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The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this…

This paper introduces a novel kernel density estimator (KDE) based on the generalised exponential (GE) distribution, designed specifically for positive continuous data. The proposed GE KDE offers a mathematically tractable form that avoids…

The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…

In many applications, we are given access to noisy modulo samples of a smooth function with the goal being to robustly unwrap the samples, i.e., to estimate the original samples of the function. In a recent work, Cucuringu and Tyagi…

We present a new uncertainty principle for risk-aware statistical estimation, effectively quantifying the inherent trade-off between mean squared error ($\mse$) and risk, the latter measured by the associated average predictive squared…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

Recent work has improved recommendation models remarkably by equipping them with debiasing methods. Due to the unavailability of fully-exposed datasets, most existing approaches resort to randomly-exposed datasets as a proxy for evaluating…

In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The considered class constitutes a natural…

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

If we have an unbiased estimate of some parameter of interest, then its absolute value is positively biased for the absolute value of the parameter. This bias is large when the signal-to-noise ratio (SNR) is small, and it becomes even…

Unbinned likelihood fits aim at maximizing the information one can extract from experimental data, yet their application in realistic statistical analyses is often hindered by the computational cost of profiling systematic uncertainties.…

Generalization is a central problem in Machine Learning. Indeed most prediction methods require careful calibration of hyperparameters usually carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of…

Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…

We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics…

This paper considers mean square error (MSE) analysis for stochastic gradient sampling algorithms applied to underdamped Langevin dynamics under a global convexity assumption. A novel discrete Poisson equation framework is developed to…

In contrast to the standard learning paradigm where all classes can be observed in training data, learning with augmented classes (LAC) tackles the problem where augmented classes unobserved in the training data may emerge in the test…

We introduce Renet, a principled generalization of the Relaxed Lasso to the Elastic Net family of estimators. While, on the one hand, $\ell_1$-regularization is a standard tool for variable selection in high-dimensional regimes and, on the…

Sharpness-Aware Minimization (SAM) has emerged as a powerful method for improving generalization in machine learning models by minimizing the sharpness of the loss landscape. However, despite its success, several important questions…

Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…

The generic risk estimator addresses the problem of denoising images corrupted by additive white noise without placing any restriction on the statistical distribution of the noise. In this paper, we discuss an efficient FPGA implementation…