Related papers: Depth for curve data and applications
We argue that while this discourse on data ethics is of critical importance, it is missing one fundamental point: If more and more efforts in business, government, science, and our daily lives are data-driven, we should pay more attention…
Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the…
Traditional machine learning (ML) algorithms, such as multiple regression, require human analysts to make decisions on how to treat the data. These decisions can make the model building process subjective and difficult to replicate for…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
The estimation of depth in two-dimensional images has long been a challenging and extensively studied subject in computer vision. Recently, significant progress has been made with the emergence of Deep Learning-based approaches, which have…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
Investigation of the underlying physics or biology from empirical data requires a quantifiable notion of similarity - when do two observed data sets indicate nearly identical generating processes, and when they do not. The discriminating…
As organizations face the challenges of processing exponentially growing data volumes, their reliance on analytics to unlock value from this data has intensified. However, the intricacies of big data, such as its extensive feature sets,…
Differential privacy is widely considered the formal privacy for privacy-preserving data analysis due to its robust and rigorous guarantees, with increasingly broad adoption in public services, academia, and industry. Despite originating in…
Linear regression is a fundamental tool for statistical analysis. This has motivated the development of linear regression methods that also satisfy differential privacy and thus guarantee that the learned model reveals little about any one…
Computer science theory provides many different measures of complexity of a system including Kolmogorov complexity, logical depth, computational depth, and Levin complexity. However, these measures are all defined only for deterministic…
A median-radius framework for assessing centrality in multivariate data using median distances is proposed. Based on the proposed framework, a scale invariant measure of radial dispersion is defined and used to establish a depth function…
Point cloud has drawn more and more research attention as well as real-world applications. However, many of these applications (e.g. autonomous driving and robotic manipulation) are actually based on sequential point clouds (i.e. four…
Topological Data Analysis (TDA) has been praised by researchers for its ability to capture intricate shapes and structures within data. TDA is considered robust in handling noisy and high-dimensional datasets, and its interpretability is…
We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the…
This article is due to appear in the Handbook of Statistics, Vol. 43, Elsevier/North-Holland, Amsterdam, edited by Arni S. R. Srinivasa Rao and C. R. Rao. In modern day analytics, there is ever growing need to develop statistical models to…
This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…
The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…