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.
Paper tackles inconsistent CATE estimation across group assignments.
We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold, respectively. Furthermore, we functorially assign isomorphisms to (based) diffeomorphisms, and show…
Quantum theory uses modular group representations to assign invariants to 3-manifolds.
Optimizes balanced treatment assignment for experiments.
Parity functors assign labels to knot diagrams based on crossing parity.
Extends quantum annular homology to infinite sets.
Study of 13,456 hot stellar systems reveals multi-layered grouping.
Study compares methods for treatment assignment, finding A-learner best for playlist generation.
Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario, referred to as extreme clustering, datasets are enormous and the number of represent…
moment maps arise as a generalization of genuine moment maps on symplectic manifolds when the symplectic structure is discarded, but the relation between the mapping and the action is kept. Particular examples of abstract moment maps had been used in Hamiltonian mechanics for some time, but the abstract notion originat…
Discovering and clustering subspaces in high-dimensional data is a fundamental problem of machine learning with a wide range of applications in data mining, computer vision, and pattern recognition. Earlier methods divided the problem into two separate stages of finding the similarity matrix and finding clusters. Simil…
AI helps build particle physics theories more efficiently.
To a presentation of an oriented link as the closure of a braid we assign a complex of bigraded vector spaces. The Euler characteristic of this complex (and of its triply-graded cohomology groups) is the HOMFLYPT polynomial of the link. We show that the dimension of each cohomology group is a link invariant.
Paper tackles group robustness with partially labeled data.
Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization problem. In this paper, we reinterpret these results as performing MAP estimation u…
We use Fox calculus to assign a marked polytope to a `nice' group presentation with two generators and one relator. Relating the marked vertices to Novikov-Sikorav homology we show that they determine the Bieri-Neumann-Strebel invariant of the group. Furthermore we show that in many cases the marked polytope is an inva…
We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, one obtains the relations from the knot group, and from the core group. Using the ternary o…
The paper shows how demographic data can lead to biased predictions, proposing 'Affirmative Information' as a solution.
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the - and -norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…
The -means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a -means type algorithm that assigns observations to groups while estimating their skewness-transformation parameters. The resulting groups and transformation reveal general-structured cl…
We define link and graph invariants from entropic magmas modeling them on the Kauffman bracket and Tutte polynomial. We define the homology of entropic magmas. We also consider groups that can be assigned to the families of compatible entropic magmas.
Researchers provide a simple topological method for Burau representations of loop braid groups.
We assign to a finite -complex and an element in its first cohomology group a twisted version of the -Euler characteristic and study its main properties. In the case of an irreducible orientable -manifold with empty or toroidal boundary and infinite fundamental group we identify it with the Thurston norm. W…
We construct finite volume hyperbolic manifolds with large symmetry groups. The construction makes use of the presentations of finite Coxeter groups provided by Barot and Marsh and involves mutations of quivers and diagrams defined in the theory of cluster algebras. We generalize our construction by assigning to every …
Every singular foliation has an associated topological groupoid, called holonomy groupoid (see arXiv:math/0612370). In this note we exhibit some functorial properties of this assignment: if a foliated manifold is the quotient of a foliated manifold along a surjective submersion w…
Unified view on selective credit assignment for reinforcement learning.
If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by E(X). In the present work we establish a topological classification of such bundles in…
The paper contains a survey of train constructions for infinite symmetric groups and related groups. For certain pairs (a group , a subgroup ), we construct categories, whose morphisms are two-dimensional surfaces tiled by polygons and colored in a certain way. A product of morphisms is a gluing of combinatorial …
Heegaard Floer theory is a kind of topological quantum field theory, assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented 4-dimensional cobordisms. Bordered Heegaard Floer homology is an extension of Heegaard Floer homology to 3-manifolds with boundary, with ext…
Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. We show that the natural action of the group of volume-preserving diffeomorphisms by push-forward has a group-valued momentum map that assigns to a…
Unsupervised clustering is one of the most fundamental challenges in machine learning. A popular hypothesis is that data are generated from a union of low-dimensional nonlinear manifolds; thus an approach to clustering is identifying and separating these manifolds. In this paper, we present a novel approach to solve th…
Holonomy groups of metric connections converge in a monotonic way.
The knot invariant Upsilon, defined by Ozsvath, Stipsicz, and Szabo, induces a homomorphism from the smooth knot concordance group to the group of piecewise linear functions on the interval [0,2]. Here we define a set of related secondary invariants, each of which assigns to a knot a piecewise linear function on [0,2].…
New method estimates individual treatment effects using domain generalization.
A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges within a cluster and between different clusters. We assume that the cluster ass…
New deep Cox mixture model improves survival analysis performance.
We face network data from various sources, such as protein interactions and online social networks. A critical problem is to model network interactions and identify latent groups of network nodes. This problem is challenging due to many reasons. For example, the network nodes are interdependent instead of independent o…
A new method estimates treatment effects without strong assumptions.
EgalMAB solves fair resource allocation in stochastic bandits.
Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic for use in the permutation tests of worst likely assignments that improves error b…
Assignment methods are at the heart of many algorithms for unsupervised learning and clustering - in particular, the well-known K-means and Expectation-Maximization (EM) algorithms. In this work, we study several different methods of assignment, including the "hard" assignments used by K-means and the ?soft' assignment…
COCOA improves credit assignment in reinforcement learning by measuring contributions to rewards.
Two spectral algorithms for community detection in graphs with covariates are compared.
In this short note, we compare the combinatorial sign assignment of Manolescu, Ozsvath, Szabo and Thurston for grid homology of knots and links in 3-sphere with the sign assignment coming from a coherent system of orientations on Whitney disks. Although these constructions produce different signs, a small modification …
This paper introduces a novel, well-founded, betweenness measure, called the Bag-of-Paths (BoP) betweenness, as well as its extension, the BoP group betweenness, to tackle semisupervised classification problems on weighted directed graphs. The objective of semi-supervised classification is to assign a label to unlabele…
3-manifolds with toral boundary are uniquely determined by their profinite completions.
New methods optimize personalized treatment assignment in trials with many arms.
In this paper we complete the topological description of the space of representations of the fundamental group of a punctured surface in SL(2,R) with prescribed behavior at the punctures and nonzero Euler number, following the strategy employed by Hitchin in the unpunctured case and exploiting Hitchin-Simpson correspon…