On qualitative robustness of support vector machines
Support vector machines (SVMs) have attracted much attention in theoretical and in applied statistics. The main topics of recent interest are consistency, learning rates and robustness. We address the open problem whether SVMs are qualitatively robust. Our results show that SVMs are qualitatively robust for any fixed regularization parameter [lambda]. However, under extremely mild conditions on the SVM, it turns out that SVMs are not qualitatively robust any more for any null sequence [lambda]n, which are the classical sequences needed to obtain universal consistency. This lack of qualitative robustness is of a rather theoretical nature because we show that, in any case, SVMs fulfill a finite sample qualitative robustness property. For a fixed regularization parameter, SVMs can be represented by a functional on the set of all probability measures. Qualitative robustness is proven by showing that this functional is continuous with respect to the topology generated by weak convergence of probability measures. Combined with the existence and uniqueness of SVMs, our results show that SVMs are the solutions of a well-posed mathematical problem in Hadamard's sense.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 102 (2011)
Issue (Month): 6 (July)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
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.:
- Bartlett, Peter L. & Jordan, Michael I. & McAuliffe, Jon D., 2006. "Convexity, Classification, and Risk Bounds," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 138-156, March.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:102:y:2011:i:6:p:993-1007. 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: (Dana Niculescu)
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.