相关论文: A Tribute to Charles Stein
The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. We use this approach to prove a non-smooth function distance for multivariate normal approximation for standardized…
The Frechet mean is a useful description of location for a probability distribution on a metric space that is not necessarily a vector space. This article considers simultaneous estimation of multiple Frechet means from a decision-theoretic…
For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type…
Large-scale kernel approximation is an important problem in machine learning research. Approaches using random Fourier features have become increasingly popular [Rahimi and Recht, 2007], where kernel approximation is treated as empirical…
In this paper we derive the optimal linear shrinkage estimator for the high-dimensional mean vector using random matrix theory. The results are obtained under the assumption that both the dimension $p$ and the sample size $n$ tend to…
Stein's unbiased risk estimate (SURE) gives an unbiased estimate of the $\ell_2$ risk of any estimator of the mean of a Gaussian random vector. We focus here on the case when the estimator minimizes a quadratic loss term plus a convex…
Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target.…
Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any nonnegative random vector. Theorem 1.2 requires multivariate size bias…
Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and…
To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…
We extend Stein's lemma for averages that explicitly contain the Gaussian random variable at a power. We present two proofs for this extension of Stein's lemma, with the first being a rigorous proof by mathematical induction. The…
We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined…
In the framework of matrix valued observables with low rank means, Stein's unbiased risk estimate (SURE) can be useful for risk estimation and for tuning the amount of shrinkage towards low rank matrices. This was demonstrated by Cand\`es…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…
Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an expectation of a test function along the sample path of a…
This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…
The estimation of the mean matrix of the multivariate normal distribution is addressed in the high dimensional setting. Efron-Morris-type linear shrinkage estimators based on ridge estimators for the precision matrix instead of the…
Insights into complex, high-dimensional data can be obtained by discovering features of the data that match or do not match a model of interest. To formalize this task, we introduce the "data selection" problem: finding a lower-dimensional…
The paper presents a general introduction to the astonishing method for deriving probability approximations that was invented by Charles Stein around 50 years ago.