LFD Book Forum The VC dimension, complexity, and hypothesis set

#1
04-16-2016, 09:00 AM
 lirongr Junior Member Join Date: Apr 2016 Posts: 2
The VC dimension, complexity, and hypothesis set

Dear Professor Abu Mostafa,
We said that the larger the hypothesis set the lower the out of sample error would be. My question is how do we measure the size of the hypothesis set? Since in one of the lectures you said that the perceptron has an infinite large set of hypothesis (an infinite number of w's if I understand it correctly). Yet the perceptron is supposed to be a very simple model, so I would expect a large out of sample error.
So I may be confusing the number of the hypothesis we can generate for a given model with the its complexity, but how can we estimate the complexity? Is it by the VC dimension of the model? What is the relationship between the VC dimension, the complexity of the model and the number of hypothesis we can generate and how we can asses the complexity it the cases when VC dimension is not defined (ie regression).
Thank you very very much for your time and help,
Liron

 Thread Tools Display Modes Linear 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 08:38 PM.