Related papers: On the estimation of persistence intensity functio…
Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…
In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram. Statistical research for persistence diagrams have been actively…
Persistence diagrams are two-dimensional plots that summarize the topological features of functions and are an important part of topological data analysis. A problem that has received much attention is how deal with sets of persistence…
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…
Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
Persistent homology is a tool from Topological Data Analysis (TDA) used to summarize the topology underlying data. It can be conveniently represented through persistence diagrams. Observing a noisy signal, common strategies to infer its…
To our knowledge, the analysis of convergence rates for persistence diagrams estimation from noisy signals has predominantly relied on lifting signal estimation results through sup-norm (or other functional norm) stability theorems. We…
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…
Persistence diagrams are common objects in the field of Topological Data Analysis. They are topological summaries that capture both topological and geometric structure within data. Recently there has been a surge of interest in developing…
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…
Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
Let P be a distribution with support S. The salient features of S can be quantified with persistent homology, which summarizes topological features of the sublevel sets of the distance function (the distance of any point x to S). Given a…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been…