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 consider the problem of learning fair decision systems in complex scenarios in which a sensitive attribute might affect the decision along both fair and unfair pathways. We introduce a causal approach to disregard effects along unfair pathways that simplifies and generalizes previous literature. Our method corrects …
A recent trend of fair machine learning is to define fairness as causality-based notions which concern the causal connection between protected attributes and decisions. However, one common challenge of all causality-based fairness notions is identifiability, i.e., whether they can be uniquely measured from observationa…
Machine learning is used to make decisions for individuals in various fields, which require us to achieve good prediction accuracy while ensuring fairness with respect to sensitive features (e.g., race and gender). This problem, however, remains difficult in complex real-world scenarios. To quantify unfairness under su…
Predictive models learned from historical data are widely used to help companies and organizations make decisions. However, they may digitally unfairly treat unwanted groups, raising concerns about fairness and discrimination. In this paper, we study the fairness-aware ranking problem which aims to discover discriminat…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a third observed multinomial distribution. We study the entire relaxation path for thi…
Recently there has been sustained interest in modifying prediction algorithms to satisfy fairness constraints. These constraints are typically complex nonlinear functionals of the observed data distribution. Focusing on the path-specific causal constraints proposed by Nabi and Shpitser (2018), we introduce new theoreti…
Regulating causal effects through averaged constraints fails to enforce conditional independence.
problem Enforcing conditional independence in regulatory and analytic settings.
method Formulated causal masking as a linear program and analyzed the resulting enforcement problem from both regulator and optimizer perspectives.
result Averaged-constraint optimization often violates stratum-wise requirements while satisfying the averaged one exactly, and detection requires conditional-independence tests.
This paper deals with the concept of curvature of framed space curves, their higher-order derivatives, variations, and co-rotational derivatives. We realize that parametrizing rotation tensor using the Gibbs vector is effective in deriving a closed form formula to obtain any order derivative of the curvature tensor as …
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and margining, which incur funding costs. We derive a partial differential equation …
We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier work. Examples of higher derived brackets naturally appear in geometry and mathem…
We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restric…
We calculate the higher derivatives of length functions on Teichmuller space along earthquake deformations. This generalizes the cosine formula for the first derivative by Kerckhoff and Wolpert and the sine formula for second derivative by Wolpert.
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…
We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and include existence and classification of various deformation quantisations.