Related papers: Optimal rates of estimation for multi-reference al…
We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…
This paper focuses on $\alpha$-divergence minimisation methods for Variational Inference. More precisely, we are interested in algorithms optimising the mixture weights of any given mixture model, without any information on the underlying…
This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
We study the problem of estimating piecewise monotone vectors. This problem can be seen as a generalization of the isotonic regression that allows a small number of order-violating changepoints. We focus mainly on the performance of the…
In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…
This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…
Object pose estimation is a long-standing problem in computer vision. Recently, attention-based vision transformer models have achieved state-of-the-art results in many computer vision applications. Exploiting the permutation-invariant…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
In the multidimensional setting, we consider the errors-in-variables model. We aim at estimating the unknown nonparametric multivariate regression function with errors in the covariates. We devise an adaptive estimator based on projection…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…
We provide a theoretical treatment of over-specified Gaussian mixtures of experts with covariate-free gating networks. We establish the convergence rates of the maximum likelihood estimation (MLE) for these models. Our proof technique is…
In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…
Straightforward methods for adapting the familiar chi^2 statistic to histograms of discrete events and other Poisson distributed data generally yield biased estimates of the parameters of a model. The bias can be important even when the…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
In this paper, we extend the Beta divergence family to multivariate power spectral densities. Similarly to the scalar case, we show that it smoothly connects the multivariate Kullback-Leibler divergence with the multivariate Itakura-Saito…
We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x-ray spectrum that can accurately model the x-ray transmission curves and reflects a realistic shape of the typical energy…
This paper studies the interpretability of neural network features from a Bayesian Gaussian view, where optimizing a cost is reaching a probabilistic bound; learning a model approximates a density that makes the bound tight and the cost…