相关论文: Normal-bundle Bootstrap

In this paper, we propose new nonparametric approach to network inference that may be viewed as a fusion of block sampling procedures for temporally and spatially dependent processes with the classical network methodology. We develop…

Efficient and accurate prediction of Multiphysics evolution across diverse cell geometries is fundamental to the design, management and safety of lithium-ion batteries. However, existing computational frameworks struggle to capture the…

A natural way to quantify uncertainties in Gaussian mixture models (GMMs) is through Bayesian methods. That said, sampling from the joint posterior distribution of GMMs via standard Markov chain Monte Carlo (MCMC) imposes several…

Standard gradient descent methods yield point estimates with no measure of confidence. This limitation is acute in overparameterized and low-data regimes, where models have many parameters relative to available data and can easily overfit.…

A structure-preserving kernel ridge regression method is presented that allows the recovery of globally defined, potentially high-dimensional, and nonlinear Hamiltonian functions on Poisson manifolds out of datasets made of noisy…

For more than $50$ years the {\it Mean Measure of Divergence} (MMD) has been one of the most prominent tools used in anthropology for the study of non-metric traits. However, one of the problems, in anthropology including palaeoanthropology…

Bootstrap techniques (also called resampling computation techniques) have introduced new advances in modeling and model evaluation. Using resampling methods to construct a series of new samples which are based on the original data set,…

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

In this paper we propose a Bayesian method for estimating architectural parameters of neural networks, namely layer size and network depth. We do this by learning concrete distributions over these parameters. Our results show that regular…

Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified…

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

Non-probability sampling, for example in the form of online panels, has become a fast and cheap method to collect data. While reliable inference tools are available for classical probability samples, non-probability samples can yield…

We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…

In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we…

We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the…

Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. However, their invertibility constraint imposes limitations on data distributions that reside on…

The bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large datasets, the computation of bootstrap-based quantities can be prohibitively demanding. As an alternative, we…

Data augmentation for deep learning benefits model training, image transformation, medical imaging analysis and many other fields. Many existing methods generate new samples from a parametric distribution, like the Gaussian, with little…

We develop a new approach for estimating the risk of an arbitrary estimator of the mean vector in the classical normal means problem. The key idea is to generate two auxiliary data vectors, by adding carefully constructed normal noise…

This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used with success for analyzing complex engineering systems. The…