TY - JOUR

T1 - Learning unions of high-dimensional boxes over the reals

AU - Beimel, Amos

AU - Kushilevitz, Eyal

N1 - Funding Information:
∗Corresponding author. Email: eyalk@cs.technion.ac.il. http:// www.cs.technion.ac.il/∼eyalk. This research was supported by a GIF fund, by Technion V.P.R. Fund 120-872, by Japan Technion Society Research Fund, and by the fund for the promotion of research at the Technion.

PY - 2000/3/31

Y1 - 2000/3/31

N2 - Beimel and Kushilevitz (1997) presented an algorithm that exactly learns (using membership queries and equivalence queries) several classes of unions of boxes in high dimension over finite discrete domains. The running time of the algorithm is polynomial in the logarithm of the size of the domain and other parameters of the target function (in particular, the dimension). We go one step further and present a PAC+MQ algorithm whose running time is independent of the size of the domain. Thus, we can learn such classes of boxes over infinite domains. Specifically, we learn unions of t disjoint n-dimensional boxes over the reals in time polynomial in n and t, and unions of O(log n) (possibly intersecting) n-dimensional boxes over the reals in time polynomial in n.

AB - Beimel and Kushilevitz (1997) presented an algorithm that exactly learns (using membership queries and equivalence queries) several classes of unions of boxes in high dimension over finite discrete domains. The running time of the algorithm is polynomial in the logarithm of the size of the domain and other parameters of the target function (in particular, the dimension). We go one step further and present a PAC+MQ algorithm whose running time is independent of the size of the domain. Thus, we can learn such classes of boxes over infinite domains. Specifically, we learn unions of t disjoint n-dimensional boxes over the reals in time polynomial in n and t, and unions of O(log n) (possibly intersecting) n-dimensional boxes over the reals in time polynomial in n.

UR - http://www.scopus.com/inward/record.url?scp=0033890028&partnerID=8YFLogxK

U2 - 10.1016/S0020-0190(00)00024-7

DO - 10.1016/S0020-0190(00)00024-7

M3 - Article

AN - SCOPUS:0033890028

VL - 73

SP - 213

EP - 220

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 5

ER -