Proposes a new method for interpreting feature importance and effects in dependent feature models.
problem Challenges in interpreting feature importance when features are dependent and interactions are present.
method Conditional Subgroup Approach
result Conditional PFI and PDP estimates based on this approach often outperform existing methods.
Generic groups satisfy a chain condition for subgroups.
problem Understanding subgroup structures in generic groups.
method Proving for fixed integers m,t,k in generic m-generator t-relator groups. result Generic groups satisfy the Ascending Chain Condition for k-generated subgroups. 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.
We give several sufficient conditions for a double of a free group along a cyclic subgroup to contain a surface subgroup.
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.
Posterior conformal prediction improves prediction interval validity for subgroups.
problem Marginal and conditional prediction interval validity for subgroups.
method Modeling conditional nonconformity score distribution as a mixture of cluster distributions.
result PCP produces tighter prediction intervals, especially for well-represented clusters.
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 provides conditions for amalgamation of certain subgroups and preserves convexity properties.
problem Conditions for amalgamation of subgroups in hierarchically hyperbolic groups.
method Study of amalgamation conditions and preservation of convexity properties.
result Conditions under which amalgamation preserves hierarchical quasiconvexity and strong quasiconvexity.
For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two relatively quasiconvex subgroups Q1 and Q2 is relatively quasiconvex and isomorphic to Q1∗Q1∩Q2Q2. The main theorem extends results for quasiconvex subgroups of word-hyperbolic groups, an…
Conditions for Baumslag-Solitar subgroups in mapping class groups.
problem Characterizing Baumslag-Solitar subgroups in mapping class groups.
method Analyzing necessary and sufficient conditions for subgroup embeddings.
result Conditions for embedding BS(p,q) in Mod(Sg), including ∣p∣=∣q∣ and reducibility. The paper defines Dirichlet domains for Anosov subgroups in Lie groups.
problem Finding finite-sided Dirichlet domains for Anosov subgroups in Lie groups.
method Introducing a sufficient condition for finite-sided Dirichlet domains in semisimple Lie groups for polyhedral Finsler metrics.
result Finitely generated subgroups of semisimple Lie groups can have finite-sided Dirichlet domains under certain conditions.
The study examines conditions for symmetric and alternating subgroups in mapping class groups of surfaces.
problem Conditions for torsion elements to generate symmetric or alternating subgroups.
method Analyzes mapping class groups of surfaces, derives necessary and sufficient conditions for conjugates of torsion elements to generate symmetric or alternating subgroups.
result Symmetric or alternating subgroups cannot contain irreducible mapping classes and hyperelliptic involutions.
The study shows subgroup separability conditions for specific groups.
problem Conditions for subgroup separability in free-by-cyclic and deficiency 1 groups.
method Analyzes polynomially growing monodromy and asymptotic probability of random groups.
result Random deficiency 1 groups are not subgroup separable with positive probability.
Study subgroups of pro-p PD^3 groups, finding specific conditions.
problem Characterize subgroups of pro-p PD^3 groups. method Analyzes properties of subnormal and finitely presented subgroups.
result Conditions on subgroups of pro-p PD^3 groups. The paper proves an ascending chain condition for subgroups in hyperbolic and graph 3-manifolds.
problem Proving an ascending chain condition for subgroups in specific types of 3-manifolds.
method Uses profinite techniques and geometric proofs for hyperbolic and graph manifolds.
result Established the ascending chain condition for free subgroups of constant rank in closed hyperbolic and graph 3-manifolds.
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 extends Kobayashi's method to non-reductive subgroups for homogeneous spaces.
problem Existence of compact Clifford-Klein forms in homogeneous spaces.
method Extend Kobayashi's method to non-reductive subgroups and compare Cartan projections and non-compact dimensions.
result Examples of homogeneous spaces without compact Clifford-Klein forms.
We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group A(Γ) fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups Mod(S). In particular, such subgroups are quasiconvex in A(Γ). In addition, we identify a milder cond…
Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly disconnected). We characterise the subsurfaces which lead to virtually abelian ge…
The paper extends quasimorphisms on subgroups to larger groups.
problem Extending quasimorphisms from subgroups to larger groups.
method Provides a general sufficient condition for extendability of quasimorphisms on subgroups.
result New results for quasimorphisms on normal subgroups, including bi-Lipschitz equivalence of stable commutator length and group-theoretic Dehn filling.
New Klein-Maskit theorems for Anosov subgroups.
problem Creating new Kleinian groups from old ones.
method Analogous combination theorems for Anosov subgroups.
result Construct new Kleinian groups using old ones for Anosov subgroups.
The study characterizes subgroups of braid groups and their finite quotients.
problem Understanding the relationship between braid groups and their congruence subgroups.
method Characterization and computation of finite quotients of braid groups.
result Explicit generators and free subgroups are found for certain braid groups.
We study infinite covolume discrete subgroups of higher rank semisimple Lie groups, motivated by understanding basic properties of Anosov subgroups from various viewpoints (geometric, coarse geometric and dynamical). The class of Anosov subgroups constitutes a natural generalization of convex cocompact subgroups of ran…
Article provides conditions for embedding braid groups into mapping class groups.
problem Embedding braid groups into mapping class groups.
method Necessary and sufficient condition for embedding finite index subgroups.
result Conditions for embedding braid groups into mapping class groups.
The paper defines conditions for a free-by-free group to be hyperbolic.
problem Conditions for a free-by-free group to be relatively hyperbolic.
method Necessary and sufficient conditions involving exponentially growing automorphisms and invariant subgroup systems.
result A subgroup system can be used to construct peripheral subgroups making the extension hyperbolic.
The paper explores conditions for quasi-isometric subgroups and their filtered ends.
problem Conditions for quasi-isometric subgroups and their filtered ends.
method Exploring sufficient conditions for quasi-isometric subgroups and their filtered ends.
result If G and H are quasi-isometric groups and P is a qi-characteristic collection of subgroups of G, then there is a collection of subgroups Q of H such that (G,P) and (H,Q) are quasi-isometric pairs. The paper explores infinite metacyclic subgroups in mapping class groups of surfaces.
problem Existence and properties of infinite metacyclic subgroups in mapping class groups.
method Provided necessary and sufficient conditions for the existence of infinite metacyclic subgroups.
result Established the existence of specific infinite metacyclic subgroups and derived bounds on their periodic generators.
This paper is a study of the subgroups of the mapping class groups of Riemann surfaces, called "geometric" subgroups, corresponding to the inclusion of subsurfaces. Our analysis includes surfaces with boundary and with punctures. The centres of all the mapping class groups are calculated. We determine the kernel of inc…
The paper studies Riemannian metrics on Lie groups with specific commutator subgroups.
problem Investigating Riemannian metrics on Lie groups with commutator subgroups of dimensions 1 and 2.
method Explicitly provided Levi-Civita connection, sectional curvature, and Ricci curvature; computed necessary and sufficient conditions for Ricci solitons; characterized Ricci solitons on Lie groups with one-dimensional commutator subgroups; examined indecomposable Lie groups with two-dimensional commutator subgroups.
result Characterization of all Ricci solitons on Lie groups with one-dimensional commutator subgroups and examination of indecomposable Lie groups with two-dimensional commutator subgroups.
The paper examines random walks on metric spaces and finds commensurable subgroups.
problem Determining commensurable subgroups via stationary measures in metric spaces.
method Analyzing random walks on isometry groups of metric spaces with non-singular stationary measures.
result Subgroups generated by random walks are commensurable under mild conditions.
Geometric limits of cyclic subgroups in specific groups studied.
problem Understanding geometric limits of cyclic subgroups in SO_0(1, k+1) and SU(1, k+1).
method Construction of sequences of subgroups and analysis of their geometric limits.
result Examples of sequences with geometric limits strictly containing algebraic limits.
The study explores deformations of discrete subgroups in non-compact homogeneous spaces.
problem Addressing the proper discontinuity of discrete subgroups in non-compact homogeneous spaces.
method Classification results for deformations of standard discontinuous groups in pseudo-Riemannian homogeneous spaces.
result Conditions for local rigidity and Zariski-dense deformations in standard quotients.
In this paper, we give some necessary and sufficient conditions for a normal subgroup of an amalgamated product of groups to be finitely generated. We apply these conditions together with Stallings' fibering theorem to prove that an irreducible multilink in a homology 3-sphere fibers if and only if each of its multilin…
The paper solves conditions for metacyclic actions on surfaces, including upper bounds and subgroup classifications.
problem Conditions for metacyclic actions on surfaces and their properties.
method Derives necessary and sufficient conditions for conjugates of torsion elements to generate finite metacyclic subgroups.
result Complete solution to liftability of periodic mapping classes under finite cyclic covers, including upper bounds and subgroup classifications.
Study on subgroups' evolution in 3D Lie groups using mean curvature flow.
problem Existence of solutions to Mean Curvature Flow for 2D Lie subgroups in 3D Lie groups.
method Investigation of Lie groups with fixed left-invariant metrics, focusing on non-unimodular cases.
result Evolution of Lie subgroups is self-similar for abelian subgroups, but not for others.
ShapShift explains shifts in model predictions due to data distribution changes.
problem Prediction shifts caused by changes in input distribution.
method Subgroup Conditional Shapley Values applied to decision trees and ensembles.
result Simple, faithful, and near-complete explanations of prediction shifts across model classes.
The study finds conditions for certain groups to be dense in a specific mathematical space.
problem Conditions for linear reflection groups to be dense in a projective space.
method Analyzes necessary and sufficient conditions for Zariski-density, applies to Coxeter groups and surface subgroups.
result Establishes conditions for Zariski-dense subgroups in SLn(Z) for various n. We investigate the gauging of the Wess-Zumino term of a sigma model with boundary. We derive a set of obstructions to gauging and we interpret them as the conditions for the Wess-Zumino term to extend to a closed form in a suitable equivariant relative de Rham complex. We illustrate this with the two-dimensional sigma …
Selective regression allows abstention to improve fairness criteria.
problem Selective regression can exacerbate disparities between subgroups.
method Proposes new fairness criteria and two approaches to mitigate performance disparity.
result Proposed fairness criteria ensures performance improvement for every subgroup with reduced coverage.
We discover subgroups for Cox model survival analysis, improving model accuracy.
problem Finding interpretable subsets of data where Cox model is highly accurate.
method Developed new metrics (EPE, CRS) and algorithms to solve subgroup discovery problem.
result Our methods improve model fit and recover known nonlinearities in data.
Connected weakly irreducible not irreducible subgroups of Sp(1,n+1)⊂SO(4,4n+4) that satisfy a certain additional condition are classified. This will be used to classify connected holonomy groups of pseudo-hyper-Kählerian manifolds of index 4.
A Kleinian group Γ<Isom(H3) is called convex cocompact if any orbit of Γ in H3 is quasiconvex or, equivalently, Γ acts cocompactly on the convex hull of its limit set in ∂H3. Subgroup stability is a strong quasiconvexity condition in finitely generated groups which…
We state and prove a condition under which the strong Atiyah Conjecture carries over to subgroups. Moreover, we show that if a group satisfies the (strong) Atiyah Conjecture then any quotient with finite kernel does.
Chiseling finds valid subgroups interactively, improving on existing methods.
problem Finding valid subgroups with inferential guarantees in regression and causal inference.
method Interactive subgroup refinement with inferential validity guarantees.
result Chiseling identifies better subgroups than existing methods with inferential guarantees.
We study different notions of quasiconvexity for a subgroup H of a relatively hyperbolic group G. The first result establishes equivalent conditions for H to be relatively quasiconvex. As a corollary we obtain that the relative quasiconvexity is equivalent to the dynamical quasiconvexity. This answers to a questi…
Exact sequence results show infinite index quasiconvex subgroups in certain groups.
problem Understanding quasiconvex subgroups in specific group structures.
method Analyzing exact sequences of hyperbolic groups and their subgroups.
result Infinite index quasiconvex subgroups in G1 are quasiconvex in G under mild conditions. We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G in Mod(S) satisfies certain conditions that imply G is quasi-isometrically embedded in Mod(S), then a purely pseudo-Anosov subgroup H of …
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.