zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Generalization bounds for ranking algorithms via algorithmic stability. (English) Zbl 1235.68123
Summary: The problem of ranking, in which the goal is to learn a real-valued ranking function that induces a ranking or ordering over an instance space, has recently gained much attention in machine learning. We study generalization properties of ranking algorithms using the notion of algorithmic stability; in particular, we derive generalization bounds for ranking algorithms that have good stability properties. We show that kernel-based ranking algorithms that perform regularization in a reproducing kernel Hilbert space have such stability properties, and therefore our bounds can be applied to these algorithms; this is in contrast with generalization bounds based on uniform convergence, which in many cases cannot be applied to these algorithms. Our results generalize earlier results that were derived in the special setting of bipartite ranking to a more general setting of the ranking problem that arises frequently in applications.
MSC:
68T05Learning and adaptive systems