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.
We clarify what fairness guarantees we can and cannot expect to follow from unconstrained machine learning. Specifically, we characterize when unconstrained learning on its own implies group calibration, that is, the outcome variable is conditionally independent of group membership given the score. We show that under r…
The assumption of positivity in causal inference (also known as common support and co-variate overlap) is necessary to obtain valid causal estimates. Therefore, confirming it holds in a given dataset is an important first step of any causal analysis. Most common methods to date are insufficient for discovering non-posi…
The paper shows how to use proxy attributes for fairness in machine learning models with missing sensitive group data.
problem Measuring and enforcing fairness in machine learning models with incomplete sensitive group data.
method Using proxy-sensitive attributes to derive upper bounds on multiaccuracy and multicalibration violations and adjust models to satisfy these fairness notions.
result Provable upper bounds on multiaccuracy and multicalibration violations can be derived using proxy-sensitive attributes in the absence of sensitive group data.
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group,…
A number of machine learning (ML) methods have been proposed recently to maximize model predictive accuracy while enforcing notions of group parity or fairness across sub-populations. We propose a desirable property for these procedures, slack-consistency: For any individual, the predictions of the model should be mono…
Study on hyperbolic groups, focusing on separability and splittings.
problem Coarse separability and splittings in hyperbolic groups.
method Quantitative analysis of volume growth and cut-sets, focusing on thickened spheres.
result One-ended hyperbolic groups that are not virtually surface groups are coarsely separable by a subset of subexponential growth if and only if they split over a virtually cyclic subgroup.
We use the theory of group actions on profinite trees to prove that the fundamental group of a finite, 1-acylindrical graph of free groups with finitely generated edge groups is conjugacy separable. This has several applications: we prove that positive, C′(1/6) one-relator groups are conjugacy separable; we provide a…
We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontry…
The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes …
Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric sp…
Elementarily free groups are the finitely generated groups with the same elementary theory as free groups. We prove that elementarily free groups are subgroup separable, answering a question of Zlil Sela.
The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski to…
Singing voice separation attempts to separate the vocal and instrumental parts of a music recording, which is a fundamental problem in music information retrieval. Recent work on singing voice separation has shown that the low-rank representation and informed separation approaches are both able to improve separation qu…
Let M be a hyperbolizable, nontrivial compression body without toroidal boundary components. In this paper, we characterize which discrete and faithful representations of the fundamental group of M into PSL(2,C) are separable-stable. The set of separable-stable representations forms a domain of discontinuity for the ac…
Generalizes underlap coefficient for multivariate group separation.
problem Quantifying distributional separation across groups in statistical learning.
method Generalizes underlap coefficient (UNL) to multivariate settings, studies its relationship with Bayes risk and mutual information, proposes an efficient importance sampling estimator.
result UNL as a measure of dependence between group labels and variables of interest, interpretable measure of partition-covariate dependence in clustering.
We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.
We prove that if S is a properly embedded incompressible surface in a compact 3-manifold M, then the fundamental group of S is separable in the fundamental group of M.