W1D3 T2 - Why are we assuming independence resulting in Poisson for input current for LIF model?

,
1

In tutorial two, it says -
“Given no other information about the input neurons, we will also assume that the distribution has a mean (i.e. mean rate, or number of spikes received per timestep), and that the spiking events of the input neuron(s) are independent in time. Are these reasonable assumptions in the context of real neurons?”

Are they reasonable assumptions?

I don’t know because what does ‘independence’ here mean? Is it that one post-synaptic potential on the test neuron is independent of the previous one?
Wouldn’t it matter when the previous spike came - because -

  1. there is refractory time for the input neuron
  2. for an input neuron firing at say, a constant rate, the next spike needs to know when the previous spike happened - does it mean they are dependent?
  3. how can we say the inputs are independent when they themselves are being driven by some other process, that is not random?

I’m sorry, I’m not from a math background so I’m not even sure if my question makes any sense.
Or are these concerns valid and is just an imperfect assumption we need to deal with?

3 Likes
2

This is a good question.

Here, independent essentially means no memory - that knowing the previous spikes gives no information about the current spike times.

Directly answer your concerns:

  1. Refractory time would be an issue, but is often extremely short - approx 1-2ms. So if the time steps are as large as the refractory period, then essentially we are abiding by the refractory period. If we want more granular time steps, we may want to account for it in our model.
  2. This is exactly what we are saying DOESN’T matter: a Poisson distribution doesn’t care, and we are using a poisson. So the question is then, does our model fit the data? If so, then it appears it does not matter! If the fit is poor, then I guess it does!
  3. We are saying the spike times are independent, having no information about other variables like input potentials, behavior etc. It is possible (likely) we would find the spike times dependent on those variables - but here, we are saying only that the spikes don’t depend on the previous spikes of the same neuron. We don’t know anything about those other variables!

I hope this helps.

1 Like