Vapnik-Chervonenkis Dimension of Parallel Arithmetic Computations

Authors:
César L. Alonso;José Luis Montaña
Affiliations:
Centro de Inteligencia Artificial, Universidad de Oviedo, Campus de Viesques, 33271 Gijón, Spain;Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
Venue:
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Year:
2007

Citing 10
Cited 1

Parallel arithmetic computations: a survey

Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
Complexity of deciding Tarski algebra

Journal of Symbolic Computation
Bounding the Vapnik-Chervonenkis Dimension of Concept Classes Parameterized by Real Numbers

Machine Learning - Special issue on COLT '93
Polynomial bounds for VC dimension of sigmoidal and general Pfaffian neural networks

Journal of Computer and System Sciences - Special issue: dedicated to the memory of Paris Kanellakis
Complexity and real computation

Complexity and real computation
A Polynomial Linear Search Algorithm for the n-Dimensional Knapsack Problem

Journal of the ACM (JACM)
Time-space tradeoffs in algebraic complexity theory

Journal of Complexity
Combinatorial Hardness Proofs for Polynomial Evaluation

MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Lower bounds for algebraic computation trees

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Proving simultaneous positivity of linear forms

Journal of Computer and System Sciences

VC Dimension Bounds for Analytic Algebraic Computations

COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We provide upper bounds for the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers whose membership tests are programs described by bounded-depth arithmetic networks. Our upper bounds are of the kind O(k2d2), where dis the depth of the network (representing the parallel running time) and kis the number of parameters needed to codify the concept. This bound becomes O(k2d) when membership tests are described by Boolean-arithmetic circuits. As a consequence we conclude that families of concepts classes having parallel polynomial time algorithms expressing their membership tests have polynomial VC dimension.