Related papers: $\beta$-integrated local depth and corresponding p…

We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers them to obtain a global embedding. The local views are…

In the field of artificial intelligence, AI models are frequently described as `black boxes' due to the obscurity of their internal mechanisms. It has ignited research interest on model interpretability, especially in attribution methods…

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…

The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

This paper presents an unsupervised deep-learning framework named Local Deep-Feature Alignment (LDFA) for dimension reduction. We construct neighbourhood for each data sample and learn a local Stacked Contractive Auto-encoder (SCAE) from…

Traditional deep network training methods optimize a monolithic objective function jointly for all the components. This can lead to various inefficiencies in terms of potential parallelization. Local learning is an approach to…

Local differential privacy (LDP) is a recently proposed privacy standard for collecting and analyzing data, which has been used, e.g., in the Chrome browser, iOS and macOS. In LDP, each user perturbs her information locally, and only sends…

This paper describes a localized algorithm for the topological simplification of scalar data, an essential pre-processing step of topological data analysis (TDA). Given a scalar field f and a selection of extrema to preserve, the proposed…

Local intrinsic dimension (LID) estimation methods have received a lot of attention in recent years thanks to the progress in deep neural networks and generative modeling. In opposition to old non-parametric methods, new methods use…

Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space.…

We present the analysis of the topological graph descriptor Local Degree Profile (LDP), which forms a widely used structural baseline for graph classification. Our study focuses on model evaluation in the context of the recently developed…

Precision mapping of landslide inventory is crucial for hazard mitigation. Most landslides generally co-exist with other confusing geological features, and the presence of such areas can only be inferred unambiguously at a large scale. In…

The geography of innovation offers a framework to understand how territorial characteristics shape innovation, often via spatial and cognitive proximity. Empirical research has focused largely on national and regional scales, while urban…

In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…

Uncertainty estimation is crucial in safety-critical applications, where robust out-of-distribution (OOD) detection is essential. Traditional Bayesian methods, though effective, are often hindered by high computational demands. As an…

This thesis contributes to the theoretical understanding of local update algorithms, especially Local SGD, in distributed and federated optimization under realistic models of data heterogeneity. A central focus is on the bounded…

Robust local feature representations are essential for spatial intelligence tasks such as robot navigation and augmented reality. Establishing reliable correspondences requires descriptors that provide both high discriminative power and…

In this work, we design, analyze, and optimize sequential and shared-memory parallel algorithms for partitioned local depths (PaLD). Given a set of data points and pairwise distances, PaLD is a method for identifying strength of pairwise…

This is a review of recent developments in the theory of beta ensembles of random matrices and their relations with conformal filed theory (CFT). There are (almost) no new results here. This article can serve as a guide on appearances and…