Related papers: Adaptive spectral regularizations of high dimensio…

Model regularization requires extensive manual tuning to balance complexity against overfitting. Cross-regularization resolves this tradeoff by directly adapting regularization parameters through validation gradients during training. The…

Deep Neural Networks are well known for efficiently fitting training data, yet experiencing poor generalization capabilities whenever some kind of bias dominates over the actual task labels, resulting in models learning "shortcuts". In…

A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|\beta^\mathsf{T}X)$ and a degenerate $\mathrm{var}(X|\beta^\mathsf{T}X)$…

We consider a real Gaussian process $X$ having a global unknown smoothness $(r_{\scriptscriptstyle 0},\beta_{\scriptscriptstyle 0})$, $r_{\scriptscriptstyle 0}\in \mathds{N}_0$ and $\beta_{\scriptscriptstyle 0} \in]0,1[$, with…

We propose a new space-variant regularization term for variational image restoration based on the assumption that the gradient magnitudes of the target image distribute locally according to a half-Generalized Gaussian distribution. This…

Let y=A\beta+\epsilon, where y is an N\times1 vector of observations, \beta is a p\times1 vector of unknown regression coefficients, A is an N\times p design matrix and \epsilon is a spherically symmetric error term with unknown scale…

Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This in turn can be achieved by variational regularization…

This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…

Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target…

The sample covariance matrix becomes non-invertible in high-dimensional settings, making classical multivariate statistical methods inapplicable. Various regularization techniques address this issue by imposing a structured target matrix to…

Deep learning models, including modern systems like large language models, are well known to offer unreliable estimates of the uncertainty of their decisions. In order to improve the quality of the confidence levels, also known as…

We study the construction and updating of spectral preconditioners for regularized Newton methods and their application to electromagnetic inverse medium scattering problems. Moreover, we show how a Lepski\u{i}-type stopping rule can be…

Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal $f: \mathbb{R} \to \mathbb{R}$ from many observations that have been randomly…

We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of possibly unknown dimension $d < D$ under a reach condition. We study nonparametric kernel…

We consider the problem of estimating a rank-one nonsymmetric matrix under additive white Gaussian noise. The matrix to estimate can be written as the outer product of two vectors and we look at the special case in which both vectors are…

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

We study the matrix denoising problem of estimating the singular vectors of a rank-$1$ signal corrupted by noise with both column and row correlations. Existing works are either unable to pinpoint the exact asymptotic estimation error or,…

Tikhonov regularization is studied in the case of linear pseudodifferential operator as the forward map and additive white Gaussian noise as the measurement error. The measurement model for an unknown function $u(x)$ is \begin{eqnarray*}…