TY - GEN

T1 - Sample Compression for Real-Valued Learners

AU - Hanneke, Steve

AU - Kontorovich, Aryeh

AU - Sadigurschi, Menachem

PY - 2019

Y1 - 2019

N2 - We give an algorithmically efficient version of the learner-to-compression scheme conversion in Moran and Yehudayoff (2016). We further extend this technique to real-valued hypotheses, to obtain a bounded-size sample compression scheme via an efficient reduction to a certain generic real-valued learning strategy. To our knowledge, this is the first general compressed regression result (regardless of efficiency or boundedness) guaranteeing uniform approximate reconstruction. Along the way, we develop a generic procedure for constructing weak real-valued learners out of abstract regressors; this result is also of independent interest. In particular, this result sheds new light on an open question of H. Simon (1997). We show applications to two regression problems: learning Lipschitz and bounded-variation functions.

AB - We give an algorithmically efficient version of the learner-to-compression scheme conversion in Moran and Yehudayoff (2016). We further extend this technique to real-valued hypotheses, to obtain a bounded-size sample compression scheme via an efficient reduction to a certain generic real-valued learning strategy. To our knowledge, this is the first general compressed regression result (regardless of efficiency or boundedness) guaranteeing uniform approximate reconstruction. Along the way, we develop a generic procedure for constructing weak real-valued learners out of abstract regressors; this result is also of independent interest. In particular, this result sheds new light on an open question of H. Simon (1997). We show applications to two regression problems: learning Lipschitz and bounded-variation functions.

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

VL - 98

T3 - Proceedings of Machine Learning Research

SP - 466

EP - 488

BT - Proceedings of the 30th International Conference on Algorithmic Learning Theory

A2 - Garivier, Aurélien

A2 - Kale, Satyen

PB - PMLR

CY - Chicago, Illinois

ER -