TY - GEN

T1 - Learning boxes in high dimension

AU - Beimel, Amos

AU - Kushilevitz, Eyal

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - We present exact learning algorithms that learn several classes of (discrete) boxes in {0,..., ℓ−1}n. In particular we learn: (1) The class of unions of O(log n) boxes in time poly(n, log ℓ) (solving an open problem of [15, 11]). (2) The class of unions of disjoint boxes in time poly(n, t,log ℓ), where t is the number of boxes. (Previously this was known only in the case where all boxes are disjoint in one of the dimensions). In particular our algorithm learns the class of decision trees (over n variables that take values in {0,..., ℓ−1}) with comparison nodes in time poly (n, t, log ℓ), where t is the number of leaves (this was an open problem in [8] which was shown in [3] to be learnable in time poly(n, t, ℓ)). (3) The class of unions of O(1)-degenerate boxes (that is, boxes that depend only on O(1) variables) in time poly(n, t, log ℓ) (generalizing the learnability ofO(1)-DNF and of boxes in O(1) dimensions). The algorithm for this class uses only equivalence queries and it can also be used to learn the class of unions ofO(1) boxes (from equivalence queries only).

AB - We present exact learning algorithms that learn several classes of (discrete) boxes in {0,..., ℓ−1}n. In particular we learn: (1) The class of unions of O(log n) boxes in time poly(n, log ℓ) (solving an open problem of [15, 11]). (2) The class of unions of disjoint boxes in time poly(n, t,log ℓ), where t is the number of boxes. (Previously this was known only in the case where all boxes are disjoint in one of the dimensions). In particular our algorithm learns the class of decision trees (over n variables that take values in {0,..., ℓ−1}) with comparison nodes in time poly (n, t, log ℓ), where t is the number of leaves (this was an open problem in [8] which was shown in [3] to be learnable in time poly(n, t, ℓ)). (3) The class of unions of O(1)-degenerate boxes (that is, boxes that depend only on O(1) variables) in time poly(n, t, log ℓ) (generalizing the learnability ofO(1)-DNF and of boxes in O(1) dimensions). The algorithm for this class uses only equivalence queries and it can also be used to learn the class of unions ofO(1) boxes (from equivalence queries only).

UR - http://www.scopus.com/inward/record.url?scp=84949236839&partnerID=8YFLogxK

U2 - 10.1007/3-540-62685-9_2

DO - 10.1007/3-540-62685-9_2

M3 - Conference contribution

AN - SCOPUS:84949236839

SN - 3540626859

SN - 9783540626855

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 3

EP - 15

BT - Computational Learning Theory - 3rd European Conference, EuroCOLT 1997, Proceedings

A2 - Ben-David, Shai

PB - Springer Verlag

T2 - 3rd European Conference on Computational Learning Theory, EuroCOLT 1997

Y2 - 17 March 1997 through 19 March 1997

ER -