LFD Book Forum  

Go Back   LFD Book Forum > General > General Discussion of Machine Learning

Reply
 
Thread Tools Display Modes
  #1  
Old 04-20-2012, 05:39 AM
DASteines DASteines is offline
Junior Member
 
Join Date: Apr 2012
Posts: 1
Default A Modification to the Learning Diagram

How does the learning problem change if the training samples are drawn from an indexed set of distributions? That is, suppose our training samples, x and y, are drawn from:

p(x,y,\theta) where \theta = {1,2,...,k}

Suppose I am trying to classify groups of pixels in images. I have 10 images that I can draw groups of pixels from. The images are indexed by theta, with k=10. How do we account for the grouping of the training data? What strategies exist to build a "good" (unbiased) training set in cases like this?
Reply With Quote
  #2  
Old 04-20-2012, 12:04 PM
dudefromdayton dudefromdayton is offline
Invited Guest
 
Join Date: Apr 2012
Posts: 140
Default Re: A Modification to the Learning Diagram

There are perhaps additional details I might need to give a correct answer for your situation. But as I understand your problem, I would try to produce a training set that is representative of your images, perhaps sampling from all or from a (ideally) unbiased subset. If your sampling is representative of actual use, your E[in] and E[out] relationships should all hold true.
Reply With Quote
  #3  
Old 04-22-2012, 03:20 PM
magdon's Avatar
magdon magdon is offline
RPI
 
Join Date: Aug 2009
Location: Troy, NY, USA.
Posts: 590
Default Re: A Modification to the Learning Diagram

This is an interesting example. What you actually describe is a restriction of the paradigm from a general P(x,y) to one that is of the form you mention which arises by mixing 10 different distributions. This additional knowledge about the nature of your problem can inform how to choose your hypothesis set, and one appropriate model is (appropriately) called a mixture model tailored for situations like this.

I did not understand the question about the training data. Typically the training data is given. Or is your task to develop an algorithm to separate the observed 'signal' into the components coming from each image. This is called a source separation problem, and is different from a multi-class problem. In a multi-class problem, each data point belongs to one of the classes and the goal is to determine which.

Quote:
Originally Posted by DASteines View Post
How does the learning problem change if the training samples are drawn from an indexed set of distributions? That is, suppose our training samples, x and y, are drawn from:

p(x,y,\theta) where \theta = {1,2,...,k}

Suppose I am trying to classify groups of pixels in images. I have 10 images that I can draw groups of pixels from. The images are indexed by theta, with k=10. How do we account for the grouping of the training data? What strategies exist to build a "good" (unbiased) training set in cases like this?
__________________
Have faith in probability
Reply With Quote
Reply

Thread Tools
Display Modes

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 Jump


All times are GMT -7. The time now is 07:21 AM.


Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2017, 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.