相关论文: Statistical Learnability of Generalized Additive M…

Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools…

Traditional statistical learning theory relies on the assumption that data are identically and independently distributed (i.i.d.). However, this assumption often does not hold in many real-life applications. In this survey, we explore…

We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…

In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with $L^{2}$ data fitting term. We examine some properties of this model and we calculate exact solutions using simple…

In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings…

Identifying the discontinuous diffusion coefficient in an elliptic equation with observation data of the gradient of the solution is an important nonlinear and ill-posed inverse problem. Models with total variational (TV) regularization…

Standard autoregressive seq2seq models are easily trained by max-likelihood, but tend to show poor results under small-data conditions. We introduce a class of seq2seq models, GAMs (Global Autoregressive Models), which combine an…

We propose two new variational models aimed to outperform the popular total variation (TV) model for image restoration with L$_2$ and L$_1$ fidelity terms. In particular, we introduce a space-variant generalization of the TV regularizer,…

Recently, non-convex regularisation models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies $\phi$ in the total variation type functional…

Generalized additive models (GAMs) have long been a powerful white-box tool for the intelligible analysis of tabular data, revealing the influence of each feature on the model predictions. Despite the success of neural networks (NNs) in…

We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting,…

The Generalized Linear Model (GLM) for the Gamma distribution (glmGamma) is widely used in modeling continuous, non-negative and positive-skewed data, such as insurance claims and survival data. However, model selection for GLM depends on…

Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for…

Existing Rademacher complexity bounds for neural networks rely only on norm control of the weight matrices and depend exponentially on depth via a product of the matrix norms. Lower bounds show that this exponential dependence on depth is…

Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of…

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved…

We introduce Generalized Integrated Gradients (GIG), a formal extension of the Integrated Gradients (IG) (Sundararajan et al., 2017) method for attributing credit to the input variables of a predictive model. GIG improves IG by explaining a…

We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…

An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values,…

Invariant risk minimization is an important general machine learning framework that has recently been interpreted as a total variation model (IRM-TV). However, how to improve out-of-distribution (OOD) generalization in the IRM-TV setting…