Related papers: Quantifying uncertainty in spectral clusterings: e…

Determining the quality of the results obtained by clustering techniques is a key issue in unsupervised machine learning. Many authors have discussed the desirable features of good clustering algorithms. However, Jon Kleinberg established…

We present a sampling-free approach for computing the epistemic uncertainty of a neural network. Epistemic uncertainty is an important quantity for the deployment of deep neural networks in safety-critical applications, since it represents…

Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…

We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at…

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

The uncertainty of Compton backscattering process is studied by virtue of analytical formulas, and the special effects of variant energy spread and energy drift on the systematic uncertainty estimation are also studied with Monte Carlo…

Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper…

Interpreting experimental data in high school experiments can be a difficult task for students, especially when there is large variation in the data. At the same time, calculating the standard deviation poses a challenge for students. In…

Clustering is a fundamental task for analyzing unlabeled data based solely on its underlying distribution. Spectral clustering is a clustering method that represents a dataset as a graph and uses the relationships between data points.…

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…

Following the work of arXiv:2101.09512, we are interested in clustering a given multi-variate series in an unsupervised manner. We would like to segment and cluster the series such that the resulting blocks present in each cluster are…

Cluster analysis is a popular unsupervised learning tool used in many disciplines to identify heterogeneous sub-populations within a sample. However, validating cluster analysis results and determining the number of clusters in a data set…

Understanding and quantifying uncertainty in black box Neural Networks (NNs) is critical when deployed in real-world settings such as healthcare. Recent works using Bayesian and non-Bayesian methods have shown how a unified predictive…

In a wide range of modern applications, we observe a large number of time series rather than only a single one. It is often natural to suppose that there is some group structure in the observed time series. When each time series is modelled…

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…

Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…

Constrained clustering has been well-studied for algorithms such as $K$-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode…

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…

Empirical relationships are derived for the expected sampling error of quantile estimations using Monte Carlo experiments for two frequency distributions frequently encountered in climate sciences. The relationships found are expressed as a…

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.…