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1 Proof of Theorem 1 The first assertion is a direct consequence of Lemma 3.3 and Corollary 4.1 of [2]. The second
 

Summary: 1 Proof of Theorem 1
The first assertion is a direct consequence of Lemma 3.3 and Corollary 4.1 of [2]. The second
assertion is based on an Assouad's type lower bound ([1, Inequality (8.19)]. Let y2 = 2a - y1 and
~m = log2 |G| . We use the notation introduced in [1, Section 8.1]. We consider a ~m, 1
n+1 1
~m , 1 -
hypercube of probability distributions with h1 argminyY y1
(y) and h2 argminyY y2
(y). We
obtain
ER(^g) - min
gG
R(g) log2 |G|
n+1 1 dI 1 - 1
n+1 1
log2 |G|
n
log2 |G|
n+1 1 dIe-1
,

  

Source: Audibert, Jean-Yves - Département d'Informatique, École Normale Supérieure

 

Collections: Computer Technologies and Information Sciences