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.
Geodesic rays and chordal distances link algebraic and geometric properties of positive metrics.
New metric spaces for geodesic rays in cohomology classes.
In this paper we characterize compact extended Ptolemy metric spaces with many circles up to Möbius equivalence. This characterization yields a Möbius characterization of the -dimensional spheres and hemispheres when endowed with their chordal metrics. In particular, we show that every compact extended…
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…
New algorithm computes flag mean and median on flag manifolds.
Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the chordal structure of a probabilistic model from data. The algorithm is a greedy hill-climbing search algorithm that uses t…
A new invariant captures geometric features of circle embeddings.
A highly influential ingredient of many techniques designed to exploit sparsity in numerical optimization is the so-called chordal extension of a graph representation of the optimization problem. The definitive relation between chordal extension and the performance of the optimization algorithm that uses the extension …
We study the class N of graphs, the right-angled Artin groups defined on which do not contain surface subgroups. We prove that a presumably smaller class N' is closed under amalgamating along complete subgraphs, and also under adding bisimplicial edges. It follows that chordal graphs and chordal bipartite graphs belong…
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems. Recently, we have shown that the sparsity pattern of the optimal solution of GL is equiv…
New method simplifies causal inference with tiered background knowledge.
A method to complete incomplete correlation matrices using maximum entropy.
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the prism of Riemannian submersions, with shape space metrics being induced from metrics…
Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the assumption of chordality which ensures that efficient scoring methods can be used. In ge…
We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of experiments to discover the causal directions of all the edges in a causal graph. Previou…
We prove that for all a shellable -dimensional simplicial complex with at most vertices is extendably shellable. The proof involves considering the structure of `exposed' edges in chordal graphs as well as a connection to linear quotients of quadratic monomial ideals.
A new method scores contextual Markov networks without assuming chordality.
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank \cite{Frank1978} of estimating the number of connected components in a large graph based …
We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of interventions with minimum total cost, that can uniquely identify any causal graph with…
Adversarial attacks have always been a serious threat for any data-driven model. In this paper, we explore subspaces of adversarial examples in unitary vector domain, and we propose a novel detector for defending our models trained for environmental sound classification. We measure chordal distance between legitimate a…
Develops a method to efficiently learn causal DAGs using directed clique trees.
Each of the four critical Severi varieties arises from a minimal holomorphic nilpotent orbit in a simple regular rank 3 hermitian Lie algebra and each such variety lies as singular locus in a cubic--the chordal variety--in the corresponding complex projective space; the cubic and projective space are identified in term…
We show that the classification performance of graph convolutional networks (GCNs) is related to the alignment between features, graph, and ground truth, which we quantify using a subspace alignment measure (SAM) corresponding to the Frobenius norm of the matrix of pairwise chordal distances between three subspaces ass…
Grassmannian packings improve CNN kernels' diversity and reduce sparsity.
This paper clarifies vine copula structures using graph and matrix representations.
New algorithms bound graph structure sampling and learning high-dimensional graphical models.
Estimates log-concave densities in graphical models using tent functions.
Markov networks are widely studied and used throughout multivariate statistics and computer science. In particular, the problem of learning the structure of Markov networks from data without invoking chordality assumptions in order to retain expressiveness of the model class has been given a considerable attention in t…
A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only up to Markov equivalence, based on conditional independence relations among the v…
Geometric regularisation improves statistical models by avoiding degeneracy loci.
BacHMMachine harmonizes Baroque chorales using theory-driven principles and Hidden Markov Models.
Communities in social networks or graphs are sets of well-connected, overlapping vertices. The effectiveness of a community detection algorithm is determined by accuracy in finding the ground-truth communities and ability to scale with the size of the data. In this work, we provide three contributions. First, we show t…
A method to compute divergences between decomposable models, useful in supervised learning.
Memory-efficient optimizers fail to track a subspace, leading to unpredictable model performance.
This thesis surveys various metrics on Riemann surface spaces.
Proves existence and uniqueness of weighted metrics for smooth spaces.
New Finsler metrics constructed from -metrics.
In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature without the restriction of strong convexity (regularity). The classification result for the case is provided, which is similar to the famous Bao-Robles-Shen's result for strongly convex Rand…
We prove the equivalences of several classical complete metrics on the Teichmüller and the moduli spaces of Riemann surfaces. We use as bridge two new Kähler metrics, the Ricci metric and the perturbed Ricci metric and prove that the perturbed Ricci metric is a complete Kähler metric with bounded negative holomorphic s…
New metric defined for bounded symmetric domains.
Introduces Finslerian convolution metrics and their properties.
Survey of recent metric geometry in Kähler metrics space.
Study on geodesics of Finsler metrics derived from Riemannian metrics.
We consider geometries on the space of Riemannian metrics conformally equivalent to the widely studied Ebin L^2 metric. Among these we characterize a distinguished metric that can be regarded as a generalization of Calabi's metric on the space of Kähler metrics to the space of Riemannian metrics, and we study its geome…
New Kähler metrics generalize Calabi's and relate to Fano manifolds.
New Finsler metrics defined by Riemannian and 1-forms are studied.
We study the geodesic equation for the Dirichlet (gradient) metric in the space of Kaehler potentials. We first solve the initial value problem for the geodesic equation of the combination metric, including the gradient metric. We then discuss a comparison theorem between it and the Calabi metric. As geometric motivati…
Sharp estimates for Finsler metrics in convex domains.