Related papers: Adaptive spectral regularizations of high dimensio…
The support vector machine (SVM) is a widely used machine learning tool for classification based on statistical learning theory. Given a set of training data, the SVM finds a hyperplane that separates two different classes of data points by…
In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile.…
This paper presents a Bayesian algorithm for linear spectral unmixing of hyperspectral images that accounts for anomalies present in the data. The model proposed assumes that the pixel reflectances are linear mixtures of unknown endmembers,…
In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
In this paper, we consider the problem of signal recovery from 1-bit noisy measurements. We present an efficient method to obtain an estimation of the signal of interest when the measurements are corrupted by white or colored noise. To the…
We develop a flexible framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple bootstrap algorithm. Effectively, our procedure seeks an autoencoding basis for the observed…
In this paper, we develop a novel regularization method for deep neural networks by penalizing the trace of Hessian. This regularizer is motivated by a recent guarantee bound of the generalization error. We explain its benefits in finding…
We consider a semiparametric convolution model. We observe random variables having a distribution given by the convolution of some unknown density $f$ and some partially known noise density $g$. In this work, $g$ is assumed exponentially…
An accurate and substantial dataset is essential for training a reliable and well-performing model. However, even manually annotated datasets contain label errors, not to mention automatically labeled ones. Previous methods for label…
Across many disciplines from neuroscience and genomics to machine learning, atmospheric science and finance, the problems of denoising large data matrices to recover signals obscured by noise, and of estimating the structure of these…
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…
This paper deals with model order selection in context of correlated noise. More precisely, one considers sources embedded in an additive Complex Elliptically Symmetric (CES) noise, with unknown parameters. The main difficultly for…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
In this work, we are trying to extent the existing photometric redshift regression models from modeling pure photometric data back to the spectra themselves. To that end, we developed a PCA that is capable of describing the input…
The consideration of predictive uncertainty in medical imaging with deep learning is of utmost importance. We apply estimation of both aleatoric and epistemic uncertainty by variational Bayesian inference with Monte Carlo dropout to…
We study higher order approximations in the renormalization group approach to matrix models. We use constraint equations on the free energy resulting from a freedom of field redefinitionsand obtain the effective beta function for a single…
In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For…
This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…