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Multi-grade deep learning (MGDL) has been shown to significantly outperform the standard single-grade deep learning (SGDL) across various applications. This work aims to investigate the computational advantages of MGDL focusing on its…
The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we generalize classical depth to directional outlyingness for functional data. We investigate theoretical…
Monocular depth estimation is an ambiguous problem, thus global structural cues play an important role in current data-driven single-view depth estimation methods. Panorama images capture the complete spatial information of their…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
One of the challenges in studying the interactions in large graphs is to learn their diverse pattern and various interaction types. Hence, considering only one distribution and model to study all nodes and ignoring their diversity and local…
The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying…
The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was…
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…
We propose a new notion called `extremal depth' (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme `outlyingness'. ED has several…
Federated Graph Learning (FGL) enables collaborative learning over distributed graph data, yet existing approaches largely rely on a closed-world assumption, limiting their applicability in dynamic environments where novel categories…
Graph-level anomaly detection (GAD) describes the problem of detecting graphs that are abnormal in their structure and/or the features of their nodes, as compared to other graphs. One of the challenges in GAD is to devise graph…
Sleep stage classification is crucial for detecting patients' health conditions. Existing models, which mainly use Convolutional Neural Networks (CNN) for modelling Euclidean data and Graph Convolution Networks (GNN) for modelling…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…
To build safe and reliable graph machine learning systems, unsupervised graph-level anomaly detection (GLAD) and unsupervised graph-level out-of-distribution (OOD) detection (GLOD) have received significant attention in recent years. Though…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
Geometry-grounded learning asks models to respect structure in the problem domain rather than treating observations as arbitrary vectors. Motivated by this view, we revisit a classical but underused primitive for comparing datasets: linear…
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local…
This work proposes and investigates a novel method for anomaly detection and shows it to be competitive in a variety of Euclidean and non-Euclidean situations. It is based on an extension of the depth quantile functions (DQF) approach. The…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…