Children learn effortlessly by example and exhibit a remarkable capacity of generalization. The field of machine learning, on the other hand, stumbles along clumsily in search of algorithms and methods, but nothing available today comes even close to an average two-year-old toddler. So, modestly, we present some results on one of the main paradigms in machine learningnearest neighbor methods. Rummaging through old data for the closest match seems like a sensible thing to do, and that primitive idea can be formalized and made rigorous. In the field of nonparametric statistics, where one is concerned with the estimation of densities, distribution functions, regression functions, and functionals, the nearest neighbor family of methods was in the limelight from the very beginning and has achieved some level of maturity.

Community detection is a fundamental problem in social network analysis. It is desirable to have fast community detection algorithm that applicable to large-scale networks we see today and also have reliable community detection results. This paper proposes Spectral Clustering On Ratios-of-eigenvectors (SCORE) as such an algorithm. The algorithm is fast in computation, is applicable to real large networks, and is competitive in real data performance when applied to some representative data sets in this area. We study the algorithm with the Degree-Corrected Block Model (DCBM). Compare to most works in this area that focus on the much narrower Block Models, our analysis is more difficult and requires new techniques. The novelty of our algorithm lies in that it uses entry-wise ratios between leading eigenvectors of the adjacency to reduce a seemingly hard problem to a problem that is very much tractable.

A practical and accessible introduction to the bootstrap methodnewly revised and updated Over the past decade, the application of bootstrap methods to new areas of study has expanded, resulting in theoretical and applied advances across various fields. Bootstrap Methods, Second Edition is a highly approachable guide to the multidisciplinary, real-world uses of bootstrapping and is ideal for readers who have a professional interest in its methods, but are without an advanced background in mathematics. Updated to reflect current techniques and the most up-to-date work on the topic, the Second Edition features: The addition of a second, extended bibliography devoted solely to publications from 19992007, which is a valuable collection of references on the latest research in the field A discussion of the new areas of applicability for bootstrap methods, including use in the pharmaceutical industry for estimating individual and population bioequivalence in clinical trials A revised chapter on when and why bootstrap fails and remedies for overcoming these drawbacks Added coverage on regression, censored data applications, P-value adjustment, ratio estimators, and missing data New examples and illustrations as well as extensive historical notes at the end of each chapter With a strong focus on application, detailed explanations of methodology, and complete coverage of modern developments in the field, Bootstrap Methods, Second Edition is an indispensable reference for applied statisticians, engineers, scientists, clinicians, and other practitioners who regularly use statistical methods in research. It is also suitable as a supplementary text

Using locally polynomial regression, we develop nonparametric estimators for the conditional density function and its square root, and their partial derivatives. Two measures of sensitivity to initial conditions in nonlinear stochastic dynamic systems are proposed, one of which relates Fisher information with initial-value sensitivity in dynamical systems. We propose estimators for these, and show asymptotic normality for one of them. We further propose a simple method for choosing the bandwidth. The methods are illustrated by simulation of two well-known models in dynamical systems.

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication cost can prohibit the computation of PCA in a central location and distributed algorithms for PCA are thus needed. This paper proposes and studies a distributed PCA algorithm: each node machine computes the top K eigenvectors and transmits them to the central server; the central server then aggregates the information from all the node machines and conducts a PCA based on the aggregated information. We investigate the bias and variance for the resulting distributed estimator of the top K eigenvectors. In particular, we show that for distributions with symmetric innovation, the empirical top eigenspaces are unbiased, and hence the distributed PCA is unbiased. We derive the