Related papers: A Locally Adaptive Normal Distribution
This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…
Taking into account that a proper description of disordered systems should focus on distribution functions, the authors develop a powerful numerical scheme for the determination of the probability distribution of the local density of states…
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…
In recent years, with the large-scale expansion of graph data, there has been an increased focus on Riemannian manifold data spaces other than Euclidean space. In particular, the development of hyperbolic spaces has been remarkable, and…
This article introduces a Bayesian neural network estimation method for quantile regression assuming an asymmetric Laplace distribution (ALD) for the response variable. It is shown that the posterior distribution for feedforward neural…
Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics,…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other…
The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and…
Deep neural networks often generalize well despite heavy over-parameterization, challenging classical parameter-based analyses. We study generalization from a representation-centric perspective and analyze how the geometry of learned…
This paper establishes an approximation theorem for randomized neural networks (RaNNs) whose hidden-layer parameters are uniformly sampled from a prescribed bounded domain. Our analysis shows that, for RaNNs of the form $\mathop{\sum}_i W_i…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…
The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift, and it naturally arises from the optimization of two-layer neural networks via (noisy) gradient…
We study a Markovian agent-based model (MABM) in this paper. Each agent is endowed with a local state that changes over time as the agent interacts with its neighbours. The neighbourhood structure is given by a graph. In a recent paper…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…