Related papers: Randomized weakly admissible meshes
Most networks encountered in nature, society, and technology have weighted edges, representing the strength of the interaction/association between their vertices. Randomizing the structure of a network is a classic procedure used to…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
A large class of spatial models contains intractable normalizing functions, such as spatial lattice models, interaction spatial point processes, and social network models. Bayesian inference for such models is challenging since the…
This paper presents a minimalist neural regression network as an aggregate of independent identical regression blocks that are trained simultaneously. Moreover, it introduces a new multiplicative parameter, shared by all the neural units of…
Anomaly detection (AD) is a crucial task in machine learning with various applications, such as detecting emerging diseases, identifying financial frauds, and detecting fake news. However, obtaining complete, accurate, and precise labels…
In medical imaging, obtaining large amounts of labeled data is often a hurdle, because annotations and pathologies are scarce. Anomaly detection is a method that is capable of detecting unseen abnormal data while only being trained on…
Polynomial meshes (called sometimes "norming sets") allow us to estimate the supremum norm of polynomials on a fixed compact set by the norm on its discrete subset. We give a general construction of polynomial weakly admissible meshes on…
The Adversarially Learned Mixture Model (AMM) is a generative model for unsupervised or semi-supervised data clustering. The AMM is the first adversarially optimized method to model the conditional dependence between inferred continuous and…
In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains represent a cross-section of a three-dimensional system…
Neural networks with random hidden nodes have gained increasing interest from researchers and practical applications. This is due to their unique features such as very fast training and universal approximation property. In these networks…
Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical…
Classical results on the statistical complexity of linear models have commonly identified the norm of the weights $\|w\|$ as a fundamental capacity measure. Generalizations of this measure to the setting of deep networks have been varied,…
Weak amenability of discrete groups was introduced by Haagerup and co-authors in the 1980's. It is an approximation property known to be stable under direct products and free products. In this paper we show that graph products of weakly…
The Segment Anything Model (SAM) is a foundation model for general image segmentation. Although it exhibits impressive performance predominantly on natural images, understanding its robustness against various image perturbations and domains…
Randomized smoothing is a defensive technique to achieve enhanced robustness against adversarial examples which are small input perturbations that degrade the performance of neural network models. Conventional randomized smoothing adds…
Generating realistic graph-structured data is challenging due to discrete structures, variable sizes, and class-specific connectivity patterns that resist conventional generative modelling. While recent graph generation methods employ…
In this paper, we introduce generalized dichotomies for nonautonomous random linear dynamical systems acting on arbitrary Banach spaces, and obtain their complete characterization in terms of an appropriate admissibility property. These…
In conducting non-linear dimensionality reduction and feature learning, it is common to suppose that the data lie near a lower-dimensional manifold. A class of model-based approaches for such problems includes latent variables in an unknown…
Feedforward neural networks with random hidden nodes suffer from a problem with the generation of random weights and biases as these are difficult to set optimally to obtain a good projection space. Typically, random parameters are drawn…
Randomly censored survival data are frequently encountered in applied sciences including biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to…