The paper explores fairness in machine learning by setting subgroup sample complexity bounds and advocating for human intervention.
problem Machine learning models often show different performance metrics for different subgroups, due to various factors.
method The paper presents lower bounds of subgroup sample complexity for metric-fair learning and proposes an approach using individual fairness definitions for cases where subgroup samples are insufficient.
result For a classifier to be fair, adequate subgroup population samples are necessary, and model dimensionality must align with subgroup population distributions.
A new method clusters heterogeneous subgroups for accurate causal learning.
problem Diverse causal relationships across different time spans, regions, or strategies.
method Nonlinear Causal Kernel Clustering
result Reduction in prediction error through enhanced causal learning.
A new metric MSD detects bias in datasets efficiently.
problem Detecting bias in AI systems and datasets.
method Introduced Maximum Subgroup Discrepancy (MSD) metric and a practical algorithm based on MIO.
result MSD provides a linear sample complexity for practical applications, distinguishing biases effectively.
Study shows how to reduce data needed for learning under geometric constraints.
problem Learning high-dimensional data with geometric priors.
method Spherical harmonic decompositions and kernel methods for invariance and geometric stability.
result Improvements in sample complexity by leveraging group invariance, with asymptotic behavior depending on spectral properties.
Estimates sample size for subgroup analysis in randomized experiments.
problem Determining sample size for accurate subgroup analysis.
method Turns inference problem into simultaneous inference, calculates sample size based on confidence level and margin of error.
result Allows inversion of sample size to feasible number of treatment arms or partition complexity.
The paper defines parabolic subgroups for complex braid groups and proves they form a lattice.
problem Defining and characterizing parabolic subgroups in complex braid groups.
method Introducing and studying parabolic subgroups of generalized braid groups associated with complex reflection groups.
result Parabolic subgroups form a lattice in most cases, with specific properties and conjectures about hyperbolicity.
Completes results on complex braid group parabolic subgroups.
problem Proves properties of complex braid group parabolic subgroups.
method Uses Garside groupoid structure of B(G31) to extend results.
result Proves main theorems for B(G31) parabolic subgroups.
Study of subgroups in complex hyperbolic lattice triangle groups.
problem Characterizing subgroups of finite index in complex hyperbolic lattice triangle groups.
method Explicit construction and analysis of subgroups, examination of their properties.
result Identification of neat subgroups, subgroups with positive first Betti number, and homomorphisms onto non-Abelian free groups.
Characterizes groups arising as fixed subgroups of RAAG automorphisms.
problem Identifying groups that can be fixed by finite-order automorphisms of RAAGs.
method Geometric characterisation using divisible cube complexes.
result Surface groups and commutator subgroups of RAAGs are fixed subgroups.
Study geometric properties of a complex hyperbolic group action.
problem Geometric properties of a specific modular group action.
method Explicit description of subgroups and conjugacy classes.
result Explicit description of a torsion-free subgroup of index 336.
New method combines randomization tests and flexible models for valid inference without splitting data.
problem Valid inference in randomized panel experiments with complex effect heterogeneity.
method Model-assisted randomization tests that estimate unsigned CATE from residualized outcomes.
result CATE-assisted tests control Type I error and achieve higher power than alternatives.
Extends folding techniques to study subgroups of CAT(0) cube complexes.
problem Studying subgroups of non-positively curved cube complexes.
method Folding-like techniques applied to CAT(0) cube complexes.
result Effective algorithmic representation of subgroups.
Study complex hyperbolic lattices and their subgroups, proving new finiteness properties.
problem Characterize subgroups of complex hyperbolic lattices.
method Analyzing homomorphisms and using arithmetic lattice properties.
result Deep subgroups of complex hyperbolic lattices admit homomorphisms to Z with specific kernel types.
We show that, in an Artin-Tits group of spherical type, the intersection of two parabolic subgroups is a parabolic subgroup. Moreover, we show that the set of parabolic subgroups forms a lattice with respect to inclusion. This extends to all Artin-Tits groups of spherical type a result that was previously known for bra…
New method constructs non-quasiconvex subgroups in hyperbolic groups.
problem Creating non-quasiconvex subgroups in hyperbolic groups.
method Using Stallings-like techniques on right-angled Coxeter groups (RACGs).
result Explicit examples of non-quasiconvex subgroups constructed.
Study C-Fuchsian subgroups of non-arithmetic lattices.
problem Understand structure and fundamental domains of C-Fuchsian subgroups. method General procedure to analyze structure and show fundamental domains lie on a complex geodesic.
result Fundamental domains of C-Fuchsian subgroups lie on a complex geodesic homeomorphic to the unit disk. Explicit polynomial bound found for subgroup Dehn function.
problem Finding explicit bounds on Dehn functions of subgroups of hyperbolic groups.
method Constructing a specific example of a non-hyperbolic subgroup and analyzing its Dehn function.
result Explicit polynomial upper bound n96 on the Dehn function of a non-hyperbolic subgroup. This paper classifies Ricci solitons in complex hyperbolic spaces.
problem Understanding Ricci solitons in complex hyperbolic spaces.
method Analyzing homogeneous expanding Ricci solitons as submanifolds of complex hyperbolic spaces.
result Classification and analysis of Lie subgroups with Ricci soliton induced metric in complex hyperbolic spaces.
A square complex is a 2-complex formed by gluing squares together. This article is concerned with the fundamental group Γ of certain square complexes of nonpositive curvature, related to quaternion algebras. The abelian subgroup structure of Γ is studied in some detail.
We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.
For a compact almost complex 4-manifold (M,J), we study the subgroups HJ± of H2(M,R) consisting of cohomology classes representable by J-invariant, respectively, J-anti-invariant 2-forms. If b+=1, we show that for generic almost complex structures on M, the subgroup HJ− is trivial. …
New combinatorial structures represent subgroups of surface groups, analogous to Stallings core graphs.
problem Representing subgroups of surface groups in a combinatorial way.
method Introducing core surfaces as 2-dimensional complexes made up of vertices, labeled edges, and 4g-gons.
result Core surfaces are compact when corresponding subgroups are finitely generated.
Let G be a group hyperbolic relative to a finite collection of subgroups P. Let F be the family of subgroups consisting of all the conjugates of subgroups in P, all their subgroups, and all finite subgroups. Then there is a cocompact model for EFG. This result was known…
Study new bounds on TC of spaces with subgroup inclusions.
problem Lower bounds on TC of spaces with subgroup inclusions.
method Generalizes TC results from aspherical spaces to spaces with subgroup inclusions.
result Establishes new lower bounds on sequential TCs of aspherical spaces.
Proposes a new method for subgroup analysis using optimal trees with parameter fusion.
problem Challenges of greedy heuristics and overfitting in tree-based recursive partitioning methods.
method Fused optimal causal tree method leveraging mixed integer optimization (MIO) for globally optimal partitions and parameter fusion.
result Substantial improvement in subgroup discovery accuracy and statistical efficiency.
The Cartesian subgroup in graph products of groups is studied with bounds and algorithms.
problem Understanding the structure of Cartesian subgroups in graph products of groups.
method Theory of polyhedral products, lower and upper bounds, algorithm for small presentations.
result Bounds on the number of relations and deficiency in presentations of Cartesian groups.
Proposes a method to detect anomalies in multi-subgroup normal data.
problem Anomaly detection with limited labeled anomalies and multi-subgroup normal data.
method Learn multi-normal prototypes with deep embedding clustering and contrastive learning. Estimate the likelihood of unlabeled samples being normal during training.
result Superior performance compared to state-of-the-art methods on various datasets.
A new method improves AI fairness assessment by estimating performance across intersectional subgroups.
problem Limited evaluation of AI systems across intersectional subgroups due to small sample sizes.
method Structured regression approach to disaggregated evaluation.
result Our method yields more accurate performance estimates, especially for small subgroups.
We study the complex of partial bases of a free group, which is an analogue for $\Aut(F_n)$ of the curve complex for the mapping class group. We prove that it is connected and simply connected, and we also prove that its quotient by the Torelli subgroup of $\Aut(F_n)$ is highly connected. Using these results, we give a…
We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We use completions to show that reflection subgroups are quasiconvex, as are one-end…
New normal subgroups found in mapping class groups.
problem Finding normal subgroups in mapping class groups.
method New windmill apparatus tailored to projection complexes.
result Normal subgroups isomorphic to non-free right-angled Artin groups.
We consider high-dimensional regression over subgroups of observations. Our work is motivated by biomedical problems, where disease subtypes, for example, may differ with respect to underlying regression models, but sample sizes at the subgroup-level may be limited. We focus on the case in which subgroup-specific model…
Let G be a non-elementary discrete subgroup of Sp(2,1). We show that if the sum of diagonal entries of each element of G is a complex number, then G is conjugate to a subgroup of U(2,1).
CRL approach improves understanding of heterogeneous treatment effects in complex diseases.
problem Estimating heterogeneous treatment effects in complex diseases.
method Causal rule learning (CRL) workflow consisting of rule discovery, selection, and analysis.
result CRL outperforms other methods in providing interpretable estimates of HTE.
Smooth knots in complex hyperbolic plane limit sets to chains or R-circles.
problem Characterizing limit sets of knots in complex hyperbolic geometry.
method Analyzing embeddings of knots as limit sets of discrete subgroups of PU(2, 1).
result Knots are either chains or R-circles as limit sets.
The paper studies hyperbolic quotients of projection complexes and their actions.
problem Understanding the structure and properties of quotients of projection complexes.
method Analyzing the quotient of projection complexes by normal subgroups and studying the resulting actions.
result The quotient complex is δ-hyperbolic under certain conditions, and the quotient group is acylindrically hyperbolic.
GAME improves matrix completion by considering subgroup-specific latent structures.
problem Heterogeneous data with overlapping categories, smoothing away subgroup-specific variation.
method Group-Aware Matrix Estimation (GAME) with overlapping nuclear-norm penalties.
result GAME outperforms global low-rank estimators in structured missingness regimes.
The braid group of a complex reflection group is shown to be an index d subgroup.
problem Understanding the structure of braid groups associated with complex reflection groups.
method Presented a compatible presentation for the braid group of the orbifold quotient and a tagged triangulation of the disk.
result The braid group of the complex reflection group G(d,d,n) is an index d subgroup of the braid group of the orbifold quotient. The study finds a limit on subgroup complexity in hyperbolic 3-manifold groups.
problem Understanding subgroups of bounded rank in hyperbolic 3-manifold groups.
method Proving a finiteness theorem for subgroups of bounded rank.
result Every bounded rank covering tower of closed hyperbolic 3-manifolds is a tower of finite covers associated to a fibration over a 1-orbifold.
Suppose that (W,S) is a Coxeter system with associated Artin group A and with a simplicial complex L as its nerve. We define the notion of a "standard abelian subgroup" in A. The poset of such subgroups in A is parameterized by the poset of simplices in a certain subdivision L⊘ of L. This complex o…
The intersection pattern of the translates of the limit set of a quasi-convex subgroup of a hyperbolic group can be coded in a natural incidence graph, which suggests connections with the splittings of the ambient group. A similar incidence graph exists for any subgroup of a group. We show that the disconnectedness of …
New holistic approach measures sample-level adversarial vulnerability for trustworthy systems.
problem Inherent bias in adversarial attacks across subgroups.
method Combining high-frequency feature reliance and sample-distance to decision boundary.
result Holistic approach improves adversarial vulnerability estimation and system trustworthiness.
Proposes a new method for finding non-redundant, standout subgroups in numeric datasets.
problem Mining large numbers of redundant subgroups in numeric datasets.
method Dispersion-aware problem formulation based on MDL principle for subgroup set discovery.
result Empirically demonstrates SSD++ returns outstanding subgroup lists.
Criterion for congruence RFRS towers in hyperbolic lattices.
problem Criteria for hyperbolic lattices to have congruence RFRS towers.
method Criterion based on congruence subgroups.
result Virtually fibered Bianchi groups and new RFRS Kähler groups.
Robust subgroup discovery finds non-redundant, statistically significant subgroups.
problem Finding interpretable, robust subgroups from data.
method Formulated subgroup lists for univariate and multivariate targets, used MDL principle and greedy heuristic SSD++.
result SSD++ outperforms previous methods in quality and size of subgroup lists.
New algorithm tackles subgroup fairness in AI with multiple sensitive attributes.
problem Heavy computational burdens and data sparsity in subgroup fairness for multiple sensitive attributes.
method Doubly Regressing Adversarial learning (DRAF) for subgroup fairness, focusing on subgroups with sufficient sample sizes and marginal fairness.
result DRAF algorithm reduces a surrogate fairness gap for supIPM with less computation than directly reducing supIPM.
Let S be a connected, compact and orientable surface of genus two having exactly one boundary component. We study automorphisms of the Torelli complex for S, and describe any isomorphism between finite index subgroups of the Torelli group for S. More generally, we study superinjective maps from the Torelli complex for …
Kakimizu complex of a knot is a flag simplicial complex whose vertices correspond to minimal genus Seifert surfaces and edges to disjoint pairs of such surfaces. We discuss a general setting in which one can define a similar complex. We prove that this complex is contractible, which was conjectured by Kakimizu. More ge…