IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Strong minimax lower bounds for learning

Listed author(s):

Minimax lower bounds for concept learning state, for example, that for each sample size $n$ and learning rule $g_n$, there exists a distribution of the observation $X$ and a concept $C$ to be learnt such that the expected error of $g_n$ is at least a constant times $V/n$, where $V$ is the VC dimension of the concept class. However, these bounds do not tell anything about the rate of decrease of the error for a {\sl fixed} distribution--concept pair.\\ In this paper we investigate minimax lower bounds in such a--stronger--sense. We show that for several natural $k$--parameter concept classes, including the class of linear halfspaces, the class of balls, the class of polyhedra with a certain number of faces, and a class of neural networks, for any {\sl sequence} of learning rules $\{g_n\}$, there exists a fixed distribution of $X$ and a fixed concept $C$ such that the expected error is larger than a constant times $k/n$ for {\sl infinitely many n}. We also obtain such strong minimax lower bounds for the tail distribution of the probability of error, which extend the corresponding minimax lower bounds.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
File Function: Whole Paper
Download Restriction: no

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 197.

in new window

Date of creation: Jan 1997
Handle: RePEc:upf:upfgen:197
Contact details of provider: Web page:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  1. Lugosi, Gábor, 1995. "Improved upper bounds for probabilities of uniform deviations," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 71-77, October.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:197. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.