Related papers: Optimal linear prediction with functional observat…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
The linear minimum mean squared error (LMMSE) estimator is the best linear estimator for a Bayesian linear inverse problem with respect to the mean squared error. It arises as the solution operator to a Tikhonov-type regularized inverse…
A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that…
The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests…
Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing…
Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…
An asymptotic theory is established for linear functionals of the predictive function given by kernel ridge regression, when the reproducing kernel Hilbert space is equivalent to a Sobolev space. The theory covers a wide variety of linear…
We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the maximum absolute deviation of errors. Such problems find application in the solution of…
Estimation of the prediction error of a linear estimation rule is difficult if the data analyst also use data to select a set of variables and construct the estimation rule using only the selected variables. In this work, we propose an…
We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however…
Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…