Related papers: Measuring Depth of Matroids
Statistical depth, a commonly used analytic tool in non-parametric statistics, has been extensively studied for multivariate and functional observations over the past few decades. Although various forms of depth were introduced, they are…
We study paving matroids, their realization spaces, and their closures, along with matroid varieties and circuit varieties. Within this context, we introduce three distinct methods for generating polynomials within the associated ideals of…
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…
Information retrieval (IR) evaluation measures are cornerstones for determining the suitability and task performance efficiency of retrieval systems. Their metric and scale properties enable to compare one system against another to…
We investigate the parameterized complexity of finding diverse sets of solutions to three fundamental combinatorial problems, two from the theory of matroids and the third from graph theory. The input to the Weighted Diverse Bases problem…
Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…
In this paper we consider the task of image-guided depth completion where our system must infer the depth at every pixel of an input image based on the image content and a sparse set of depth measurements. We propose a novel approach that…
Time series anomaly detection is widely used in IoT and cyber-physical systems, yet its evaluation remains challenging due to diverse application objectives and heterogeneous metric assumptions. This study introduces a problem-oriented…
Matroids are a fundamental object of study in combinatorial optimization. Three closely related and important problems involving matroids are maximizing the size of the union of $k$ independent sets (that is, $k$-fold matroid union),…
Tree roots can support and transmit nutrients for trees healthy growth aboveground, which greatly improve trees productivity and have significant effect on maintaining the normal operation of ecosystem. In order to map the tree roots more…
Transparent and reflective objects in everyday environments pose significant challenges for depth sensors due to their unique visual properties, such as specular reflections and light transmission. These characteristics often lead to…
Given two finite matroids on the same ground set, a celebrated result of Edmonds says that the ground set can be partitioned into two disjoint subsets in a manner that there is a common independent set in both matroids whose intersection…
We propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features…
This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics;…
There have been numerous recently proposed methods for monocular depth prediction (MDP) coupled with the equally rapid evolution of benchmarking tools. However, we argue that MDP is currently witnessing benchmark over-fitting and relying on…
The adoption of machine learning (ML) and, more specifically, deep learning (DL) applications into all major areas of our lives is underway. The development of trustworthy AI is especially important in medicine due to the large implications…
Properties of Boolean functions on the hypercube invariant with respect to linear transformations of the domain are among the most well-studied properties in the context of property testing. In this paper, we study the fundamental class of…
We investigate the asymptotic behavior of entropy polymatroids associated with algebraic matroids over finite fields. Given an algebraic matroid ${\sf M}:=(\mathcal{E},r)$ and the irreducible variety $V$ associated with ${\sf M}$, we…
There is an ongoing and dedicated effort to estimate bounds on the generalization error of deep learning models, coupled with an increasing interest with practical metrics that can be used to experimentally evaluate a model's ability to…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…