Related papers: Adaptive Regularization of B-Spline Models for Sci…
Recently, a variety of regularization techniques have been widely applied in deep neural networks, such as dropout, batch normalization, data augmentation, and so on. These methods mainly focus on the regularization of weight parameters to…
We address the problem of constructing varying-coefficient models based on basis expansions along with the technique of regularization. A crucial point in our modeling procedure is the selection of smoothing parameters in the regularization…
Most image smoothing filters in the literature assume a piecewise constant model of smoothed output images. However, the piecewise constant model assumption can cause artifacts such as gradient reversals in applications such as image detail…
In Astronomy, Survival Analysis and Epidemiology, among many other fields, doubly truncated data often appear. Double truncation generally induces a sampling bias, so ordinary estimators may be inconsistent. In this paper, smoothing spline…
Data augmentation has been proven to be an effective technique for developing machine learning models that are robust to known classes of distributional shifts (e.g., rotations of images), and alignment regularization is a technique often…
Locally refined spline surfaces (LRB) is a representation well suited for scattered data approximation. When a data set has local details in some areas and is largely smooth in other, LR B-splines allow the spatial distribution of degrees…
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…
Image segmentation is to extract meaningful objects from a given image. For degraded images due to occlusions, obscurities or noises, the accuracy of the segmentation result can be severely affected. To alleviate this problem, prior…
One-class anomaly detection aims to detect objects that do not belong to a predefined normal class. In practice training data lack those anomalous samples; hence state-of-the-art methods are trained to discriminate between normal and…
Surface-based data is commonly observed in diverse practical applications spanning various fields. In this paper, we introduce a novel nonparametric method to discover the underlying signals from data distributed on complex surface-based…
Data assimilation combines information from physical observations and numerical simulation results to obtain better estimates of the state and parameters of a physical system. A wide class of physical systems of interest have solutions that…
We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…
One classical approach to regularize color is to tream them as two dimensional surfaces embedded in a five dimensional spatial-chromatic space. In this case, a natural regularization term arises as the image surface area. Choosing the…
The paper discusses regularization properties of artificial data for deep learning. Artificial datasets allow to train neural networks in the case of a real data shortage. It is demonstrated that the artificial data generation process,…
We derive a divergence formula for a group of regularization methods with an L2 constraint. The formula is useful for regularization parameter selection, because it provides an unbiased estimate for the number of degrees of freedom. We…
We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…