Related papers: The Stein Effect for Frechet Means
To consider model uncertainty in global Fr\'{e}chet regression and improve density response prediction, we propose a frequentist model averaging method. The weights are chosen by minimizing a cross-validation criterion based on Wasserstein…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is…
Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
Motivated by questions about dense (non-sparse) signals in high-dimensional data analysis, we study the unconditional out-of-sample prediction error (predictive risk) associated with three popular linear estimators for high-dimensional…
Regression trees and random forests are popular and effective non-parametric estimators in practical applications. A recent paper by Athey and Wager shows that the random forest estimate at any point is asymptotically Gaussian; in this…
We establish finite-sample error bounds in expectation for transformed Fr\'echet means in Hadamard spaces under minimal assumptions. Transformed Fr\'echet means provide a unifying framework encompassing classical and robust notions of…
We address the following foundational question: what is the population, and sample, Frechet mean (or median) graph of an ensemble of inhomogeneous Erdos-Renyi random graphs? We prove that if we use the Hamming distance to compute distances…
In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed…
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.…
Importance-weighting is a popular and well-researched technique for dealing with sample selection bias and covariate shift. It has desirable characteristics such as unbiasedness, consistency and low computational complexity. However,…
The consensus problem -- achieving agreement among a network of agents -- is a central theme in both theory and applications. Recently, this problem has been extended from Euclidean spaces to the space of probability measures, where the…
The existence of universal scaling in the vicinity of the jamming transition of sheared granular materials is predicted by a phenomenology. The critical exponents are explicitly determined, which are independent of the spatial dimension.…
This paper revisits an adaptation of the random forest algorithm for Fr\'echet regression, addressing the challenge of regression in the context of random objects in metric spaces. Recognizing the limitations of previous approaches, we…
This paper studies the estimation of smooth functionals $f(\theta)$ of a mean parameter $\theta = \mathbb{E}_P[W]$ for a distribution $P$ on a general Banach space. We propose a cross-fitted estimator based on a single sample splitting and…
The infinite-dimensional Hilbert sphere $S^\infty$ has been widely employed to model density functions and shapes, extending the finite-dimensional counterpart. We consider the Fr\'echet mean as an intrinsic summary of the central tendency…
We study the Stein equation associated with the one-dimensional Gamma distribution, and provide novel bounds, allowing one to effectively deal with test functions supported by the whole real line. We apply our estimates to derive new…
We consider the problem of estimating the missing mass, partition function or evidence and its probability distribution in the case that for each sample point in the discrete sample space its (unnormalized) probability mass is revealed.…
We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…
We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…