arXiv research

We present a novel subset scan method to detect if a probabilistic binary classifier has statistically significant bias -- over or under predicting the risk -- for some subgroup, and identify the characteristics of this subgroup. This form of model checking and goodness-of-fit test provides a way to interpretably detec…

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…

Proposes a method to detect anomalies in multi-subgroup normal data.

The notions of stable and Morse subgroups of finitely generated groups generalize the concept of a quasiconvex subgroup of a word-hyperbolic group. For a word-hyperbolic group $G$, Kapovich provided a partial algorithm which, on input a finite set $S$ of $G$, halts if $S$ generates a quasiconvex subgroup of $G$ and run…

We determine the Riemannian manifolds for which the group of exact volume preserving diffeomorphisms is a totally geodesic subgroup of the group of volume preserving diffeomorphisms, considering right invariant $L^2$-metrics. The same is done for the subgroup of Hamiltonian diffeomorphisms as a subgroup of the group of…

Proposes a method to identify subgroup structure and estimate covariate effects for multivariate response data.

A new metric MSD detects bias in datasets efficiently.

We detect Hilbert manifolds among isometrically homogeneous metric spaces and apply the obtained results to recognizing Hilbert manifolds among homogeneous spaces of the form G/H where G is a metrizable topological group and H is a closed balanced subgroup of G.

Let G be a finitely presented group, and let p be a prime. Then G is 'large' (respectively, 'p-large') if some normal subgroup with finite index (respectively, index a power of p) admits a non-abelian free quotient. This paper provides a variety of new methods for detecting whether G is large or p-large. These relate t…

New method detects strong calibration in ML models, even for small poorly calibrated subgroups.

GLMM trees identify subgroups with different growth patterns in longitudinal data.

The paper proposes a method to find subgroups with significant treatment effects in noisy data.

We give a short proof of the following theorem of Sang-hyun Kim: if $A(Γ)$ is a right-angled Artin group with defining graph $Γ$, then $A(Γ)$ contains a hyperbolic surface subgroup if $Γ$ contains an induced subgraph $\bar{C}_n$ for some $n \geq 5$, where $\bar{C}_n$ denotes the complement graph of an $n$-cycle. Furthe…

We introduce the (general) homotopy groups of spheres as link invariants for Brunnian-type links through the investigations on the intersection subgroup of the normal closures of the meridians of strongly nonsplittable links. The homotopy groups measure the difference between the intersection subgroup and symmetric com…

Interview study reveals considerations for designing semi-automated bias detection tools.

We study biinvariant word metrics on groups. We provide an efficient algorithm for computing the biinvariant word norm on a finitely generated free group and we construct an isometric embedding of a locally compact tree into the biinvariant Cayley graph of a nonabelian free group. We investigate the geometry of cyclic …

We show the mapping class group, CAT(0) groups, the fundamental groups of closed 3-manifolds, and certain relatively hyperbolic groups have a local-to-global property for Morse quasi-geodesics. This allows us to generalize combination theorems of Gitik for quasiconvex subgroups of hyperbolic groups to the stable subgro…

We provide new information about the structure of the abelian group of topological concordance classes of knots in $S^3$. One consequence is that there is a subgroup of infinite rank consisting entirely of knots with vanishing Casson-Gordon invariants but whose non-triviality is detected by $L^{(2)}$ signatures.

The paper breaks down AUC into cluster-level components for better model diagnostics.

Develops a new criterion for subgroup fairness in algorithmic decision support.

Simulated Bifurcation outperforms quantum machines in community detection.

We show that a non-trivial, non-central normal subgroup of the braid groups contains a braid whose closure is a hyperbolic knot with arbitrary large genus. This shows that non-faithfulness of a quantum representation implies that the corresponding quantum invariant fails to detect the unknot. The proof utilizes the Deh…

Simulation study evaluates causal ML models under confounding violations.

Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group of a closed hyperbolic surface, or Out(F_n) for n>1). We prove that, in degree 3, the bounded cohomology of G with real coefficients is infi…

New ML method detects incomplete bid-rigging cartels.

Novel strategy benchmarks observational studies against randomized trials.

CondMTL improves toxicity detection by learning group-specific representations.

Bayesian framework detects symmetries in chaotic dynamical systems.

By analyzing how the Borel regulator classes vanish on various groups related to $\mathrm{GL}(n,\mathrm{Z})$, we define three series of secondary characteristic classes for subgroups of automorphism groups of free groups. The first case is the $\mathrm{IA}$-automorphism groups and we show that our classes coincide with…

Paper proposes robust method to detect risk heterogeneity across ethnic groups.

In the monitoring of a complex electric grid, it is of paramount importance to provide operators with early warnings of anomalies detected on the network, along with a precise classification and diagnosis of the specific fault type. In this paper, we propose a novel multi-stage early warning system prototype for electr…

Geometric approach connects Burau representation to sphere metrics, identifying kernels.

We present FlipTest, a black-box technique for uncovering discrimination in classifiers. FlipTest is motivated by the intuitive question: had an individual been of a different protected status, would the model have treated them differently? Rather than relying on causal information to answer this question, FlipTest lev…

Bayesian model for cost-effectiveness analysis with subgroup discovery.

New invariant detects infinite order cabled knots.

Study shows complex K3 surfaces have infinite free abelian subgroup in their diffeomorphism group.

BICauseTree improves causal effect estimation by identifying clusters and balancing treatment allocation.

AI detects heart disease from ECGs with improved interpretability and performance.

New algorithm for biclustering with improved performance.

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 …

New invariant detects more elements in 4D diffeomorphism group.

Regular subgroups of SL3(R) are identified and ruled out.

Study on braid group quotients by congruence subgroups.

The paper explores geometric finiteness in mapping class groups and constructs new examples of these subgroups.

Proposes a new method for finding non-redundant, standout subgroups in numeric datasets.

Proves Congruence Subgroup Property for two types of groups.

New method constructs non-quasiconvex subgroups in hyperbolic groups.

Characterizes knotted subgroups of Lie groups and provides examples.