Related papers: Noiseless regularisation by noise
Algorithms which minimize the averaged loss have been widely designed for dealing with noisy labels. Intuitively, when there is a finite training sample, penalizing the variance of losses will improve the stability and generalization of the…
In this paper we prove strong well-posedness for a system of stochastic differential equations driven by a degenerate diffusion satisfying a weak-type H\"ormander condition, assuming H\"older regularity assumptions on the drift coefficient.…
We study the surface quasi-geostrophic equation driven by a generic additive noise process $W$. By means of convex integration techniques, we establish existence of weak solutions whenever the stochastic convolution $z$ associated with $W$…
We investigate a McKean-Vlasov stochastic differential equation with an additive common noise and in which the interaction is through the conditional expectation. We show that, in the presence of an additive individual noise, existence and…
Despite the strong focus of regularization on ill-posed problems, the general construction of such methods has not been fully explored. Moreover, many previous studies cannot be clearly adapted to handle more complex scenarios, albeit the…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
Deep neural networks achieve high prediction accuracy when the train and test distributions coincide. In practice though, various types of corruptions occur which deviate from this setup and cause severe performance degradations. Few…
We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
This paper studies linear overparameterized models in economic forecasting and highlights that including noise variables (regressors with no predictive power) regularizes the estimator. We consider a setting where both the outcome variable…
Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is…
We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient…
Pulse stabilization of cycles with Prediction-Based Control including noise and stochastic stabilization of maps with multiple equilibrium points is analyzed for continuous but, generally, non-smooth maps. Sufficient conditions of global…
We study regularization of ill-posed equations involving multiplication operators when the multiplier function is positive almost everywhere and zero is an accumulation point of the range of this function. Such equations naturally arise…
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…
We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…
Multiplicative noise arises in inverse problems when, for example, uncertainty on measurements is proportional to the size of the measurement itself. The likelihood that arises is hence more complicated than that from additive noise. We…
In this paper, we study a mixed variational problem subject to perturbations, where the noise term is modelled by means of a bilinear form that has to be understood to be "small" in some sense. Indeed, we consider a family of such problems…
We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first…
We study a regularization by noise phenomenon for the continuous parabolic Anderson model with a potential shifted along paths of fractional Brownian motion. We demonstrate that provided the Hurst parameter is chosen sufficiently small,…