A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Uniformly branching trees are equivalent to certain metric spaces.
Novel algorithm optimizes decision trees for nonlinear metrics.
Existence and uniqueness of discrete Einstein metrics on trees proven.
Differentiable optimization bridges arbitrary metrics to tree metrics.
Paper presents a new method for learning hyperbolic representations using tree structures.
New metric learning approach for tree data reduces computation cost.
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…
The paper explores metrics on tree moduli spaces and a new topological group.
Optimal transport for measures on noisy tree metrics is solved with robust approach.
A new supervised tree-Wasserstein distance improves document classification.
Conditions for reducing quasi-actions to tree actions and group properties.
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…
Study of Ricci flow on trees, focusing on edge weights and curvatures.
Completing segments of a real tree doesn't yield a complete space.
Positive-curvature metrics on trees identified for specific configurations.
The paper studies geometric properties of quasi-trees and tree approximations.
A new metric for comparing measures on tree systems reduces computational burden.
It is known that PQ-symmetric maps on the boundary characterize the quasi-isometry type of visual hyperbolic spaces, in particular, of geodesically complete \br-trees. We define a map on pairs of PQ-symmetric ultrametric spaces which characterizes the branching of the space. We also show that, when the ultrametric spac…
Reduces conjecture to tree-based Artin groups.
Asymptotic subcone of an unbounded metric space is another metric space, capturing the structure of the original space at infinity. In this paper we define a functional metric space S which is an asymptotic subcone of the hyperbolic plane. This space is a real tree branching at every its point. Moreover, it is a homoge…
Paper develops a new method to analyze 3D tree-like objects.
Researchers analyze geodesic complexity in robot paths on tree graphs.
Generalizes Rips' result on hyperbolic spaces to metric spaces, showing collapses for tree metrics.
In this paper we prove that if we consider the standard real metric on simplicial rooted trees then the category Tower-Set of inverse sequences can be described by means of the bounded coarse geometry of the naturally associated trees. Using this we give a geometrical characterization of Mittag-Leffler property in inve…
Proves finite step termination of Kähler-Einstein metric singularity formation.
Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We consider in this work a specific family of cost metrics, namely \textit{tree me…
We study in this paper a variant of Wasserstein barycenter problem, which we refer to as tree-Wasserstein barycenter, by leveraging a specific class of ground metrics, namely tree metrics, for Wasserstein distance. Drawing on the tree structure, we propose an efficient algorithmic approach to solve the tree-Wasserstein…
We show that for each n\ge 2 there is a quasi-isometric embedding of the hyperbolic space H^n in the product T^n=Tx...xT of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding H^2 --> TxR^m for any metric tree T and any m\ge 0.
Counting HCMU sphere components using weighted trees.
Two trees in the boundary of outer space are said to be \emph{primitive-equivalent} whenever their translation length functions are equal in restriction to the set of primitive elements of . We give an explicit description of this equivalence relation, showing in particular that it is nontrivial. This question is …
We show that every inner metric space X is the metric quotient of a complete R-tree via a free isometric action, which we call the covering R-tree of X. The quotient mapping is a weak submetry (hence, open) and light. In the case of compact 1-dimensional geodesic space X, the free isometric action is via a subgroup of …
New relation on paths is not transitive.
We present a construction, called the limit of a tree system of spaces (or, less formally, a tree of spaces). The construction is designed to produce compact metric spaces that resemble fractals, out of more regular spaces, such as closed manifolds, compact polyhedra, compact Menger manifolds, etc. Such spaces are pote…
We prove that if X is a complete geodesic metric space with uniformly generated first homology group and is metrically proper on the connected components and bornologous, then X is quasi-isometric to a tree. Using this and adapting the definition of hyperbolic approximation we obtain an intrinsic sufficent …
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
For a finitely generated group , we introduce an asymmetric pseudometric on projectivized deformation spaces of -trees, using stretching factors of -equivariant Lipschitz maps, that generalizes the Lipschitz metric on Outer space and is an analogue of the Thurston metric on Teichmüller space. We show that in t…
Proposes a new phylogenetic tree space with biologically principled geometry.
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants of OT in the recent literature, one of the most notable being the \textit{slice…
The paper improves decision tree stability for health care applications.
Tree Mover's Distance measures graph attributes and improves GNN performance.
Explains visual metrics on hyperbolic space boundaries.
In this paper, we study the weak compactness of the set of conformal metrics in any Riemann surface without boundary whose Calabi energy and area are uniformly bounded. We prove that for any sequence of such metrics, there alwasy exists a subsequence which converges in H\sp{2,2}_\sb{loc} everywhere except a finite numb…
There is a well-known correspondence between infinite trees and ultrametric spaces which can be interpreted as an equivalence of categories and comes from considering the end space of the tree. In this equivalence, uniformly continuous maps between the end spaces are translated to some classes of coarse maps (or even c…
Geodesic currents on hyperbolic surfaces have dual spaces that are metric trees.
New method for comparing different mass measures on tree structures using entropy partial transport.
Since its inception in the 1980s, ID3 has become one of the most successful and widely used algorithms for learning decision trees. However, its theoretical properties remain poorly understood. In this work, we introduce a novel metric of a decision tree algorithm's performance, called mean iteration statistical consis…
Maximal representations are studied using tree embeddings and geodesic currents.
Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in:…