Page 47 / Lecture 6 (10 min) Partitioning the table
I am struggling with one of more simpler bits of chapter 2.
On page 47 (Lecture 6  9 ~ 12 mins), I do not understanding how the table is constructed. "Some dichotomies on these N1 points appear only once" Okay, so to me, this implies we have 2^(n1) rows for the first set (S1). "The remaining dichotomies on the first n1 appear twice, once with +1 and once with 1" How can this be true...? To me, "the remaining dichotomies on the first n1" would mean (2^n) less (2^n1) = 2^n1. But these appear twice! So we have 2*(2^n1) = 2^n for set S2. This seems as though we are counting twice. S1 = 2^n1 S2 = 2^n The total of S1 + S2 is greater than 2^n. Surely, I must be missing something really simple here. But what...? Please help. Thanks, Mark 
Re: Page 47 / Lecture 6 (10 min) Partitioning the table
Thank you very much for replying.
I read the answers and think that I understand the points being made in regards to the maximum being 2^(n1). But on reflection, perhaps my misunderstanding could have been expressed more clearly. So, I am sorry about the following tables, but perhaps these help to demonstrate what I am missing in regards to partitioning the original set into 3 disjoint sets. The following assumes a space of 4 points  a maximum of 16 dichotomies. I have labelled each row with its base 10 equivalence. Here is alpha (N1 appears once, with XN either 1 or 0) X1 X2 X3 XN ID 0 0 0 0 0 0 0 1 1 3 0 1 0 0 4 0 1 1 1 7 1 0 0 0 8 1 0 1 1 11 1 1 0 0 12 1 1 1 1 15 We are left with 8 rows remaining If these have XN being either 1 or 1, then these 8 rows are split into the following two partitions (S2+ and S2). [S2+] X1 X2 X3 XN ID 0 0 0 1 1 0 1 0 1 5 1 0 0 1 9 1 1 0 1 13 [S2] X1 X2 X3 XN ID 0 0 1 0 2 0 1 1 0 6 1 0 1 0 10 1 1 1 0 14 So, given the partitions above, I seem to get that X1, X2 appears twice but this is not N1 appearing twice (i.e. X1, X2, X3). I understand we are attempting to describe situations were there is a break point and all the combinations listed above will not exist. But given the instructions in the book and using a niceandneat 2n construction, I do not understand how the exhaustive and exclusive 3 sets are derived. Thanks in advance, Mark 
Re: Page 47 / Lecture 6 (10 min) Partitioning the table
Quote:

Re: Page 47 / Lecture 6 (10 min) Partitioning the table
Got it!!
Thank you very much for your patience. 
All times are GMT 7. The time now is 02:29 PM. 
Powered by vBulletin® Version 3.8.3
Copyright ©2000  2020, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. AbuMostafa, Malik MagdonIsmail, and HsuanTien Lin, and participants in the Learning From Data MOOC by Yaser S. AbuMostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.