Related papers: Random Smoothing Regularization in Kernel Gradient…
Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…
To improve the off-sample generalization of classical procedures minimizing the empirical risk under potentially heavy-tailed data, new robust learning algorithms have been proposed in recent years, with generalized median-of-means…
Trustworthy machine learning necessitates meticulous regulation of model reliance on non-robust features. We propose a framework to delineate and regulate such features by attributing model predictions to the input. Within our approach,…
Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…
The strength of machine learning models stems from their ability to learn complex function approximations from data; however, this strength also makes training deep neural networks challenging. Notably, the complex models tend to memorize…
We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems. We model the regularization function as the composition of the $l_{2,1}$ norm and a smooth but nonconvex feature mapping…
Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption…
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
Smoothness is a key inductive bias in machine learning and is closely related to generalization. Existing smoothness-inducing methods typically rely either on explicit gradient regularization, which often incurs substantial computational…
We propose Sobolev-regularized Maximum Mean Discrepancy (SrMMD) gradient flow, a regularized variant of maximum mean discrepancy (MMD) gradient flow based on a gradient penalty on the witness function. The proposed regularization mitigates…
This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with non-homogeneous smoothness across the domain. Two challenging issues that arise in this context are the evaluation…
Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…
We propose a new method for feature learning and function estimation in supervised learning via regularised empirical risk minimisation. Our approach considers functions as expectations of Sobolev functions over all possible one-dimensional…
Super-resolution and denoising are ill-posed yet fundamental image restoration tasks. In blind settings, the degradation kernel or the noise level are unknown. This makes restoration even more challenging, notably for learning-based…
It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and…
The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…