New theorem bounds group quotient size to subgroups index.
problem Understanding subgroup structure in hyperbolic groups.
method Proved quotient size bounds on Eilenberg-MacLane spaces.
result One-ended hyperbolic groups cannot have isomorphic finite-index subgroups.
For n at least 7 and n equal to 5, we give generating sets of size 2 for the commutator subgroup of the braid group on n strands. These generating sets are of the smallest possible cardinality. For n equal to 4 or 6, we give generating sets of size three. We also prove that the commutator subgroup of the braid …
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.
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.
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…
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.
Algorithm identifies interpretable subgroups with elevated treatment effects.
problem Estimating high-dimensional, uninterpretable CATE results.
method Rule sets summarizing CATE estimates, optimizing subgroup size and effect size.
result Frontier of Pareto optimal rule sets for subgroup identification.
Cluster algorithms are increasingly popular in biomedical research due to their compelling ability to identify discrete subgroups in data, and their increasing accessibility in mainstream software. While guidelines exist for algorithm selection and outcome evaluation, there are no firmly established ways of computing a…
Method provides statistical guarantees for identifying subgroups in ML studies.
problem Bias and noise in estimating conditional average treatment effects (CATE).
method Develops uniform confidence bands (GATES) for estimating group average treatment effects (GATEs).
result Identifies subgroups with statistical guarantees, regardless of effect size.
In this paper we prove that for suitable sequences of congruence subgroups of Bianchi groups, including the standard exhaustive sequences of a congruence subgroup, and even symmetric powers of the standard representation of Sl_2(C) the size of the torsion part in the first homology grows exponentially. This extends res…
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…
Traditional medicine typically applies one-size-fits-all treatment for the entire patient population whereas precision medicine develops tailored treatment schemes for different patient subgroups. The fact that some factors may be more significant for a specific patient subgroup motivates clinicians and medical researc…
Improved linear regression for diverse data batches.
problem Learning from multiple heterogeneous data sources.
method Gradient-based algorithm for different input distributions.
result Significant reduction in the number of required batches and sample size.
The paper explores properties of continuous actions on manifolds, proving bounds on subgroup size and fixed points.
problem Properties of continuous finite group actions on topological manifolds.
method Analyzes properties including Jordan property and almost fixed point property, proving bounds on subgroup size.
result Existence of a constant C such that for any continuous action of a finite group G on a manifold X, there is a subgroup H with [G:H] ≤ C and a fixed point.
Let G be the identity component of SO(n,1), acting linearly on a finite dimensional real vector space V. Consider a vector w_0 in V such that the stabilizer of w_0 is a symmetric subgroup of G or the stabilizer of the line Rw_0 is a parabolic subgroup of G. For any non-elementary discrete subgroup Gamma of G with w_0Ga…
Starting from the results in math.DG:1212.3161 we prove that for a given Bianchi group, certain natural coefficent modules and a lot of sequences of congruence subgroups of the size of the torsion subgroup of the first homology grows exponentially with the index (we give an explicit rate). We also prove limit multiplic…
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.
Proves a representation that separates a subgroup in RAAGs.
problem Separating a word quasiconvex subgroup in RAAGs.
method Finite dimensional representation of L that separates H in the induced Zariski topology.
result Establishes a polynomial upper bound on the size of the quotients used to separate H in L.
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.
Adapts to shifts in latent subgroup distributions without labeled target data.
problem Adapting to domain shifts when latent subgroup distributions differ.
method Uses concept and proxy variables from source domain, and unlabeled target data.
result Optimal target predictor can be identified and estimated.
In this paper we consider three arithmetic families of isospectral non-isometric Riemannian orbifolds and in each case derive an upper bound for the size of the family which is polynomial as a function of the volume of the orbifolds. The first family that we consider are those constructed by Vigneras' method. The secon…
CAPITAL algorithm identifies optimal patient subgroups for better treatment.
problem Identify maximum number of patients benefiting from better treatment.
method Constrained Policy Tree Search (CAPITAL) algorithm to find optimal subgroup selection rule (SSR).
result Maximizes the number of patients with enhanced treatment effects.
Survey on finite group actions on manifolds.
problem Understanding actions of finite groups on manifolds.
method Analyzes the restriction of actions to subgroups and considers group and manifold properties.
result Provides information on subgroup actions and their properties.
We derive a lower bound on the size of finite non-cyclic quotients of the braid group that is superexponential in the number of strands. We also derive a similar lower bound for nontrivial finite quotients of the commutator subgroup of the braid group.
Proposes a method to select features for subgroup datasets with systematic missing data.
problem Feature selection for datasets with subgroup structure and systematic missing data.
method Develops a heterogeneous graph neural network to propagate information between feature-subgroup-target variable connections.
result Demonstrates improved feature selection performance and scalability.
New methods improve subgroup analysis in trials with limited data.
problem Limited sample sizes in subgroup analyses of randomized controlled trials.
method Two TMLEs that borrow information from non-subgroup participants.
result Improved precision in subgroup-specific treatment effect estimates.
Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup of the mapping class group has a finite generating set whose size grows cubically with respect to the genus of the surface. Our main tool is a new space called the handle graph on which the Torelli group acts cocompactly.
Unified framework for fair decision-making across diverse groups.
problem Statistical brittleness in fairness testing for small subgroups.
method Size-adaptive hypothesis testing framework.
result Validated approach for interpretable, statistically rigorous decisions.
Study 2-complexes' homology properties and torsion growth.
problem Quantitative connections between 1-cycle filling inequalities and homology complexities.
method Geometric lower bounds on first homology of finite covers.
result Geometric lower bound on first homology size of finite covers.
New insights into profinite rigidity of Kleinian groups and their subgroups.
problem Characterizing profinite completions of Kleinian groups and their subgroups.
method Analyzing profinite completions and using finite index subgroups to distinguish completions.
result Profinite completions of certain subgroups of finite index in Kleinian groups are not isomorphic.
Simulation study evaluates causal ML models under confounding violations.
problem Assessing conditional exchangeability in causal machine learning models.
method Simulation study with varying confounding, sample size, and NCO structures.
result Causal ML models fail to recover true treatment effect heterogeneity under violations of conditional exchangeability.
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.
PCS-UQ framework improves uncertainty quantification for machine learning models.
problem Ensuring trustworthy uncertainty quantification for machine learning models in high-stakes domains.
method PCS-UQ framework based on Predictability, Computability, and Stability principles, integrating prediction-checking, bootstrap samples, and multiplicative calibration.
result PCS-UQ maintains target coverage while outperforming or matching conformal methods in interval width and subgroup coverage.
On geometrically finite hyperbolic manifolds Γ\Hd, including those with non-maximal rank cusps, we give upper bounds on the number N(R) of resonances of the Laplacian in disks of size R as R→∞. In particular, if the parabolic subgroups of Γ satisfy a certain Diophantine condition, the bou…
The study proves a tube theorem for complex hyperbolic manifolds.
problem Understanding the geometry of complex hyperbolic manifolds.
method Tubular neighborhood theorem and geometric combination theorem.
result Explicit estimates and bounds for tube widths in complex hyperbolic manifolds.
Optimizes subgroup selection in clinical trials.
problem Identifying regions in feature space where a regression function exceeds a threshold.
method Formulates subgroup selection as constrained optimisation, determining minimax optimal rate for regret.
result Determines the minimax optimal rate for regret in sample size and Type I error probability.
The study uses transfer learning to compare surgical outcomes across racial/ethnic subgroups.
problem Difficulty in comparing surgical outcomes due to racial/ethnic and geographic differences.
method Causal inference framework and transfer learning to incorporate data from multiple populations.
result Racial and ethnic differences in surgical outcomes are found, with non-Hispanic Black patients experiencing wide variability.
A statistical toolbox for analyzing model performance in medical imaging.
problem Analyzing model performance by patient and recording properties, especially in medical imaging.
method Selection of appropriate performance metrics, correction of multiple comparisons, and finding interesting subgroups.
result Enables rigorous assessment of model performance for potential subgroup disparities.
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.
In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is …
Regular subgroups of SL3(R) are identified and ruled out.
problem Identifying and characterizing regular subgroups of SL3(R).
method Using Kapovich–Leeb–Porti and Guichard–Wienhard divergent subgroups criteria, and Oh's results.
result Regular subgroups of SL3(R) are precisely lattices in minimal horospherical subgroups.
Study on braid group quotients by congruence subgroups.
problem Understanding the image of congruence subgroups in GL(n,Z).
method Characterization through symplectic congruence subgroups.
result Open problem solved: image of congruence subgroups in GL(n,Z).
The paper explores geometric finiteness in mapping class groups and constructs new examples of these subgroups.
problem Understanding geometric finiteness in mapping class groups and constructing new examples.
method Examined several constructions of subgroups and determined conditions for geometric finiteness.
result Provides new examples of parabolically geometrically finite and reducibly geometrically finite subgroups.
Randomized Controlled Trials (RCTs) are the gold standard for comparing the effectiveness of a new treatment to the current one (the control). Most RCTs allocate the patients to the treatment group and the control group by uniform randomization. We show that this procedure can be highly sub-optimal (in terms of learnin…
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.
Proves Congruence Subgroup Property for two types of groups.
problem Proving Congruence Subgroup Property for specific groups.
method Elementary proof of Johnson filtration and geometric subsurface inclusions.
result Proves Congruence Subgroup Property for nilpotent quotients and subsurface subgroups.
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.
Characterizes knotted subgroups of Lie groups and provides examples.
problem Defining and understanding knotted subgroups of Lie groups.
method Geometric equivalence, one-parameter subgroups, infinitesimal elements, canonical forms, spectrum analysis.
result Completely classified knotted subgroups of SL(2,R) and SL(3,R).