相关论文: Topological Residual Asymmetry for Bivariate Causa…

We introduce Causal Computational Asymmetry (CCA), a principle for causal direction identification based on optimization dynamics in which one neural network is trained to predict $Y$ from $X$ and another to predict $X$ from $Y$, and the…

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…

Spatially incoherent light sources, such as spontaneously emitting atoms, naively require Maxwell's equations to be solved many times to obtain the total emission, which becomes computationally intractable in conjunction with large-scale…

With the rapid growth of video data, Composed Video Retrieval (CVR) has emerged as a novel paradigm in video retrieval and is receiving increasing attention from researchers. Unlike unimodal video retrieval methods, the CVR task takes a…

We introduce a construction and an algorithm, both based on Topological Data Analysis (TDA), to tackle the problem of the isomorphism check of Orthogonal Arrays (OAs). Specifically, we associate to any binary OA a persistence diagram, one…

Classical topological descriptors used in topological data analysis (TDA) are invariant under permutations of spatial axes and therefore cannot represent the loading direction, which is essential for modeling anisotropic mechanical…

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…

Deep topological data analysis (TDA) offers a principled framework for capturing structural invariants such as connectivity and cycles that persist across scales, making it a natural fit for anomaly segmentation (AS). Unlike thresholdbased…

Large sample statistical analysis of threshold autoregressive (TAR) models is usually based on the assumption that the underlying driving noise is uncorrelated. In this paper, we consider a model, driven by Gaussian noise with geometric…

Inhomogeneous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. When they are robust against continuous deformations of parameters, such waves are said to be of…

Persistent homology is an area within topological data analysis (TDA) that can uncover different dimensional holes (connected components, loops, voids, etc.) in data. The holes are characterized, in part, by how long they persist across…

Constructing valid and informative conformal prediction regions for multi-dimensional outputs remains a fundamental challenge. While conformal prediction provides finite-sample, distribution-free coverage guarantees, its practical…

Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…

A novel topological-data-analytical (TDA) method is proposed to distinguish, from noise, small holes surrounded by high-density regions of a probability density function. The proposed method is robust against additive noise and outliers.…

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…

Across many scientific domains, practitioners rely on coarse, discretized summaries to track the evolving structure of complex systems under noise, measurement error, and changing system size. Understanding when such summaries are reliable…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…

Qualitative methods such as the linear sampling method and the factorization method reconstruct acoustic scatterers through sampling indicators. In practice, these indicators are gray-scale fields on a prescribed sampling window and a…

Introduction: Methods now exist to detect residual confounding. One requires an "indicator" with two key properties: conditional independence of the outcome (given exposure and measured covariates) absent confounding and other model…