Related papers: Large margin classifier with graph-based adaptive …
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…
Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…
Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…
Calibration and uncertainty estimation are crucial topics in high-risk environments. We introduce a new diversity regularizer for classification tasks that uses out-of-distribution samples and increases the overall accuracy, calibration and…
Many classification problems involve data instances that are interlinked with each other, such as webpages connected by hyperlinks. Techniques for "collective classification" (CC) often increase accuracy for such data graphs, but usually…
In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…
We discuss the global regularity of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain $\Omega\subset\mathbb R^n$ has a nonnegative mean curvature and prove an optimal…
Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The…
We tackle the problem of Selective Classification where the objective is to achieve the best performance on a predetermined ratio (coverage) of the dataset. Recent state-of-the-art selective methods come with architectural changes either…
Deep neural networks generalize well despite being exceedingly overparameterized and being trained without explicit regularization. This curious phenomenon has inspired extensive research activity in establishing its statistical principles:…
We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…
Selecting hyperparameters for unsupervised learning problems is challenging in general due to the lack of ground truth for validation. Despite the prevalence of this issue in statistics and machine learning, especially in clustering…
Various applications in different fields, such as gene expression analysis or computer vision, suffer from data sets with high-dimensional low-sample-size (HDLSS), which has posed significant challenges for standard statistical and modern…
Hypergraph neural networks have been promising tools for handling learning tasks involving higher-order data, with notable applications in web graphs, such as modeling multi-way hyperlink structures and complex user interactions. Yet, their…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…
We build a solvability theory of elliptic boundary-value problems in normed Sobolev spaces of generalized smoothness for any integrability exponent $p>1$. The smoothness is given by a number parameter and a supplementary function parameter…
Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…
Learning and reasoning over graphs is increasingly done by means of probabilistic models, e.g. exponential random graph models, graph embedding models, and graph neural networks. When graphs are modeling relations between people, however,…