Annals of Mathematical Statistics

By Emanuel Parzen. 1962

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Citations in the corpus

On the convergence properties of a K-step averaging stochastic gradient descent algorithm for nonconvex optimization (2017, background): “The asymptotic optimal convergence rate of SGD was proved by [Chung, 1954] and [Sacks, 1958] to be O(1/N) with twice continuously differentiable and strongly convex objectives.”
A spectral algorithm for learning Hidden Markov Models (2008, methodology): “Thus far, the predominant learning algorithms have been local search heuristics, such as the Baum-Welch / EM algorithm [Baum et al., 1970, Dempster et al., 1977].”
Evolution of broad-line emission from active galactic nuclei (2013, methodology): “Another widely used method is the Mann-Whitney (MW; Mann & Whitney 1947) rank sum test.”
Towards constraining warm dark matter with stellar streams through neural simulation-based inference (2020, methodology): “(11) As a result of Wilks’ theorem (Wilks 1938), we can directly convert the test statistic into a confidence level (CL) under the assumption that the statistic is X2 𝑘 -distributed with 𝑘 degrees of freedom (in function of 𝜗’s dimensionality).”
Generalized Fractal Kinetics in Complex Systems ( Application to Biophysics and Biotechnology) (2006, background): “We first note that c n,α (t) = c(0)[(1 + (n − 1) (t/τ n,α ) α ] − 1 n−1 (23) is related to the Burr XII distribution function (B a,b,c (x) = 1 − (1 + ax b ) −c , x > 0) [28], named by reference to the number it occupies in the main Table of Burr's original paper [29]).”
Scalable detection of statistically significant communities and hierarchies, using message passing for modularity (2014, background): “Scalable detection of statistically significant communities and hierarchies, using message passing for modularity”
Self-Adapted Multi-Task Clustering (2016, background): “j are the probability distributions of cluster i in the target task Xt and cluster j in the source task Xs respectively, D(P ||Q) denotes the Kullback-Leibler divergence [Kullback and Leibler, 1951] between two probability distributions P and Q.”
Efficient Label Contamination Attacks Against Black-Box Learning Models (2017, methodology): “(9) to the upper level problem, which is derived from the Representer Theorem [Kimeldorf and Wahba, 1970]. w = ∑n i=1 αiy ′ iφ(xi) (9)”
LDP-FL: Practical Private Aggregation in Federated Learning with Local Differential Privacy (2020, methodology): “Next, each local model uses Stochastic Gradient Descent (SGD) [Robbins and Monro, 1951] to optimize the distinct local models’ weights in parallel.”
On the Estimation of Confidence Intervals for Binomial Population Proportions in Astronomy: The Simplicity and Superiority of the Bayesian Approach (2010, methodology): “Under the assumptions of this ‘normal approximation’ (also called the ‘Poisson error’) one may employ the standard Wald test criterion, established by Wald & Wolfowitz (1939), to construct a two-sided confidence interval for p. Specifically, at a confidence level of c¼ 1 a one may expect that the…”
Power-Law Distributions in Empirical Data (2007, methodology): “A more refined analysis, using a kind of probabilistic version of L’Hopital’s rule, shows that in fact R adopts a chi-squared distribution as n becomes large (Wilks, 1938).”
6.856 — Randomized Algorithms (2002, unknown): “(b) The following solution owes to [Elias72].”