Related papers: Extremal Depth for Functional Data and Application…

Outlier detection refers to the identification of data points that deviate from a general data distribution. Existing unsupervised approaches often suffer from high computational cost, complex hyperparameter tuning, and limited…

Functional Data Analysis represents a field of growing interest in statistics. Despite several studies have been proposed leading to fundamental results, the problem of obtaining valid and efficient prediction sets has not been thoroughly…

Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

Based on the framework of the directional distance function, we conduct a systematic analysis on the measurement of super-efficiency in order to achieve two main objectives. Our primary purpose is developing two generalized directional…

We measure the Out-of-domain uncertainty in the prediction of Neural Networks using a statistical notion called ``Lens Depth'' (LD) combined with Fermat Distance, which is able to capture precisely the ``depth'' of a point with respect to a…

We report on an improvement to the implementation of the Maximum Entropy Method (MEM). It amounts to departing from the search space obtained through a singular value decomposition (SVD) of the Kernel. Based on the shape of the SVD basis…

In this work, we propose a deep neural network method to perform nonparametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with ReLU activation function. By properly choosing…

One of the most important tasks for improving data quality and the reliability of data analytics results is Entity Resolution (ER). ER aims to identify different descriptions that refer to the same real-world entity, and remains a…

The Maximum Depth was the first attempt to use data depths instead of multivariate raw data to construct a classification rule. Recently, the DD-classifier has solved several serious limitations of the Maximum Depth classifier but some…

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 study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…

A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…

High-dimensional data poses unique challenges in outlier detection process. Most of the existing algorithms fail to properly address the issues stemming from a large number of features. In particular, outlier detection algorithms perform…

A key feature of out-of-distribution (OOD) detection is to exploit a trained neural network by extracting statistical patterns and relationships through the multi-layer classifier to detect shifts in the expected input data distribution.…

Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance),…

Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

Empirical Mode Decomposition(EMD) is an adaptive data analysis technique for analyzing nonlinear and nonstationary data[1]. EMD decomposes the original data into a number of Intrinsic Mode Functions(IMFs)[1] for giving better physical…

The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by…

Uncertainty-based deep learning models have attracted a great deal of interest for their ability to provide accurate and reliable predictions. Evidential deep learning stands out achieving remarkable performance in detecting…