Related papers: The $S$-diagnostic -- an a posteriori error assess…
We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and…
Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…
Semi-supervised medical image segmentation (SSMIS) has been demonstrated the potential to mitigate the issue of limited medical labeled data. However, confirmation and cognitive biases may affect the prevalent teacher-student based SSMIS…
In this paper we study convergence estimates for a multigrid algorithm with smoothers of successive subspace correction (SSC) type, applied to symmetric elliptic PDEs. First, we revisit a general convergence analysis on a class of multigrid…
This paper introduces a new recovery-based a posteriori error estimator for the lowest order Nedelec finite element approximation to the H(curl) interface problem. The error estimator is analyzed by establishing both the reliability and the…
We present a Linearized Coupled Cluster (LCC) correction based on an Antisymmetric Product of 1 reference orbital Geminals (AP1roG) reference state. In our LCC ansatz, the cluster operator is restricted to double and to single and double…
In-flight sensor fault diagnosis and recursive combination of residual signals via the Dempster-Shafer (DS) theory have been considered in this study. In particular, a novel evidence-based combination rule of residual errors as a function…
In many applications of Bayesian clustering, posterior sampling on the discrete state space of cluster allocations is achieved via Markov chain Monte Carlo (MCMC) techniques. As it is typically challenging to design transition kernels to…
In this paper, we evaluate the accuracy of the Hermitian form of the downfolding procedure utilizing the double unitary coupled cluster Ansatz (DUCC) on the H6 and H8 benchmark systems. The computational infrastructure employs the…
Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential…
Singleton mentions, i.e.~entities mentioned only once in a text, are important to how humans understand discourse from a theoretical perspective. However previous attempts to incorporate their detection in end-to-end neural coreference…
Compared to the classical Lanczos algorithm, the $s$-step Lanczos variant has the potential to improve performance by asymptotically decreasing the synchronization cost per iteration. However, this comes at a cost. Despite being…
We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: Computers \& Mathematics with Applications. \textbf{91}, 192-201 (2021)] and derive new a posteriori error estimates for H(curl)-elliptic…
In semantic segmentation, even state-of-the-art deep learning models fall short of the performance required in certain high-stakes applications such as medical image analysis. In these cases, performance can be improved by allowing a model…
In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
Correspondence-based statistical shape modeling (SSM) stands as a powerful technology for morphometric analysis in clinical research. SSM facilitates population-level characterization and quantification of anatomical shapes such as bones…
Unsupervised anomaly detection (AD) is a fundamental problem in machine learning and statistics. A popular approach to unsupervised AD is clustering-based detection. However, this method lacks the ability to guarantee the reliability of the…
We present a novel confidence refinement scheme that enhances pseudo labels in semi-supervised semantic segmentation. Unlike existing methods, which filter pixels with low-confidence predictions in isolation, our approach leverages the…
Heterogeneous data, which encompass both numerical financial variables and textual records, present substantial challenges for credit monitoring. To address this issue, we propose Advanced Spectral Clustering (ASC), a method that integrates…