Chernoff bound(切诺夫界)
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马尔科夫不等式:
X为非负随机变量,E(X)存在,对任意t>0,有 Pr[x>t]<=E[X]/t
chernoff 界:
X1,X2,...,Xn为独立泊松事件,Pr[Xi=1]=pi,X=sigma(i=0,n)Xi,u=E[X],对任意的0<=&<1,有
下界 Pr[X<(1-&)u]<(e-&/(1-&)(1-&))u<e(-u&2/2)
上界 Pr[X>(1+&)u]<=(e&/(1+&)(1+&)u)
X1,X2,...,Xn为离散独立随机变量,E{Xi}=0 |Xi|<=1,i=1,2,...,n,X=sigma(i=1,n)Xi, D{X}=&2
Pr[|X|>=t]<=2e-u^2/4
Pr[X>=t]<=e-u^2/4
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