TY - GEN
T1 - Approximate consistency
T2 - European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2014
AU - Ding, Lizhong
AU - Liao, Shizhong
PY - 2014
Y1 - 2014
N2 - Kernel selection is critical to kernel methods. Approximate kernel selection is an emerging approach to alleviating the computational burdens of kernel selection by introducing kernel matrix approximation. Theoretical problems faced by approximate kernel selection are how kernel matrix approximation impacts kernel selection and whether this impact can be ignored for large enough examples. In this paper, we introduce the notion of approximate consistency for kernel matrix approximation algorithm to tackle the theoretical problems and establish the preliminary foundations of approximate kernel selection. By analyzing the approximate consistency of kernel matrix approximation algorithms, we can answer the question that, under what conditions, and how, the approximate kernel selection criterion converges to the accurate one. Taking two kernel selection criteria as examples, we analyze the approximate consistency of Nyström approximation and multilevel circulant matrix approximation. Finally, we empirically verify our theoretical findings.
AB - Kernel selection is critical to kernel methods. Approximate kernel selection is an emerging approach to alleviating the computational burdens of kernel selection by introducing kernel matrix approximation. Theoretical problems faced by approximate kernel selection are how kernel matrix approximation impacts kernel selection and whether this impact can be ignored for large enough examples. In this paper, we introduce the notion of approximate consistency for kernel matrix approximation algorithm to tackle the theoretical problems and establish the preliminary foundations of approximate kernel selection. By analyzing the approximate consistency of kernel matrix approximation algorithms, we can answer the question that, under what conditions, and how, the approximate kernel selection criterion converges to the accurate one. Taking two kernel selection criteria as examples, we analyze the approximate consistency of Nyström approximation and multilevel circulant matrix approximation. Finally, we empirically verify our theoretical findings.
UR - http://www.scopus.com/inward/record.url?scp=84907014630&partnerID=8YFLogxK
U2 - 10.1007/978-3-662-44848-9_23
DO - 10.1007/978-3-662-44848-9_23
M3 - Conference contribution
AN - SCOPUS:84907014630
SN - 9783662448472
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 354
EP - 369
BT - Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2014, Proceedings
PB - Springer Verlag
Y2 - 15 September 2014 through 19 September 2014
ER -