LFD Book Forum Problem 2.14(a + c)
 User Name Remember Me? Password
 Register FAQ Calendar Mark Forums Read

 Thread Tools Display Modes
#1
10-03-2016, 05:15 PM
 zyteka Junior Member Join Date: Sep 2016 Posts: 1
Problem 2.14(a + c)

I am having some difficulties working through problem 2.14

For a, I understand that the number of dichotomies that H can implement at most K times the number of hypothesis that H_1 can implement, which can implement N^(dvc + 1). I'm not sure how to relate this to the dvc(H).

For c, I can prove the first half of the min function using part a. For the second part of the min function, ( 7(dvc + K) log2 (dvcK) ), I plugged the function into the inequality in b, and simplified to get:
(dk)^(7(dvc+K)) > 2K(7(dvc + K) log(dvc K))^d

I am not sure how to proceed from here, and no simplifications I can do from here seem get closer to solving the inequality.
#2
10-03-2016, 09:24 PM
 leezard87 Junior Member Join Date: Aug 2016 Posts: 2
Re: Problem 2.14(a + c)

For (a), if you set the break point to k*=dvc+1 for each hypothesis, it's obvious that dvc<k*. Then the upper bound of dvc for the union hypothesis set H is Kk*, meaning dvc < Kk*=K(dvc+1). This is my solution. I'm not 100% sure though.

For (c), I have the same confusion as you. I tried to simplify that inequality for a couple of hours and got nothing closer to the result. Hope someone could shed some light...

 Thread Tools Display Modes Hybrid Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home General     General Discussion of Machine Learning     Free Additional Material         Dynamic e-Chapters         Dynamic e-Appendices Course Discussions     Online LFD course         General comments on the course         Homework 1         Homework 2         Homework 3         Homework 4         Homework 5         Homework 6         Homework 7         Homework 8         The Final         Create New Homework Problems Book Feedback - Learning From Data     General comments on the book     Chapter 1 - The Learning Problem     Chapter 2 - Training versus Testing     Chapter 3 - The Linear Model     Chapter 4 - Overfitting     Chapter 5 - Three Learning Principles     e-Chapter 6 - Similarity Based Methods     e-Chapter 7 - Neural Networks     e-Chapter 8 - Support Vector Machines     e-Chapter 9 - Learning Aides     Appendix and Notation     e-Appendices

All times are GMT -7. The time now is 04:01 AM.

 Contact Us - LFD Book - Top

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. Abu-Mostafa, Malik Magdon-Ismail, and Hsuan-Tien Lin, and participants in the Learning From Data MOOC by Yaser S. Abu-Mostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.