Related papers: Statistical Learnability of Generalized Additive M…
Generalized additive models (GAM) have been successfully applied to high dimensional data analysis. However, most existing methods cannot simultaneously estimate the link function, the component functions and the variable interaction. To…
We address the component-based regularisation of a multivariate Generalized Linear Mixed Model (GLMM). A set of random responses Y is modelled by a GLMM, using a set X of explanatory variables, a set T of additional covariates, and random…
While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or…
Over the last decades, the total variation (TV) evolved to one of the most broadly-used regularisation functionals for inverse problems, in particular for imaging applications. When first introduced as a regulariser, higher-order…
We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in $\R^3$. The normal vector is considered as a manifold-valued function, taking values on…
Generalization is the ability of a model to predict on unseen domains and is a fundamental task in machine learning. Several generalization bounds, both theoretical and empirical have been proposed but they do not provide tight bounds .In…
In this paper, we propose Total Variation Regularized Tensor-on-scalar Regression(TVTR), a novel method for estimating the association between a tensor outcome (a one dimensional or multidimensional array) and scalar predictors. While the…
Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…
The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is…
Generalized additive models (GAMs) are a widely used class of models of interest to statisticians as they provide a flexible way to design interpretable models of data beyond linear models. We here propose a scalable and well-calibrated…
Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non-Gaussian responses including binary and count data. In this paper, a new likelihood approach for fitting…
Global average pooling (GAP) is a popular component in deep metric learning (DML) for aggregating features. Its effectiveness is often attributed to treating each feature vector as a distinct semantic entity and GAP as a combination of…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…
Unfolding networks have shown promising results in the Compressed Sensing (CS) field. Yet, the investigation of their generalization ability is still in its infancy. In this paper, we perform a generalization analysis of a state-of-the-art…
We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve…
We introduce GAMSEL (Generalized Additive Model Selection), a penalized likelihood approach for fitting sparse generalized additive models in high dimension. Our method interpolates between null, linear and additive models by allowing the…
Invariant risk minimization (IRM) is an arising approach to generalize invariant features to different environments in machine learning. While most related works focus on new IRM settings or new application scenarios, the mathematical…
We investigate the generalizability of learned binary relations: functions that map pairs of instances to a logical indicator. This problem has application in numerous areas of machine learning, such as ranking, entity resolution and link…
The ability of likelihood-based probabilistic models to generalize to unseen data is central to many machine learning applications such as lossless compression. In this work, we study the generalization of a popular class of probabilistic…