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This paper generalizes the non-conforming FEM of Crouzeix and Raviart and its fundamental projection property by a novel mixed formulation for the Poisson problem based on the Helmholtz decomposition. The new formulation allows for ansatz…
Learning is the basis of both biological and artificial systems when it comes to mimicking intelligent behaviors. From the classical PPO (Proximal Policy Optimization), there is a series of deep reinforcement learning algorithms which are…
In some complicated datasets, due to the presence of noisy data points and outliers, cluster validity indices can give conflicting results in determining the optimal number of clusters. This paper presents a new validity index for…
A weighted likelihood approach for robust fitting of a mixture of multivariate Gaussian components is developed in this work. Two approaches have been proposed that are driven by a suitable modification of the standard EM and CEM…
Many applications of interest involve data that can be analyzed as unit vectors on a d-dimensional sphere. Specific examples include text mining, in particular clustering of documents, biology, astronomy and medicine among others. Previous…
Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the…
Constructing valid inferential methods for constrained parameters in normal and Poisson distributions represents two fundamental and important problems in applied statistics, for which there is currently no unified framework for statistical…
In the analysis of count data often the equidispersion assumption is not suitable, hence the Poisson regression model is inappropriate. As a generalization of the Poisson distribution, the COM-Poisson distribution can deal with under-,…
Many high-energy physics analyses require the presence of leptons from $W$, $Z$, or $H$ boson decay. For these analyses, signatures that mimic such leptons present a `fake lepton' background that must be estimated. Since the magnitude of…
Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e.…
This paper introduces novel weighted conformal p-values and methods for model-free selective inference. The problem is as follows: given test units with covariates $X$ and missing responses $Y$, how do we select units for which the…
We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including…
To quantify how well theoretical predictions of structural ensembles agree with experimental measurements, we depend on the accuracy of forward models. These models are computational frameworks that generate observable quantities from…
This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…
The NEXT Generation Health study investigates the dating violence of adolescents using a survey questionnaire. Each student is asked to affirm or deny multiple instances of violence in his/her dating relationship. There is, however,…
Many real-world clustering problems are plagued by incomplete data characterized by missing or absent features for some or all of the data instances. Traditional clustering methods cannot be directly applied to such data without…
Clustering methods seek to partition data such that elements are more similar to elements in the same cluster than to elements in different clusters. The main challenge in this task is the lack of a unified definition of a cluster,…
Relational Continuous Models (RCMs) represent joint probability densities over attributes of objects, when the attributes have continuous domains. With relational representations, they can model joint probability distributions over large…
We introduce a novel statistical significance-based approach for clustering hierarchical data using semi-parametric linear mixed-effects models designed for responses with laws in the exponential family (e.g., Poisson and Bernoulli). Within…
In this work, we present a novel method for combining predictions of object detection models: weighted boxes fusion. Our algorithm utilizes confidence scores of all proposed bounding boxes to constructs the averaged boxes. We tested method…