Thread: Question 2
View Single Post
  #3  
Old 04-12-2013, 12:01 PM
yaser's Avatar
yaser yaser is offline
Caltech
 
Join Date: Aug 2009
Location: Pasadena, California, USA
Posts: 1,478
Default Re: Question 2

Quote:
Originally Posted by jlaurentum View Post
Does fixing the hypothesis mean fixing the coins, or does it mean being able to fix a random experiment (procedure) by which we obtain the sample frequencies?
Let me focus on the correspondence between the bin world and the hypothesis world since this seems to be a source of confusion.

The bin corresponds to the input space {\cal X}, with each marble corresponding to an input point {\bf x}\in{\cal X}.

The colors in a bin correspond to how a hypothesis agrees with the target; the color of a marble being red if h({\bf x})\ne f({\bf x}) for that 'marble' {\bf x}.

Fixed hypothesis means the colors inside the bin are fixed prior to drawing the sample. What makes a hypothesis 'not fixed' is that we have a bunch of bins and we select a bin according to the sample it produced (e.g., an all green sample). The reason we call the hypothesis not fixed in this case is because which bin we pick (hence which colors are inside, hence which hypothesis we are talking about) depends on the samples that have already been produced.
__________________
Where everyone thinks alike, no one thinks very much
Reply With Quote