Quote:
Originally Posted by fredrmueller@gmail.com
The zeroth term is just a clever way to simplify the notation by adding the threshold/bias term as another term in the sum. The value of the threshold/bias, however, is not an observed quantity, though  it was chosen. So I am assuming that when updating the weights, we should NOT update the zeroth weight (the threshold/bias). Is this correct?

In fact
is just like all other weights, and should be updated in the same way (which will happen automatically when you use the PLA update rule and take
to include the zerocoordinate
). The intuitive reason is that some thresholds work better than others (similar to some weights working better than others) in separating the data, hence being part of the learning update will result in a better value.