Re: Concepts leading to Q6 and Q8
Professor, thank you for answering. I am starting to see an opening; however, I think that I am mainly confused with the learning objective of the algorithm in examples 2.2, i.e., what exactly is the machine trying to learn? The learning goal of a perceptron algorithm is easy to visualize because the learning that is taking place is easily expressed and recognizable. For example, I could learn how to distinguish a penny from a nickel given a bunch of these coins. I could test different hypotheses on the training set of coins and come up with a super accurate “g” hypothesis based on the size or weight measurements of a training set of coins.
Going back to example 2.2, specifically in the case of the Positive Rays which seems to be the easiest, what is it exactly that we want the machine to learn? We know that we have a constellation of N points that divide a line into N + 1 regions and that we do not know a priori if each point has a value 1 or 1, as you mentioned. Is the objective of learning to determine the location of point “a” so that we can separate the N points into two groups (+1’s and 1’s)? Is this a case similar to the perceptron in which we expect separation to occur? If this is the case, do the hypotheses consist of changing the location of “a” to each of the N+ 1 regions, then at each location of "a" checking each point "x" with the formula sign(xa), and comparing the result of the formula with the value (1 or +1) of each point (supervised learning)? If separation is expected to occur (the goal of learning) but does not happen with the particular set of input points given, have we still learned something? i.e., have we learned that the particular set of input points is not separable?
So I guess that I am struggling with trying to understand the most basic issue… what is the machine trying to learn in each of the three examples presented in Example 2.2 of the book (p. 43 and 44)? I think that if I can achieve some insight on this, then I will be able to better visualize the situation.
I hope that I am not being too dense here. If I am, please accept my apologies. I am most grateful for this opportunity. I intend to continue working very hard to understand this very captivating field even if I do not perform very well in the quizzes.
Thank you.
Juan
