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We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant…
The aim of the present paper is to extend the concept of a congruence from lattices to posets. We use an approach different from that used by the first author and V. Sn\'a\v{s}el. By using our definition we show that congruence classes are…
Pose Machines provide a sequential prediction framework for learning rich implicit spatial models. In this work we show a systematic design for how convolutional networks can be incorporated into the pose machine framework for learning…
We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module…
This article deals with a relationship between derived categories of modules over some partially ordered sets and triangulated categories arising from quasi-homogeneous isolated singularities. It produces heuristics for the existence of…
Given a functor $p:E \rightarrow B$ and an object $e \in E$ , we define a \emph{displacement} of $e$ along a morphism $\varepsilon: p(e) \rightarrow b$, as a map $e \rightarrow \nabla_\varepsilon(e)$ satisfying a universal property analogue…
In this paper, we establish a persistence version of the Quillen-McCord theorem for persistence finite posets. Given a map $f \colon P \rightarrow Q$ between persistence finite posets $P$ and $Q$ with weakly $\varepsilon$-contractible…
We analyze the popular ``state-space'' class of algorithms for detecting casual interaction in coupled dynamical systems. These algorithms are often justified by Takens' embedding theorem, which provides conditions under which relationships…
This paper establishes connections between three of the most prominent metrics used in the analysis of persistence diagrams in topological data analysis: the bottleneck distance, Patel's erosion distance, and Bubenik's landscape distance.…
We introduce the relation ${\rho}_{\lambda}$-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives, and present some of its essential properties. Among other things, we give…
In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…
Intrinsic location functional is a large class of random locations containing locations that one may encounter in many cases, e.g., the location of the path supremum/infimum over a given interval, the first/last hitting time, etc. It has…
Behavioural distances provide a robust alternative to notions of equivalence such as bisimilarity in the context of probabilistic transition systems. They can be defined as least fixed points, whose universal property allows us to exhibit…
Shellable complexes are homotopy equivalent to a wedge of spheres of possibly different dimensions, so that the (co)homology of the constant functor over the complex is concentrated in those degrees. In this work, we introduce the concept…
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…
Persistence diagrams (PDs) are used as signatures of point cloud data. Two clouds of points can be compared using the bottleneck distance d_B between their PDs. A potential drawback of this pipeline is that point clouds sampled from…
Heterogeneous datasets emerge in various machine learning and optimization applications that feature different input sources, types or formats. Most models or methods do not natively tackle heterogeneity. Hence, such datasets are often…
There are many metrics available to compare phylogenetic trees since this is a fundamental task in computational biology. In this paper, we focus on one such metric, the $\ell^\infty$-cophenetic metric introduced by Cardona et al. This…
We propose unsupervised representation learning and feature extraction from dendrograms. The commonly used Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level…
In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…