LFD Book Forum - Problem 2.16

LFD Book Forum (http://book.caltech.edu/bookforum/index.php)

- Chapter 2 - Training versus Testing (http://book.caltech.edu/bookforum/forumdisplay.php?f=109)

- - Problem 2.16 (http://book.caltech.edu/bookforum/showthread.php?t=4593)

Hi,

1. I'm trying to solve Problem 2.16, but somewhat confused by the notation. Does the "c" subscript in "hc" refer to the hypothesis number? If so, can I assume that c is a positive integer c= 0,1,2,3 etc? If not, what is c, and c subscript i? (I couldn't find any subscripts used in this way in the chapters of the book.)

2. I can solve 2.16 by showing that this is equivalent to a perceptron in d dimensions, with d=1, and then using the techniques used in your (excellent) video lecture to show that the VC dimension is exactly d+1. However, is there a simpler way to answer the question?

Thank you!

Re: Problem 2.16

$\mathbf{c}$ is the vector whose components are

so each $\mathbf{c}$ vector serves as an index to a hypothesis.

Mimicking the proof for the VC dimension of perceptrons sound like a plausible way of conquering the problem. Hope this helps.

Re: Problem 2.16

It does. Thank you very much for responding!