Unified framework for intersectionally fair AI models using MIO.
problem Bias in AI models for high-risk domains.
method Mixed-Integer Optimization (MIO) for fairness and interpretability.
result Improved performance in detecting and mitigating bias at intersections.
Algorithm corrects bias in classification data.
problem Underrepresentation and intersectional bias in classification data.
method Estimate group-wise drop-out rates with small unbiased data, construct reweighting scheme, and present algorithm.
result Efficiently approximate loss of any hypothesis on true distribution.
Intersectional constraints improve selection outcomes by reducing inequality.
problem Persistent inequality and reduced utility in selection processes due to implicit bias.
method Introducing intersectional constraints to mitigate the adverse effects of implicit bias in selection processes.
result Intersectional constraints can recover almost all the utility achievable in the absence of implicit bias, offering a significant advantage over non-intersectional constraints.
Social bias in machine learning has drawn significant attention, with work ranging from demonstrations of bias in a multitude of applications, curating definitions of fairness for different contexts, to developing algorithms to mitigate bias. In natural language processing, gender bias has been shown to exist in contex…
A neural framework corrects bias in estimating individual treatment effects.
problem Estimating individual treatment effects from observational data.
method An anchored neural architecture and precision-corrected intersection-bound inference.
result Corrected bias and maintained nominal coverage in high-dimensional settings.
Machine learning algorithms are extensively used to make increasingly more consequential decisions about people, so achieving optimal predictive performance can no longer be the only focus. A particularly important consideration is fairness with respect to race, gender, or any other sensitive attribute. This paper stud…
Intersectionality is a framework that analyzes how interlocking systems of power and oppression affect individuals along overlapping dimensions including race, gender, sexual orientation, class, and disability. Intersectionality theory therefore implies it is important that fairness in artificial intelligence systems b…
There is a growing body of work that proposes methods for mitigating bias in machine learning systems. These methods typically rely on access to protected attributes such as race, gender, or age. However, this raises two significant challenges: (1) protected attributes may not be available or it may not be legal to use…
This research compares two encoding methods for categorical attributes in machine learning, affecting model fairness.
problem The impact of encoding protected categorical attributes on fairness in machine learning models.
method Comparison of one-hot encoding and target encoding methods.
result Target encoding can lead to more unfair models compared to one-hot encoding due to induced bias.
Proposes a novel MTL approach based on bias-variance analysis.
problem Improving multi-task learning performance through shared knowledge.
method Two-phase iterative aggregation of targets and features using bias-variance analysis.
result Validation on synthetic and real-world datasets demonstrates the effectiveness of the proposed method.
This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the independence models represented by a set of directed and acyclic graphs under conditioning. This impli…
Enhanced survival trees improve computational efficiency and inference.
problem Censored failure time data and variable selection bias.
method Improved splitting procedure, intersected validation, fused regularization, and bootstrap-based bias correction.
result Valid confidence intervals for median survival times.
EL framework certifies and flags bias in ML models without distributional assumptions.
problem Systematic performance disparities across sensitive subpopulations in ML models.
method Empirical likelihood-based approach for non-parametric fairness auditing.
result EL framework outperforms bootstrap methods in certification and subpopulation discovery.
This paper debiases KG embeddings by filtering sensitive attributes.
problem Social and cultural biases in KG representations.
method Exploring and filtering popularity and gender biases in KGE.
result Sensitivity of KG embeddings to sensitive attributes like gender.
The growing capability and accessibility of machine learning has led to its application to many real-world domains and data about people. Despite the benefits algorithmic systems may bring, models can reflect, inject, or exacerbate implicit and explicit societal biases into their outputs, disadvantaging certain demogra…
The analysis of scientific data of increasing size and complexity requires statistical machine learning methods that are both interpretable and predictive. Union of Intersections (UoI), a recently developed framework, is a two-step approach that separates model selection and model estimation. A linear regression algori…
The paper examines how closed curves on surfaces intersect and how this intersection determines the curves.
problem Determining closed curves on surfaces based on their intersections.
method Constructing and studying k-equivalent curves, analyzing intersections with other curves. result Curves are determined by their intersections with all other curves, but non-simple curves require infinitely many intersections to distinguish.
3-manifold triangulation can be reconstructed from its intersection matrix.
problem Reconstructing the triangulation of 3-manifolds from their intersection matrix.
method Using the intersection matrix of a simplicial complex to determine the triangulation of a 3-manifold up to isomorphism.
result The intersection matrix is sufficient to determine the triangulation of a 3-manifold up to isomorphism.
The paper finds diffeomorphic complex intersections with distinct Hodge numbers.
problem Identifying complex intersections with different Hodge numbers.
method Provided three pairs of 3-dimensional and one pair of 5-dimensional complex complete intersections, all diffeomorphic but with different Hodge numbers.
result Diffeomorphic complex intersections can have different Hodge numbers.
New polynomials defined for virtual knots, calculated up to crossing 4.
problem Defining and calculating invariants for virtual knots.
method Intersection number of curves on a closed surface.
result Intersection polynomials calculated up to crossing 4.
In this paper we present the algorithms for calculating the differential geometric properties {t,n,b1,b2,b3,k1,k2,k3,k4} along-with geodesic curvature and geodesic torsion of the transversal intersection curve of four hypersurfaces (given by parametric representation) in Euclidean space R^5. In transversal intersection…
We generalize the PL intersection product for chains on PL manifolds and for intersection chains on PL stratified pseudomanifolds to products of locally finite chains on non-compact spaces that are natural with respect to restriction to open sets. This is necessary to sheafify the intersection product, an essential ste…
Conditions for curves on a torus with specific pairwise intersections.
problem Finding curves on a torus with prescribed pairwise intersections.
method Necessary and sufficient conditions for curves on a torus with given pairwise intersections.
result Necessary and sufficient conditions for the existence of curves on a torus with specific pairwise intersections.
Study self-intersections of arcs on a pair of pants, proving natural number spectrum.
problem Understanding self-intersections of arcs on a pair of pants.
method Algorithm to compute self-intersection number, bounds established in terms of word length.
result Spectrum of self-intersection numbers covers all natural numbers.
Virtual knots with same writhe polynomial have equivalent intersection graphs.
problem Equivalence of intersection graphs for virtual knots.
method Proved equivalence through writhe polynomial.
result Intersection graphs of virtual knots with the same writhe polynomial are equivalent.
Study properties of self-similar continua with finite intersection property.
problem Characterize self-similar continua with finite intersection property.
method Prove intersection graph criterion, finite order theorem, and parameter matching theorem.
result All Jordan arcs starting from a intersection point in such continuum on a plane should have the same slope parameter at that point.
Estimates intersection pairing in hyperbolic 4-manifolds.
problem Estimating intersection pairing in hyperbolic 4-manifolds.
method Using Thurston norms of homology classes.
result Proved an estimate on intersection pairing.
By considering a (not necessarily locally-flat) PL knot as the singular locus of a PL stratified pseudomanifold, we can use intersection homology theory to define intersection Alexander polynomials, a generalization of the classical Alexander polynomial invariants for smooth or PL locally-flat knots. We show that the i…
Classifies arcs on a 4-punctured sphere that intersect at most once.
problem Classifying arcs on a 4-punctured sphere with intersection constraints.
method Classification of maximal systems of arcs intersecting at most once.
result Maximal systems of arcs on the 4-punctured sphere identified.
James McClure recently showed that the domain for the intersection pairing of PL chains on a PL manifold M is a subcomplex of C∗(M)⊗C∗(M) that is quasi-isomorphic to C∗(M)⊗C∗(M) and, more generally, that the intersection pairing endows C∗(M) with the structure of a partially-defined commutati…
Novel approach for large genus intersection number asymptotics.
problem Computing intersection numbers in large genus.
method Resurgent analysis of n-point functions with quantum curve.
result Extension of Aggarwal's results and new r-spin and Theta-class intersection numbers. The paper calculates self-intersections on a pair of pants using Bowen and Series' coding.
problem Computing the number of self-intersections of closed geodesics on a pair of pants.
method Used Bowen and Series' coding to compute self-intersections.
result Proved a conjecture and provided bounds for self-intersection numbers.
Generic potential primes have no self-intersections or intersections.
problem Finding non-degenerate periodic orbits without self-intersections.
method Generic convex Hamiltonian approach and Mañé genericity.
result Prime periodic orbits do not intersect or have self-intersections.
Paper proves curves can be smoothed to reduce self-intersection by exactly 1.
problem Prove that the shortest closed geodesic self-intersects exactly k times.
method Carefully smoothing intersection points reduces self-intersection by exactly 1.
result The shortest closed geodesic self-intersects exactly k times for hyperbolic and Riemannian metrics.
The paper extends intersection theory for b-divisors, proving monotonicity and volume inequalities.
problem Intersection theory for b-divisors and monotonicity of intersection products.
method Developed general intersection theory of nef b-divisors, defined restricted volume, proved monotonicity.
result Proved quantitative monotonicity of intersection product and new volume inequalities.
Study intersection polynomials of long virtual knots with supporting genera.
problem Characterize long virtual knots using geometric invariants.
method Define and analyze 1- and 2-supporting genera, and use them to filter long virtual knots. result Provide complete realizability criteria for all twelve intersection polynomials.
Paper computes Atiyah class for DG manifolds of amplitude +1.
problem Computing the Atiyah class for DG manifolds of specific amplitude.
method Computed the Atiyah class by encoding the derived intersection of sections and zero sections of vector bundles.
result Atiyah class vanishes if and only if the intersection is clean.
Minimum algebraic intersection found in hyperbolic surfaces, growing with genus.
problem Finding the minimum algebraic intersection form in hyperbolic surfaces.
method Analyzing algebraic intersection form in moduli space of hyperbolic surfaces.
result Minimum grows in the order of (logg)−2 with genus. We continue here the investigation of the relationship between the intersection of a pair of subgroups of a Kleinian group, and in particular the limit set of that intersection, and the intersection of the limit sets of the subgroups. Of specific interest is the extent to which the intersection of the limit sets being …
In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials via intersections on moduli spaces of curves. Then we show, how intersection numbers can be expressed via Hurwitz numbers. An…
This paper presents a novel framework for accurate pedestrian intent prediction at intersections. Given some prior knowledge of the curbside geometry, the presented framework can accurately predict pedestrian trajectories, even in new intersections that it has not been trained on. This is achieved by making use of the …
Study the intersection of positive closed currents using tangent currents and King's residue formula.
problem Investigate the intersection of positive closed currents in complex manifolds.
method Employ tangent currents and King's residue formula to establish a natural condition for intersection.
result Derive an integral representation of the intersection of positive closed currents.
Unified quantum invariants via intersections of embedded Lagrangians.
problem Unified quantum invariants for Uq(sl(2)). method State sum of Lagrangian intersections in configuration spaces.
result Recovery of coloured Jones and Alexander polynomials.
Positivity of intersections in 4-manifolds leads to taming symplectic structures.
problem Taming symplectic structures in almost complex 4-manifolds.
method Proof of positivity of intersections of pseudoholomorphic curves.
result Positivity of intersections is stable and leads to taming symplectic structures.
Given a hyperbolic surface §, a classic result of Birman and Series states that for each K, all complete geodesics with at most K self-intersections can only pass through a certain nowhere dense, Hausdorff dimension 1 subset of §. We define a self-intersection function for each complete geodesic, which bounds t…
The paper explores intersectional fairness in machine learning, proving bounds on it.
problem Intersectional fairness in machine learning, especially when multiple protected attributes are involved.
method Statistical analysis and bounds on intersectional fairness, leveraging marginal fairness.
result Theoretical bounds on intersectional fairness can be computed from marginal fairness and other statistical quantities.
Based on Nielsen fixed point theory and Gröbner-Shirshov basis, we obtain a simple method to compute geometric intersection numbers and self-intersection geometric numbers of loops on surfaces.
Proves a conjecture about Lagrangian intersections using new theory.
problem Homological Arnol'd conjecture on Lagrangian intersections.
method New Lagrangian Ljusternik-Schnirelman theory and fundamental quantum factorizations.
result Uniform lower bounds on Lagrangian intersection numbers.