A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The distributional category bounds manifold invariants and imposes constraints.
New method detects novel node categories in graphs with distribution shifts.
The paper defines a new metric space invariant and computes it for various manifolds.
New probabilistic invariants bound classical topological complexity and category.
A new sampling method balances multi-label datasets by preserving category frequency order.
We continue the program of structural differential geometry that begins with the notion of a tangent category, an axiomatization of structural aspects of the tangent functor on the category of smooth manifolds. In classical geometry, having an affine structure on a manifold is equivalent to having a flat torsion-free c…
Study proves topological complexity and LS-category inequalities for specific groups and manifolds.
We empirically investigate distributions of individual consumption expenditure f or four commodity categories conditional on fixed income levels. The data stems from the Family Expenditure Survey carried out annually in the United Kingdom. W e use graphical techniques to test for normality and lognormality of these dis…
Quantum invariant derived from ternary cohomology of self-distributive structures.
The paper develops a framework for abstracting causal models using category theory.
Analytic proof for minimal rank Sard conjecture.
We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provi…
The Wallenius distribution is a generalisation of the Hypergeometric distribution where weights are assigned to balls of different colours. This naturally defines a model for ranking categories which can be used for classification purposes. Since, in general, the resulting likelihood is not analytically available, we a…
In this paper, we introduce a category of graded commutative rings with certain algebraic morphisms, to investigate the cobordism category of plumbed 3-manifolds. In particular, we define a non-associative distributive algebra that gives necessary conditions for an abstract morphism between the homologies of two plumbe…
SessionPath improves category suggestions in type-ahead search.
Adversarial MoE learns category-specific models for product search.
The crowdsourcing scenarios are a good example of having a probability distribution over some categories showing what the people in a global perspective thinks. Learn a predictive model of this probability distribution can be of much more valuable that learn only a discriminative model that gives the most likely catego…
The main contribution of this article is a new prior distribution over directed acyclic graphs, which gives larger weight to sparse graphs. This distribution is intended for structured Bayesian networks, where the structure is given by an ordered block model. That is, the nodes of the graph are objects which fall into …
Ehresmann connections in tangent categories
Reflective of income and wealth distributions, philanthropic gifting appears to follow an approximate power-law size distribution as measured by the size of gifts received by individual institutions. We explore the ecology of gifting by analysing data sets of individual gifts for a diverse group of institutions dedicat…
The paper proves Weyl projective rigidity for sub-Riemannian metrics and shows genericity of such metrics.
Prototype-based memory network learns visual categories from unlabeled data.
Neural networks classify OOD images by their nearest neighbor in training data.
New TC variant dTC better fits motion planning for some systems.
Heaps are para-associative ternary operations bijectively exemplified by groups via the operation . They are also ternary self-distributive, and have a diagrammatic interpretation in terms of framed links. Motivated by these properties, we define para-associative and heap cohomology theories…
In this paper, we model dependence between operational risks by allowing risk profiles to evolve stochastically in time and to be dependent. This allows for a flexible correlation structure where the dependence between frequencies of different risk categories and between severities of different risk categories as well …
Develops a category-theoretic approach to interpret conformal prediction.
Study examines cyber losses across sectors, finds high severity and frequency.
The paper constructs Yang-Baxter solutions using categorical augmented racks.
Controversies around race and machine learning have sparked debate among computer scientists over how to design machine learning systems that guarantee fairness. These debates rarely engage with how racial identity is embedded in our social experience, making for sociological and psychological complexity. This complexi…
Given a dataset of careers and incomes, how large a difference of income between any pair of careers would be? Given a dataset of travel time records, how long do we need to spend more when choosing a public transportation mode instead of to travel? In this paper, we propose a framework that is able to infer or…
This paper proposes a multi-layer neural network structure for few-shot image recognition of novel categories. The proposed multi-layer neural network architecture encodes transferable knowledge extracted from a large annotated dataset of base categories. This architecture is then applied to novel categories containing…
We propose a method based on finite mixture models for classifying a set of observations into number of different categories. In order to demonstrate the method, we show how the component densities for the mixture model can be derived by using the maximum entropy method in conjunction with conservation of Pythagorean m…
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (…
This paper improves operational risk modeling by selecting better loss severity distributions.
We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah sequences associated to transversal tangential distributions.
We show that a generative random field model, which we call generative ConvNet, can be derived from the commonly used discriminative ConvNet, by assuming a ConvNet for multi-category classification and assuming one of the categories is a base category generated by a reference distribution. If we further assume that the…
Understanding urban growth is one with understanding how society evolves to satisfy the needs of its individuals in sharing a common space and adapting to the territory. We propose here a quantitative analysis of the historical development of a large urban area by investigating the spatial distribution and the age of c…
Studies amenable category's monotonicity and its relation to topological complexity.
Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial issue in numerous modelling problems, particularly in the fields of biology and e…
Functor connects symplectic and contact structures via cutting and blowups.
To each oriented surface S, we associate a differential graded category Ko(S). The homotopy category Ho(Ko(S)) is a triangulated category which satisfies properties akin to those of the contact categories studied by K. Honda. These categories are also related to the algebraic contact categories of Y. Tian and to the bo…
This paper benchmarks OoDD methods for medical imaging.
Estimates unknown population sizes using the hypergeometric distribution.
Local logarithmic export distributions show non-zero skewness that changes with exporter and destination characteristics.
Formulates a new connection between topological and geometric categories.
Generative model for high-dimensional categorical data using Gaussian-Dirichlet fields.
We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.