Related papers: LARGE: A Locally Adaptive Regularization Approach …
We address the task of identifying densely connected subsets of multivariate Gaussian random variables within a graphical model framework. We propose two novel estimators based on the Ordered Weighted $\ell_1$ (OWL) norm: 1) The Graphical…
Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…
The "least absolute shrinkage and selection operator" (Lasso) method has been adapted recently for networkstructured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal…
The sparse precision matrix plays an essential role in the Gaussian graphical model since a zero off-diagonal element indicates conditional independence of the corresponding two variables given others. In the Gaussian graphical model, many…
In many applications, data come with a natural ordering. This ordering can often induce local dependence among nearby variables. However, in complex data, the width of this dependence may vary, making simple assumptions such as a constant…
Geometry-aware optimization algorithms, such as Muon, have achieved remarkable success in training deep neural networks (DNNs). These methods leverage the underlying geometry of DNNs by selecting appropriate norms for different layers and…
Graph-based tasks in the zero-shot setting remain a significant challenge due to data scarcity and the inability of traditional Graph Neural Networks (GNNs) to generalize to unseen domains or label spaces. While recent advancements have…
Many traditional signal recovery approaches can behave well basing on the penalized likelihood. However, they have to meet with the difficulty in the selection of hyperparameters or tuning parameters in the penalties. In this article, we…
Simultaneous feature selection and non-linear function estimation is challenging in modeling, especially in high-dimensional settings where the number of variables exceeds the available sample size. In this article, we investigate the…
We propose a new approach for the modeling large datasets of nonstationary spatial processes that combines a latent low rank process and a sparse covariance model. The low rank component coefficients are endowed with a flexible graphical…
In this paper, we study norm-based regularization methods for neural networks. We compare existing penalization approaches and introduce two regularization strategies that extend classical ridge- and lasso-type penalties to neural network…
Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…
Heterogeneous graph neural networks (HGNNs) have been widely applied in heterogeneous information network tasks, while most HGNNs suffer from poor scalability or weak representation when they are applied to large-scale heterogeneous graphs.…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models. For undirected graphical models, two main explicit…
Graph Neural Networks (GNNs) have evolved to understand graph structures through recursive exchanges and aggregations among nodes. To enhance robustness, self-supervised learning (SSL) has become a vital tool for data augmentation.…
We apply the network Lasso to solve binary classification and clustering problems for network-structured data. To this end, we generalize ordinary logistic regression to non-Euclidean data with an intrinsic network structure. The resulting…
We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and…
Graph contrastive learning (GCL) learns node and graph representations by contrasting multiple views of the same graph. Existing methods typically rely on fixed, handcrafted views-usually a local and a global perspective, which limits their…
This paper generalizes the proportionate-type adaptive algorithm to the graph signal processing and proposes two proportionate-type adaptive graph signal recovery algorithms. The gain matrix of the proportionate algorithm leads to faster…