Related papers: A Bayesian Framework for Persistent Homology

This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…

Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…

Marked point process data arise when events occur in a space with event-level marks. We study clustering of replicated marked Poisson point processes and introduce Dirichlet process mixtures of marked Poisson point processes, a Bayesian…

Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to the health sciences. Often, the central object of interest in a point process is the underlying intensity…

In this paper we introduce a statistic, the persistent homology transform (PHT), to model surfaces in $\mathbb{R}^3$ and shapes in $\mathbb{R}^2$. This statistic is a collection of persistence diagrams - multiscale topological summaries…

Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic,…

The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map…

This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of solutions snapshots, what…

Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…

Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…

In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Persistent homology is a popular data analysis technique that is used to capture the changing topology of a filtration associated with some simplicial complex $K$. These topological changes are summarized in persistence diagrams. We propose…

Building upon [2308.02636], we investigate the constraining power of persistent homology on cosmological parameters and primordial non-Gaussianity in a likelihood-free inference pipeline utilizing machine learning. We evaluate the ability…

Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…

Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense,…

This paper introduces persistent homology, which is a powerful tool to characterize the shape of data using the mathematical concept of topology. We explain the fundamental idea of persistent homology from scratch using some examples. We…

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…

We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a…

A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice of wavelet for a dataset of graphs, such that their…