Help explain the probabilty of a false positive classification of a list of SDR vectors

bami

#1

Hello,

I don’t understand equation 9 in SDR chapter of the BAMI book:

My expectation of what equation 9 is supposed to calculate is that if for example we have a list of SDRs, X, with only two elements x1 and x2, then equation 9 is supposed to calculate the probability that a random SDR y will match any of the SDRs in X.

This means that we should calculate:

Probability false positive between x1 and y + Probability false positive between x2 and y

But from the way equation 9 is written, it looks to me that it is calculating:

Probability of no false positive between x1 and y + Probability of no false positive between x2 and y

Can someone please explain the intuition behind equation 9 and illustrate how it works using a small example?


#2

The formula for probability of a false positive is basically its overlap set divided by its uniqueness. You can see this clearly in the HTM School code that runs behind this episode.

You can follow this down through the code to get a specific understanding. Here is how SDR uniqueness is calculated:

And here is how we use it to get the overlap set: