse. Statistiske metoder for å bestemme den underliggende læringsreglen i data fra nervecelleaktivitet kan dermed gi viktig innsikt.

Denne masteroppgaven beskriver partikkel Metropolis-Hastings for å karakterisere læringsregelen i simulert data for en synapse. Denne metoden er inspirert av (Linderman et al., 2014). I denne oppgaven brukte vi «spike-timing dependent plasticity»-læringsreglen, og utførte statistisk inferens av parameterne i denne. Nervecelleaktiviteten ble modellert som en Bernoulliprosess. De numeriske eksperimentene viste at med tilstrekkelig data og lite nok støy, kunne informasjon om parameterne i læringsregelen bestemmes fra dataen.

The brain is a system of connected neurons that communicate by transmitting electrical signals to each other. Research has revealed that the way in which neural connections develop over time seem to follow some underlying patterns. These are known as learning rules, and are essential for the brain to learn and form memories. Statistical methods for inferring the learning rule from recordings of neural activity may thus give insights on basic computationally principles in different brain areas. Furthermore it has been hypothesized that the learning rule might be disturbed by memory related diseases, such as Alzheimer’s. Therefore, being able to detect the underlying learning rule could shed light on the origin and workings of Alzheimer’s disease and even have applications in medical research as well.

This thesis covers the implementation of particle Metropolis-Hastings for characterizing the learning rule in simulated neural spike data for one synapse, inspired by the method proposed in (Linderman et al., 2014). For our purpose we used the additive spike-timingdependent plasticity (STDP) learning rule, and aimed at inferring its learning rule parameters. The neural spiking was modeled as a Bernoulli process in the Generalized Linear Model (GLM) framework. By numerical experiments it was demonstrated that with enough data and sufficiently low noise level, information of the learning rule parameters could be reconstructed from the spike data by using this method. The results indicate that it could be possible to distinguish between learning rules, by analysing spike train data with particle Metropolis-Hastings.