TY - UNPB
T1 - Concentration Inequalities for Random Sets
AU - Segal-Halevi, E.
AU - Hassidim, A.
PY - 2016/12/27
Y1 - 2016/12/27
N2 - In a large, possibly infinite population, each subject is colored red with probability p, independently of the others. Then, a finite sub-population is selected, possibly as a function of the coloring. The imbalance in the sub-population is defined as the difference between the number of reds in it and p times its size. This paper presents high-probability upper bounds (tail-bounds) on this imbalance. To present the upper bounds we define the *UI dimension* --- a new measure for the richness of a set-family. We present three simple rules for upper-bounding the UI dimension of a set-family. Our upper bounds on the imbalance in a sub-population depend only on the size of the sub-population and on the UI dimension of its support. We relate our results to known concepts from machine learning, particularly the VC dimension and Rademacher complexity.
AB - In a large, possibly infinite population, each subject is colored red with probability p, independently of the others. Then, a finite sub-population is selected, possibly as a function of the coloring. The imbalance in the sub-population is defined as the difference between the number of reds in it and p times its size. This paper presents high-probability upper bounds (tail-bounds) on this imbalance. To present the upper bounds we define the *UI dimension* --- a new measure for the richness of a set-family. We present three simple rules for upper-bounding the UI dimension of a set-family. Our upper bounds on the imbalance in a sub-population depend only on the size of the sub-population and on the UI dimension of its support. We relate our results to known concepts from machine learning, particularly the VC dimension and Rademacher complexity.
UR - http://scholar.google.com/scholar?num=3&hl=en&lr=&q=allintitle%3A%20Concentration%20Inequalities%20for%20Random%20Sets%2C%20author%3ASegal-Halevi%20OR%20author%3AHassidim&as_ylo=2016&as_yhi=&btnG=Search&as_vis=0
U2 - 10.48550/arXiv.1612.08580
DO - 10.48550/arXiv.1612.08580
M3 - פרסום מוקדם
VL - 8580
T3 - arXiv preprint arXiv:1612.,
BT - Concentration Inequalities for Random Sets
ER -