Related papers: Adversarially Robust Topological Inference
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators achieve optimal rates of convergence under minimal assumptions on the dataset.…
Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…
Such modern applications of topology as data analysis and digital image analysis have to deal with noise and other uncertainty. In this environment, topological spaces often appear equipped with a real valued function. Persistence is a…
Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to…
Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…
Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the…
Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological…
The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…
The neighbor-based method has become a powerful tool to handle the outlier detection problem, which aims to infer the abnormal degree of the sample based on the compactness of the sample and its neighbors. However, the existing methods…
We address the problem of estimating multiple modes of a multivariate density using persistent homology, a central tool in Topological Data Analysis. We introduce a method based on the preliminary estimation of the $H_0$-persistence diagram…
Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle…
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…
Magnitude homology is an emerging framework that captures the intrinsic topological and geometric features of metric spaces, demonstrating significant potential for topoplogical data analysis and geometric data analysis. This work…
A robust estimation framework for binary regression models is studied, aiming to extend traditional approaches like logistic regression models. While previous studies largely focused on logistic models, we explore a broader class of models…
In practice, network applications have to deal with failing nodes, malicious attacks, or, somehow, nodes facing highly corrupted data --- generally classified as outliers. This calls for robust, uncomplicated, and efficient methods. We…
Outliers are ubiquitous in modern data sets. Distance-based techniques are a popular non-parametric approach to outlier detection as they require no prior assumptions on the data generating distribution and are simple to implement. Scaling…
We outline a detection method for adversarial inputs to deep neural networks. By viewing neural network computations as graphs upon which information flows from input space to out- put distribution, we compare the differences in graphs…
Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metric space in which this topological summary exists. While…