The study develops a quadrature method for the generalized hyperbolic distribution using finite normal-mixture approximation.
problem Efficiently approximating and computing expectations under the generalized hyperbolic distribution.
method Derived a numerical quadrature from Gauss-Hermite quadrature, approximated the distribution as a finite normal variance-mean mixture.
result Accurately computed expectations and sampled generalized hyperbolic random variates using the proposed method.
The rebmix package provides R functions for random univariate and multivariate finite mixture model generation, estimation, clustering and classification. The paper is focused on multivariate normal mixture models with unrestricted variance-covariance matrices. The objective is to show how to generate datasets for a kn…
Study classifies mappings of bivariate normal densities, revealing three types with distinct geometric and statistical properties.
problem Understanding the properties of two-component bivariate normal mixtures.
method Classification via A-equivalence and statistical analysis. result Three distinct types of mappings with specific geometric and statistical properties, and upper bounds for the number of modes.
The paper presents a method for generating well-calibrated prediction intervals using quality-driven deep ensembles.
problem Generating reliable prediction intervals for regression analysis.
method A multi-objective loss function combining quality measures for prediction intervals and point estimates, with a penalty function to ensure semantic integrity and stability.
result The method produces well-calibrated prediction intervals and point estimates, capturing both aleatoric and epistemic uncertainty.
This paper considers the problem of measuring the credit risk in portfolios of loans, bonds, and other instruments subject to possible default under multi-factor models. Due to the amount of the portfolio, the heterogeneous effect of obligors, and the phenomena that default events are rare and mutually dependent, it is…
The paper proves consistency of GVI posteriors under minimal conditions.
problem Consistency of generalized variational inference posteriors.
method Proves consistency using Γ-convergence theory. result GVI posteriors are consistent and collapse to the population-optimal parameter value.
Paper proposes MWDE for estimating finite location-scale mixtures.
problem Estimating finite location-scale mixtures using MLE is problematic.
method Investigates minimum Wasserstein distance estimators (MWDE).
result MWDE is consistent and provides a numerical solution.
We develop a general method for estimating a finite mixture of non-normalized models. Here, a non-normalized model is defined to be a parametric distribution with an intractable normalization constant. Existing methods for estimating non-normalized models without computing the normalization constant are not applicable …
Mixture of Experts (MoE) is a popular framework in the fields of statistics and machine learning for modeling heterogeneity in data for regression, classification and clustering. MoE for continuous data are usually based on the normal distribution. However, it is known that for data with asymmetric behavior, heavy tail…
Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification and clustering. For continuous data which we consider here in the context of regression and cluster analysis, MoE usually use normal experts, that is, expert components following the Gaussian distribution. …
Examines learning efficiency in neural networks and related models.
problem Analyzing efficiency in deep learning models with singular learning coefficients.
method Examined learning coefficients in neural networks and three-layer neural networks with ReLU units.
result Extended results to include Softmax function, providing a broader understanding of learning efficiency.
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability, which extends from the previous work of Nguyen [2013] and Chen [1995] to address…
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C Bayes (B-)price. The result provides new insight in option pricing, among others obt…
We introduce normalized nonnegative models (NNM) for explorative data analysis. NNMs are partial convexifications of models from probability theory. We demonstrate their value at the example of item recommendation. We show that NNM-based recommender systems satisfy three criteria that all recommender systems should ide…
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family o…
The paper models Gasoil options using Brent benchmarks, improving volatility estimation.
problem Inability to directly model illiquid Gasoil options market.
method Jointly models Brent and Gasoil futures prices with a correlated Bachelier model, estimating volatility spread.
result The proposed framework accurately maps Brent implied volatilities to Gasoil implied volatilities.
Paper explores Bayes rule for Gaussian mixtures with missing data, outperforming supervised classifiers.
problem Improving classification accuracy in partially classified samples with missing data.
method Generative model framework with missing-data mechanism, Bayes rule allocation.
result Bayes rule classifier with missing-data mechanism outperforms fully supervised classifiers in various conditions.
Paper introduces Normalized Wasserstein measure for better handling of imbalanced mixture distributions.
problem Wasserstein distance fails for mixture distributions with imbalanced proportions.
method Introduce mixture proportions as optimization variables to normalize Wasserstein formulation.
result Normalized Wasserstein measure leads to significant performance gains for mixture distributions.
Paper predicts in-situ metro passenger density using smart card data.
problem Crowd management in metro systems.
method Statistical models and EM algorithm for time-dependent OD matrix and travel time cost estimation.
result Accurate prediction of in-situ passenger density for future time points.
Develops FSC for maxima nominated samples, improving classification in rare-event data.
problem Combining labeled and unlabeled data in rare-event scenarios.
method Introduces a latent representation to account for maxima nomination sampling.
result Improves classification performance in rare-event contamination mixtures.
Near-optimal tests and confidence sequences for non-parametric data.
problem Flexible statistical inference and decision-making with non-parametric data.
method Classic delayed-start normal-mixture sequential probability ratio tests with asymptotic guarantees.
result Asymptotically optimal type-I error and expected rejection time guarantees.
Paper extracts features from time series to improve forecasting accuracy.
problem Forecasting time series generated by Itô-type processes with unknown coefficients.
method Statistical adjustment of mixture-type models to extract features from time series data.
result Additional statistical features enhance time series prediction accuracy.
Link quandles are shown to be residually finite.
problem Residual finiteness of link quandles.
method Proving residual finiteness of free products of residually finite quandles with residually finite associated groups.
result Link quandles are residually finite.
Finite vector bundles over complex manifolds are trivializable via finite covers.
problem Understanding when holomorphic vector bundles over compact complex manifolds are trivializable.
method Introducing finite bundles and using finite étale covers to trivialize holomorphic vector bundles.
result Holomorphic vector bundles over compact complex manifolds are finite if and only if they admit a flat holomorphic connection with finite monodromy.
Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.
problem Existence of non-residually finite hyperbolic groups
method Direct implication
result Existence of non-residually finite rigid hyperbolic groups
Finite type and finitely generated homotopy groups for manifold automorphisms.
problem Finite type and homotopy group properties of manifold automorphism spaces.
method Analyzing the classifying space of diffeomorphism groups and using simple homotopy theory.
result The classifying space of diffeomorphism groups has finitely generated homotopy groups.
Optimal proof of finite small eigenvalues for specific geometric manifolds.
problem Proving finiteness of small eigenvalues for geometrically finite manifolds.
method Analyzing the spectrum of the Laplace operator on geometrically finite rank one locally symmetric manifolds.
result Optimal proof of finite small eigenvalues in a specific interval.
The study proves how groups can be split with limited complexity.
problem Understanding the complexity of group splittings.
method Analyzing trees with finite stabilizers and their quotient structures.
result Deformation spaces of trees have maximal complexity.
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core and Alexander quandles) is established. Further, residual…
Study of uncountable family of finitely generated groups.
problem Characterize a family of finitely generated residually finite groups.
method Examined groups of the form F2∗HF2 where F2 is a rank-2 free group and H is an infinitely generated subgroup. result Unveiled uncountable family of groups up to isomorphism.
Study on minimal submanifolds with finite curvature in Euclidean space.
problem Finite diffeomorphism types of complete immersed minimal submanifolds with finite total curvature.
method Adapted method from Chodosh, Ketover, and Maximo for hypersurfaces to submanifolds of arbitrary codimension.
result Proved finite diffeomorphism types for complete immersed minimal submanifolds with finite total curvature.
Finite rigid sets found in complex of curves for surfaces.
problem Finding finite rigid sets in curve complexes of surfaces.
method Exhaustion by finite rigid sets proved for surfaces of finite type and genus ≥3.
result Finite rigid sets exist in the non-separating curve complex of surfaces.
Study on finite entropy and energy in Kähler geometry.
problem Finite entropy and energy measures in Kähler geometry.
method Refined Moser-Trudinger inequalities for quasi-plurisubharmonic functions.
result Quasi-plurisubharmonic potentials with finite entropy belong to the finite energy class En−1n. A countable CW complex K is quasi-finite (as defined by A.Karasev) if for every finite subcomplex M of K there is a finite subcomplex e(M) such that any map f:A→M, where A is closed in a separable metric space X satisfying XτK, has an extension g:X→e(M). Levin's results imply that none of the Ei…
Paper proves finite Morse index for certain self-shrinkers.
problem Finite Morse index of self-shrinkers.
method Sufficient condition for finite Morse index of complete properly self-shrinkers.
result Proves finite Morse index for self-shrinkers with finite asymptotically conical or cylindrical ends.
Artin groups have finite stature based on vertex groups.
problem Understanding the finite stature of Artin groups.
method Criteria for finite stature based on vertex groups, applied to triangle Artin groups.
result Residual finiteness of Artin groups expanded.
The paper proves topological finiteness for surfaces with finite Willmore energy.
problem Understanding the topology of surfaces with finite Willmore energy.
method Combining Allard regularity theorem and Reifenberg's topological disk theorem.
result Topological finiteness for a class of properly immersed surfaces with finite Willmore energy.
We introduce the notion of regular finite decomposition complexity of a metric family. This generalizes Gromov's finite asymptotic dimension and is motivated by the concept of finite decomposition complexity (FDC) due to Guentner, Tessera and Yu. Regular finite decomposition complexity implies FDC and has all the perma…
In this paper we provide a criteria for geometric finiteness of Kleinian groups in general dimension. We formulate the concept of conformal finiteness for Kleinian groups in space of dimension higher than two, which generalizes the notion of analytic finiteness in dimension two. Then we extend the argument in the paper…
Category theory generalizes finite type invariants using diagrams systems.
problem Generalizing finite type invariants using category theory.
method Relating generating sets for generalized finite type theories with diagrams systems.
result Demonstrates the correspondence between finite type theories and diagrams systems.
We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition complexity and any space with asymptotic property C has finite APC-decomposition comp…
We construct the first explicit finite presentations for a family of Kähler groups with arbitrary finiteness properties, answering a question of Suciu.
Study on endomorphism and automorphism groups of specific quandles.
problem Characterizing endomorphism and automorphism groups of residually finite and profinite quandles.
method Proved properties of endomorphism monoids and automorphism groups for residually finite and profinite quandles.
result Endomorphism and automorphism groups of residually finite quandles are residually finite.
Finite volume ends found in quaternionic Kähler manifolds.
problem Existence of quaternionic Kähler manifolds with finite volume ends.
method Proof in all dimensions 4m≥4. result Existence of quaternionic Kähler manifolds with finite volume ends.
The paper shows plentiful non-homotopy finite Poincaré duality spaces.
problem The existence of non-homotopy finite Poincaré duality spaces.
method Constructing a finitely dominated Poincaré space with a non-trivial 2-divisible element in the reduced Grothendieck group.
result The existence of finitely dominated Poincaré spaces that are not homotopy finite.
The paper proves finiteness for stable Lagrangian fibrations with a given divisor.
problem Finiteness of deformation classes of hyperkähler Lagrangian fibrations.
method Survey and proof of finiteness for stable Lagrangian fibrations with a given discriminant divisor.
result Finiteness for stable Lagrangian fibrations with a given discriminant divisor.
We consider properly immersed finite topology minimal surfaces S in complete finite volume hyperbolic 3-manifolds N, and in M x S(1), where M is a complete hyperbolic surface of finite area. We prove S has finite total curvature equal to 2πtimes the Euler characteristic of S, and we describe the geometry of the ends of…
Study generalizes finiteness theorem using Lie theory.
problem Finiteness theorem in Hadwiger-Alesker theory.
method Generalization through Lie theory.
result Generalization of finiteness theorem.