A Graph-theoretic Generalization of the Sauer-Shelah Lemma

نویسندگان

  • Nicolò Cesa-Bianchi
  • David Haussler
چکیده

We show a natural graph-theoretic generalization of the Sauer–Shelah lemma. This result is applied to bound the ‘∞ and L1 packing numbers of classes of functions whose range is an arbitrary, totally bounded metric space. ? 1998 Elsevier Science B.V. All rights reserved.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Higher dimensional PAC - learning and VC - dimension

The VC-dimension (Vapnic-Chervonenkis dimension) was introduced in 1970’s related to computational learning theory, combinatorics, and model theory which is a branch of mathematical logic. In fact, it is well known that for given class C, PAC-learnability of C, the finiteness of VC-dimension of C, and the dependency (which is a notion in model theory) of a formula defines C are essentially the ...

متن کامل

Shattering, Graph Orientations, and Connectivity

We present a connection between two seemingly disparate fields: VC-theory and graph theory. This connection yields natural correspondences between fundamental concepts in VC-theory, such as shattering and VC-dimension, and well-studied concepts of graph theory related to connectivity, combinatorial optimization, forbidden subgraphs, and others. In one direction, we use this connection to derive...

متن کامل

Complexity of VC-classes of sequences with long repetitive runs

The Vapnik-Chervonenkis (VC) dimension (also known as the trace number) and the Sauer-Shelah lemma have found applications in numerous areas including set theory, combinatorial geometry, graph theory and statistical learning theory. Estimation of the complexity of discrete structures associated with the search space of algorithms often amounts to estimating the cardinality of a simpler class wh...

متن کامل

Boolean Functions: Cryptography and Applications

Abstract. The Vapnik-Chervonenkis (VC) dimension and the Sauer-Shelah lemma have found applications in numerous areas including set theory, combinatorial geometry, graph theory and statistical learning theory. Estimation of the complexity of discrete structures associated with the search space of algorithms often amounts to estimating the cardinality of a simpler class which is effectively indu...

متن کامل

On the VC-dimension and Boolean functions with long runs

The Vapnik-Chervonenkis (VC) dimension and the Sauer-Shelah lemma have found applications in numerous areas including set theory, combinatorial geometry, graph theory and statistical learning theory. Estimation of the complexity of discrete structures associated with the search space of algorithms often amounts to estimating the cardinality of a simpler class which is effectively induced by som...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Applied Mathematics

دوره 86  شماره 

صفحات  -

تاریخ انتشار 1998