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-   -   HW6-Q1 ambiguous/contradictory (http://book.caltech.edu/bookforum/showthread.php?t=4297)

doneit 05-18-2013 02:01 AM

HW6-Q1 ambiguous/contradictory
 
I've checked my understanding of set-notation but am I correct in thinking the question says "H' is-a-subset of H", ie, less complex?

To me the most "general" case is having a large, possibly infinite, H where the bulk would be overly complex. So my (wrong) answer assumes that by reducing complexity of the set I'm reducing the chance of over-fitting. So "in general" I'm *reducing* the chance of deterministic noise. Of course after a certain point it will increase again, limited by a flat lined solution.

So why would assuming H is already less complex be more "general" that this? Additionally, pg 124 states over-fitting increases with complexity. I scratch my head to the point of baldness :clueless:

Btw, I'm enjoying the video lectures immensely. It's like watch a soap opera with twists & turns, plots & sub-plots, and just when the situation seems impossible the magician doffs his top hat and pulls out another white rabbit :D I actually giggled at the cross-validation trick :D

yaser 05-18-2013 02:12 AM

Re: HW6-Q1 ambiguous/contradictory
 
Quote:

Originally Posted by doneit (Post 10870)
I've checked my understanding of set-notation but am I correct in thinking the question says "H' is-a-subset of H", ie, less complex?

To me the most "general" case is having a large, possibly infinite, H where the bulk would be overly complex. So my (wrong) answer assumes that by reducing complexity of the set I'm reducing the chance of over-fitting. So "in general" I'm *reducing* the chance of deterministic noise.

Your understanding is correct in that a subset will be generally less complex than the original set. I think the source of confusion is that overfitting is affected by both the level of noise and the complexity of the model, and for deterministic noise the complexity in turn affects the level of noise. The question, however, addresses deterministic noise only, not necessarily the overfitting effect that results from it. The part which is not accurate in the above quote is the last sentence that mixes the two.

Quote:

Btw, I'm enjoying the video lectures immensely. It's like watch a soap opera with twists & turns, plots & sub-plots, and just when the situation seems impossible the magician doffs his top hat and pulls out another white rabbit :D I actually giggled at the cross-validation trick :D
If I had thought of that, I would have inserted some commercial breaks at the right moments. :)

doneit 05-18-2013 02:46 AM

Re: HW6-Q1 ambiguous/contradictory
 
Quote:

Originally Posted by yaser (Post 10871)
The part which is not accurate in the above quote is the last sentence that mixes the two.

Ok, got it, thanks.

Quote:

If I had thought of that, I would have inserted some commercial breaks at the right moments. :)
:D


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