arXiv research

The paper analyzes the Rashomon ratio for infinite classifier families and shows its importance for choosing good classifiers.

We employ random geometric digraphs to construct semi-parametric classifiers. These data-random digraphs are from parametrized random digraph families called proximity catch digraphs (PCDs). A related geometric digraph family, class cover catch digraph (CCCD), has been used to solve the class cover problem by using its…

The article calculates the minimal model dimensions for classifying spaces of surface braid groups.

In this note, we classify Stein fillings of an infinite family of contact 3-manifolds up to diffeomorphism. Some contact 3-manifolds in this family can be obtained by Legendrian surgeries on $(S^3,ξ_{std})$ along certain Legendrian 2-bridge knots. We also classify Stein fillings, up to symplectic deformation, of an inf…

We define for a topological group G and a family of subgroups F two versions for the classifying space for the family F, the G-CW-version E_F(G) and the numerable G-space version J_F(G). They agree if G is discrete, or if G is a Lie group and each element in F compact, or if F is the family of compact subgroups. We dis…

We describe how an Ore category with a Garside family can be used to construct a classifying space for its fundamental group(s). The construction simultaneously generalizes Brady's classifying space for braid groups and the Stein--Farley complexes used for various relatives of Thompson's groups. It recovers the fact th…

We study tangential families, i.e. systems of rays emanating tangentially from given curves. We classify, up to Left-Right equivalence, stable singularities of tangential family germs (under deformations among tangential families) and we study their envelopes. We discuss applications of our results to the case of tange…

Classifies tight contact structures on surgeries of the Whitehead link.

Classifies toric dually flat manifolds into complex space forms.

Classifies Lie bialgebras using Darboux families.

Tangential families are 1-parameter families of rays emanating tangentially from smooth curves. We classify tangential family germs up to Left-Right equivalence: we prove that there are two infinite series and four sporadic simple singularities of tangential family germs (in addition to two stable singularities). We gi…

Improving the performance of classifiers is the realm of feature mapping, prototype selection, and kernel function transformations; these techniques aim for reducing the complexity, and also, improving the accuracy of models. In particular, our objective is to combine them to transform data's shape into another more co…

The paper classifies twisted torus links that are unlinks.

Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of classifiers are available, one natural question is which type of classifiers should be used given a particular classification task. We answer this question by investigating the asympto…

The paper classifies natural almost Hermitian structures on Lie groups with minimal conformal leaves.

We classify the 5-dimensional homogeneous geometries in the sense of Thurston. The present paper (part 3 of 3) classifies those in which the linear isotropy representation is nontrivial but reducible. Most of the resulting geometries are products. Some interesting examples include a countably infinite family of inequiv…

We give a normal form for families of 3-dimensional Poisson structures. This allows us to classify singularities with nonzero 1-jet and typical bifurcations. The Appendix contains corollaries on classification of families of integrable 1-forms on $R^3

New uniqueness concept for adversarial Bayes classifier.

The study classifies surfaces with specific curvature properties.

We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds with nilpotent, non-abelian fundamental group. We further classify the partially hyperbolic systems on these manifolds up to leaf conjugacy. …

We classify Riemannian surfaces admitting associated families in three dimensional homogeneous spaces with four-dimensional isometry groups and in a wide family of (semi-Riemannian) warped products, with an extra natural condition (namely, rotating structure vector field). We prove that, provided the surface is not tot…

Regulators require financial institutions to estimate counterparty default risks from liquid CDS quotes for the valuation and risk management of OTC derivatives. However, the vast majority of counterparties do not have liquid CDS quotes and need proxy CDS rates. Existing methods cannot account for counterparty-specific…

We use a geometric digraph family called class cover catch digraphs (CCCDs) to tackle the class imbalance problem in statistical classification. CCCDs provide graph theoretic solutions to the class cover problem and have been employed in classification. We assess the classification performance of CCCD classifiers by ex…

Earlier work with Robert Gompf and Abigail Thompson classified, via a natural slope indexed by the rationals, all two-component links which contain the square knot and from which $(S^1 \times S^2) \# (S^1 \times S^2)$ can be obtained by surgery. It was argued that a certain family $L_n$ of such links probably contradic…

We construct a new family of compact orbifolds with a positive self dual Einstein metric and a one-dimensional group of isometries. Together with another known family, these examples classify all 4-dimensional orbifolds that are quaternion Kaehler quotients by a torus of real Grassmannians.

Classifies knot traces with specific trisection genus limits.

The $k$-nearest neighbour ($k$-NN) classifier is one of the oldest and most important supervised learning algorithms for classifying datasets. Traditionally the Euclidean norm is used as the distance for the $k$-NN classifier. In this thesis we investigate the use of alternative distances for the $k$-NN classifier. We …

$KS$-algebra consists of expressions constructed with four kinds operations, the minimum, maximum, difference and additively homogeneous generalized means. Five families of $Z$-classifiers are investigated on binary classification tasks between English phonemes. It is shown that the classifiers are able to reflect well…

We address the question: how large is the family of complete metrics with nonnegative sectional curvature on S^2xR^3? We classify the connection metrics, and give several examples of non-connection metrics. We provide evidence that the family is small by proving some rigidity results for metrics more general than conne…

This article introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete h-principle when some auxiliary data is fixed. As a corollary, we show that Lorentz and orientable Cartan prolongations are cl…

Malware allegedly developed by nation-states, also known as advanced persistent threats (APT), are becoming more common. The task of attributing an APT to a specific nation-state or classifying it to the correct APT family is challenging for several reasons. First, each nation-state has more than a single cyber unit th…

The paper classifies singularities of plane congruences and affine distance functions.

The homogeneous affine surfaces have been classified by Opozda. They may be grouped into 3 families, which are not disjoint. The connections which arise as the Levi-Civita connection of a surface with a metric of constant Gauss curvature form one family; there are, however, two other families. For a surface in one of t…

An analytic index is defined for a family of cusp pseudodifferential operators, $P_b,$ on a fibration with fibres which are compact manifolds with boundaries, provided the family is elliptic and has invertible indicial family at the boundary. In fact there is always a perturbation $Q_b$ by a family of cusp operators of…

Classification is an important topic in statistics and machine learning with great potential in many real applications. In this paper, we investigate two popular large margin classification methods, Support Vector Machine (SVM) and Distance Weighted Discrimination (DWD), under two contexts: the high-dimensional, low-sa…

The study classifies tilings of the sphere by congruent quadrilaterals.

Novel neural network approximates exact distance for robust classification.

Recent work in model-agnostic explanations of black-box machine learning has demonstrated that interpretability of complex models does not have to come at the cost of accuracy or model flexibility. However, it is not clear what kind of explanations, such as linear models, decision trees, and rule lists, are the appropr…

Building classification models is an intrinsically practical exercise that requires many design decisions prior to deployment. We aim to provide some guidance in this decision making process. Specifically, given a classification problem with real valued attributes, we consider which classifier or family of classifiers …

Classifies symmetries of knots using group actions and orthogonal representation theory.

Derives asymptotic generalization error for large-margin classifiers.

In dimension 3 and above, Bredon cohomology gives an acurate purely algebraic description of the minimal dimension of the classifying space for actions of a group with stabilisers in any given family of subgroups. For some Coxeter groups and the family of virtually cyclic subgroups we show that the Bredon cohomological…

We show how to associate with each graph with a certain property (positivity) a family of simply connected solvable Lie groups endowed with left-invariant Riemannian metrics that are Ricci solitons (called solsolitons). We classify them up to isometry, obtaining families depending on many parameters of explicit example…

Proposes Decodable Information Bottleneck for optimal representation learning.

Constructs non-abelian G2-instantons on ALC members of B7 family.

Classifies shapes of yield curves in the Svensson family.

Researchers classify and decompose valuations on convex functions.

This paper reviews metrics to assess AI model calibration accuracy.