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It has been recognized that the diversity of base learners is of utmost importance to a good ensemble. This paper defines a novel measurement of diversity, termed as exclusivity. With the designed exclusivity, we further propose an ensemble…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
We introduce the notion of echeloned spaces - an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly…
We prove a sharp lower bound on the number of terms in an element of the reduced Gr\"obner basis of a Schubert determinantal ideal $I_w$ under the term order of [Knutson-Miller '05]. We give three applications. First, we give a…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
Parametric model order reduction (pMOR) is a powerful tool for accelerating finite element (FE) simulations while maintaining parametric dependencies. For geometric parameters, pMOR by matrix interpolation is a well-suited approach because…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…
Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction,…
The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…
We initiate the study of sheaves on Cech closure spaces, providing a new, unified approach to sheaf theory on many of the major classes of spaces of interest to applications: topological spaces, finite simplicial complexes (seen as $T_0$…
Lifted inference reduces the complexity of inference in relational probabilistic models by identifying groups of constants (or atoms) which behave symmetric to each other. A number of techniques have been proposed in the literature for…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a…
We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…
Euclidean Distance Matrix (EDM), which consists of pairwise squared Euclidean distances of a given point configuration, finds many applications in modern machine learning. This paper considers the setting where only a set of anchor nodes is…
An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…
We quantify the uniqueness of continuation from Cauchy or interior data. Our approach consists in extending the existing results in the linear case. As by product we obtain a new stability estimate in the linear case. We also show the…
We study extension of scalars for sheaves of vector spaces, assembling results that follow from well-known statements about vector spaces, but also developing some complements. In particular, we formulate Galois descent in this context, and…