Distribution Inequalities for the Binomial Law

By E. Slud. 1977

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Citations in the corpus

A Model of Inductive Bias Learning (2000, background): “) 6 = 1 2 Pr N m + 1 2 Pr N ( ) < m = > 1 2 Pr N ( ) m = which is half the probability that a binomial ( m; 1 = 2 = 2) random variable is at least m= . By Slud’s inequality (Slud, 1977), Pr ( f ( ) 6 = > 1 2 Pr ! Z s m 2 1 2 where Z is normal (0 ; 1) . Tate’s inequality (Tate, 1”
Comparing human-centric and robot-centric sampling for robot deep learning from demonstrations (2016, methodology): “where we have used Slud’s inequality [22] to lower bound a binomial tail by a Gaussian tail.”
Sampling best response dynamics and deterministic equilibrium selection (2015, background): “5 (Slud (1977)).”
Understanding Machine Learning: From Theory to Algorithms (2014, background): “Slud’s inequality (Slud 1977) tells us that P[X ≥ m/2] is lower bounded by the probability that a normal variable will be greater than or equal to √ m 2/(1− 2).”
A No-Free-Lunch Theorem for MultiTask Learning (2020, methodology): “ny value of n N^ P;N^ Q o ; in (20) we used the fact that for any p2[0;1], we have p1fEg= p p1fEcgp 1fEcg. The following is a known counterpart of Chernoff bounds, following from Slud’s inequalities [Slu77] for Binomials. Lemma 3 (Anticoncentration (Slud’s Inequality)). Let fX ig i2[m] denote i.i.d.”
On the inductive bias of dropout (2014, background): “Proof: If Z is a standard normal random variable and R is a binomial (`, p) random variable with p ≤ 1/2, then for `(1− p) ≤ j ≤ `p, Slud’s inequality (Slud, 1977) gives”
Prediction, learning, and games (2006, background): “5 Slud’s Inequality Here we recall, without proof, an inequality due to Slud [272] between binomial tails and their approximating normals.”
Importance weighted active learning (2008, background): “Lemma 5 (Slud (1977)) Let B be a Binomial ( n, p ) random variable with p ≤ 1 / 2 , and let Z be a standard normal.”
Random Forest for the Contextual Bandit Problem (2015, unknown): “We have: Slud’s inequality (see Slud (1977)) states that when p ≤ 1 / 2 and t ∗ k ≤ x ≤ t ∗ k .”
Near-Bayesian exploration in polynomial time (2009, methodology): “Proof of Theorem 2 We make use of the following inequality, due to Slud (1977), which gives a lower bound on the probability of large deviations from the mean in a binomial distribution.”