ﻻ يوجد ملخص باللغة العربية
In massive data analysis, training and testing data often come from very different sources, and their probability distributions are not necessarily identical. A feature example is nonparametric classification in posterior drift model where the conditional distributions of the label given the covariates are possibly different. In this paper, we derive minimax rate of the excess risk for nonparametric classification in posterior drift model in the setting that both training and testing data have smooth distributions, extending a recent work by Cai and Wei (2019) who only impose smoothness condition on the distribution of testing data. The minimax rate demonstrates a phase transition characterized by the mutual relationship between the smoothness orders of the training and testing data distributions. We also propose a computationally efficient and data-driven nearest neighbor classifier which achieves the minimax excess risk (up to a logarithm factor). Simulation studies and a real-world application are conducted to demonstrate our approach.
Statistical inference for sparse covariance matrices is crucial to reveal dependence structure of large multivariate data sets, but lacks scalable and theoretically supported Bayesian methods. In this paper, we propose beta-mixture shrinkage prior, c
Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior computations,
Last decade witnesses significant methodological and theoretical advances in estimating large precision matrices. In particular, there are scientific applications such as longitudinal data, meteorology and spectroscopy in which the ordering of the va
From an optimizers perspective, achieving the global optimum for a general nonconvex problem is often provably NP-hard using the classical worst-case analysis. In the case of Coxs proportional hazards model, by taking its statistical model structures
We develop new approaches in multi-class settings for constructing proper scoring rules and hinge-like losses and establishing corresponding regret bounds with respect to the zero-one or cost-weighted classification loss. Our construction of losses i