Related papers: Learning Barycenters from Signature Matrices

Fill each box in a Young diagram with the number of paths from the bottom of its column to the end of its row, using steps north and east. Then, any square sub-matrix of this array starting on the south-east boundary has determinant one. We…

To each totally disconnected, locally compact topological group G and each group A of automorphisms of G, a pseudo-metric space of ``directions'' has been associated by U. Baumgartner and the second author. Given a Lie group G over a local…

We show how locally smooth actions of compact Lie groups on a manifold $X$ can be used to obtain new upper bounds for the topological complexity $\TC(X)$, in the sense of Farber. We also obtain new bounds for the topological complexity of…

We introduce Bridged Clustering, a semi-supervised framework to learn predictors from any unpaired input $X$ and output $Y$ dataset. Our method first clusters $X$ and $Y$ independently, then learns a sparse, interpretable bridge between…

A unicellular map is a map which has only one face. We give a bijection between a dominant subset of rooted unicellular maps of fixed genus and a set of rooted plane trees with distinguished vertices. The bijection applies as well to the…

According to Etingof and Varchenko, the classical dynamical Yang-Baxter equation is a guarantee for the consistency of the Poisson bracket on certain Poisson-Lie groupoids. Here it is noticed that Dirac reductions of these Poisson manifolds…

In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [Gubinelli, Journal of Differential Equations, 248(4), 2010], which generalizes the classical geometric rough path. We establish a…

We consider a recursively defined random set of points and its barycenter, where the random set is constructed by the following inductive rule: Given a realization of $n-1$ points, one of them is picked at random and serves as a source the…

During the last thirty years, symplectic or Marsden--Weinstein reduction has been a major tool in the construction of new symplectic manifolds and in the study of mechanical systems with symmetry. This procedure has been traditionally…

Let $\mathfrak{g}$ be a vector space and $[,],[,]'$ be a pair of Lie brackets on $\mathfrak{g}$. By definition they are compatible if $[,]+[,]'$ is again a Lie bracket. Such pairs play important role in bihamiltonian and $r$-matrix…

We study unconditional subsequences of the canonical basis e_rc of elementary matrices in the Schatten class S^p. They form the matrix counterpart to Rudin's Lambda(p) sets of integers in Fourier analysis. In the case of p an even integer,…

We introduce a uniform method of proof for the following results. For {\em each} of the following conditions, there are $2^{\aleph_0}$ families of Steiner systems, satisfying that condition: i) Theorem~2.2.4: (extending \cite{Chicoetal})…

We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…

This article introduces planar shape signatures derived from homology nerves, which are intersecting 1-cycles in a collection of homology groups endowed with a proximal relator (set of nearness relations) that includes a descriptive…

A map graph is a graph admitting a representation in which vertices are nations on a spherical map and edges are shared curve segments or points between nations. We present an explicit fixed-parameter tractable algorithm for recognizing map…

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the…

Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a…

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative…

In the recent years, branch-and-cut algorithms have been the target of data-driven approaches designed to enhance the decision making in different phases of the algorithm such as branching, or the choice of cutting planes (cuts). In…

A left invariant metric on a nilpotent Lie group is called minimal, if it minimizes the norm of the Ricci tensor among all left invariant metrics with the same scalar curvature. Such metrics are unique up to isometry and scaling and the…