Related papers: Persistence-Based Statistics for Detecting Structu…

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying…

Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been used for this task which enjoy fewer assumptions on the distributions than the…

Geometry and topology constitute complementary descriptors of three-dimensional shape, yet existing benchmark datasets primarily capture geometric information while neglecting topological structure. This work addresses this limitation by…

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local…

Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…

Predictive geometric models deliver excellent results for many Machine Learning use cases. Despite their undoubted performance, neural predictive algorithms can show unexpected degrees of instability and variance, particularly when applied…

Change-point detection studies the problem of detecting the changes in the underlying distribution of the data stream as soon as possible after the change happens. Modern large-scale, high-dimensional, and complex streaming data call for…

Persistent spread measurement is to count the number of distinct elements that persist in each network flow for predefined time periods. It has many practical applications, including detecting long-term stealthy network activities in the…

High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two…

Recently, there has been a significant interest in performing convolution over irregularly sampled point clouds. Since point clouds are very different from regular raster images, it is imperative to study the generalization of the…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a…

In this paper, we introduce the persistence transformation, a novel methodology in Topological Data Analysis (TDA) for applications in time series data which can be obtained in various areas such as science, politics, economy, healthcare,…

We can use a method called registration to integrate some point clouds that represent the shape of the real world. In this paper, we propose highly accurate and stable registration method. Our method detects keypoints from point clouds and…

Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…

In robotic inspection, joint registration of multiple point clouds is an essential technique for estimating the transformation relationships between measured parts, such as multiple blades in a propeller. However, the presence of noise and…

Sequential (online) change-point detection involves continuously monitoring time-series data and triggering an alarm when shifts in the data distribution are detected. We propose an algorithm for real-time identification of alterations in…

Topological data analysis (TDA) has emerged as an effective approach in data science, with its key technique, persistent homology, rooted in algebraic topology. Although alternative approaches based on differential topology, geometric…

We propose a new framework for the detection of change-points in online, sequential data analysis. The approach utilizes nearest neighbor information and can be applied to sequences of multivariate observations or non-Euclidean data…

Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…