The paper extends Euler class theory to measurable cocycles.
problem Understanding the structure of measurable cocycles and their cohomology.
method Constructing a parametrized Euler class in bounded cohomology and studying semicohomologous cocycles.
result The parametrized Euler class vanishes if and only if the cocycle can be lifted and admits an equivariant family of points.
Study parametrized Kähler class for cocycles on Hermitian symmetric spaces.
problem Understanding the cohomology of measurable cocycles on Hermitian symmetric spaces.
method Define and analyze parametrized Kähler class to determine cocycles up to cohomology.
result Parametrized Kähler class completely determines the cocycle up to cohomology.
Develops flexible non-parametric ACFs using B-spline kernels.
problem Flexible modelling of the autocovariance function (ACF) in time-series, spatial, and spatio-temporal analysis.
method Derives the inverse Fourier transform of B-spline spectral bases to create a general class of non-parametric ACFs.
result Provides a provably dense, flexible, and general class of non-parametric ACFs for various types of processes.
A new parametric method studies Willmore flows and energy quantization.
problem Understanding Willmore flows and their singularities.
method Parametric approach to Willmore gradient flows.
result For small-energy weak immersions, a unique solution exists.
There are various parametric models for analyzing pairwise comparison data, including the Bradley-Terry-Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this work, we study a flexible model for pairwise comparisons, under which the probabilities of outcomes are requir…
SGD converges exponentially fast in non-convex over-parametrized learning.
problem Convergence of SGD in non-convex, over-parametrized learning.
method Analysis of SGD with constant step size for non-convex functions satisfying the PL condition.
result Exponential convergence of SGD for non-convex functions satisfying the PL condition.
Local and global classifications of Einstein submanifolds in Euclidean space.
problem Classifying Einstein submanifolds in Euclidean space.
method Local and global parametric classifications with emphasis on intrinsic assumptions.
result Local and global classifications of Einstein submanifolds of codimension two.
New method to parametrize infinite Riemann surfaces with bounded triangulations.
problem Parametrizing infinite Riemann surfaces with bounded triangulations.
method Introducing bounded ideal triangulations and proving real-analyticity of the parametrization.
result Real-analytic parametrization of Teichmüller spaces for infinite surfaces with bounded triangulations.
Unified analysis for nonlinear parametric models in Bayesian optimization.
problem Limited theoretical guarantees for nonlinear parametric models in Bayesian optimization.
method Kernel-based framework for analyzing regularized nonlinear parametric models trained on adaptively collected data.
result Unified convergence guarantees for nonlinear acquisition and surrogate models.
Capillarity functionals are parameter invariant functionals defined on classes of two-dimensionals parametric surfaces in R3 as the sum of the area integral with an anisotropic term of suitable form. In the class of parametric surfaces with the topological type of S2 and with fixed volume, extremals of capillarity func…
Proposes method for eliciting non-parametric joint priors using normalizing flows.
problem Learning complex non-parametric joint priors for model parameters.
method Expert elicitation combined with normalizing flows for generative modeling.
result Framework supports elicitation of both parametric and non-parametric priors.
IB-GAN improves multivariate time series classification under imbalance.
problem Class imbalance in multivariate time series classification.
method Unified approach combining data augmentation and classification via GANs.
result Significant performance gains for under-observed classes.
Study reveals differences in label shift problem difficulty in supervised vs. unsupervised settings.
problem Label shift problem in non-parametric classification.
method Analysis of minimax rates in supervised and unsupervised settings, focusing on class conditional distributions estimation.
result A class proportion estimation approach is minimax rate-optimal in the unsupervised setting.
Weierstrass representation is a classical parameterization of minimal surfaces. However, two functions should be specified to construct the parametric form in Weierestrass representation. In this paper, we propose an explicit parametric form for a class of parametric polynomial minimal surfaces of arbitrary degree. It …
Study contact structures on lens spaces, classifying rational knots.
problem Classify rational knots in lens spaces.
method One-parametric convex surface theory to classify Legendrian and transverse rational unknots.
result Determine the contact mapping class group of lens spaces.
Let G be a group. Two elements x,y are said to be {\it z-equivalent} if their centralizers are conjugate in G. The class equation of G is the partition of G into conjugacy classes. Further decomposition of conjugacy classes into z-classes provides an important information about the internal structure of …
This paper gives a complete parametrization of the commensurability classes of totally geodesic subspaces of irreducible arithmetic quotients of Xa,b=(H2)a×(H3)b. A special case describes all Shimura subvarieties of type A1 Shimura varieties. We produce, for any $n\geq 1…
Neural networks can learn relationships that traditional models cannot.
problem Identifying factors that differentiate neural networks from traditional models.
method Proving non-identifiability of neural networks compared to smooth parametric models.
result Neural networks can learn nontrivial relationships that traditional models cannot.
We prove that the description of pencils of compatible (N x N)-metrics of constant Riemannian curvature is equivalent to a special class of integrable N-parametric deformations of quasi-Frobenius (in general, noncommutative) algebras.
New function class characterizes loss landscape of deep neural networks without over-parametrization.
problem Complex loss landscape of deep neural networks without over-parametrization.
method Proposed a novel class of functions to characterize loss landscape without over-parametrization.
result Gradient-based optimizers possess theoretical guarantees of convergence under the new function class assumption.
We show that every strongly-cyclic branched covering of a (1,1)-knot is a Dunwoody manifold. This result, together with the converse statement previously obtained by Grasselli and Mulazzani, proves that the class of Dunwoody manifolds coincides with the class of strongly-cyclic branched coverings of (1,1)-knots. As a c…
The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level α. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people h…
Generating realistic asset-class scenarios from time series and curves
problem Simulating realistic trajectories for asset classes
method Combining parametric and resampling techniques
result More coherent and realistic simulations of yield-curve dynamics
Unified parametric assumption improves convergence guarantees for nonconvex optimization.
problem Weak convergence guarantees for nonconvex optimization.
method Introducing a novel unified parametric assumption.
result Unified convergence theorem for gradient-based methods.
Graphical models for covariance matrices improve structure learning.
problem Learning structure in graphical models for covariance matrices.
method Structural learning via ℓ1-penalized loss minimization. result Method outperforms alternatives in simulations and real-world applications.
We parametrize the commensurability classes of curves on Shimura surfaces that are totally geodesic, i.e., the commensurability classes of so-called C-Fuchsian subgroups. In particular, if a Shimura surface contains one commensurability class of totally geodesic curves, it contains infinitely many.
We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong additivity properties. In the case of cobordisms between manifolds with boundary, we pr…
Study proposes a method for identifying important variables in multi-class classification problems.
problem Lack of studies on variable selection in nonparametric classification models, especially for multi-class problems.
method Sparse non-parametric density estimation approach for identifying high impacts variables.
result Proposed method identifies important variables for each class in multi-class classification problems.
We propose a discrete surface theory in R3 that unites the most prevalent versions of discrete special parametrizations. This theory encapsulates a large class of discrete surfaces given by a Lax representation and, in particular, the one-parameter associated families of constant curvature surfaces. The theo…
Compressive learning framework adapted for semi-parametric models.
problem Handling large datasets efficiently with semi-parametric models.
method Reformulate compressive learning framework to handle semi-parametric models, capturing their inherent topology and structure.
result Demonstrated robustness and efficiency of the framework in independent component analysis and subspace clustering.
New neural network models extreme value distributions with preserved shape constraints.
problem Modeling multivariate extreme value distributions with preserved shape constraints.
method d-max-decreasing neural network architecture for non-parametric calibration and generation of MEVs.
result The proposed architecture approximates the dependence structure of MEVs at parametric rate and preserves essential shape constraints.
Study optimizes estimating linear functionals from observational data without strict overlap.
problem Estimating linear functionals from observational data with strict overlap assumption violated.
method Kernel-based approach for non-asymptotic local minimax bounds.
result Achieves optimal risk for estimating linear functionals in observational data.
New method improves Bayesian inference for parametric models, robust to misspecification.
problem Inference can be untrustworthy when parametric models are wrong.
method Adaptive nonparametric corrections for parametric Bayesian models using generalized Bayes.
result The method achieves robustness and efficiency, converging fast when the parametric model is close to true.
Optimal learning for parametric prophet inequalities with exponential-type distributions
problem Learning in prophet inequalities with unknown parameters
method Confidence-based dynamic-programming policy
result Achieves optimal asymptotic competitive ratio using online observations
Unified kernels for diverse applications in math and stats.
problem Unified kernels for diverse applications in math and stats.
method Unified parametric class of kernels, characterized by Sobolev spaces.
result Unified kernels encompass various known kernels and their properties.
New MD algorithms using Tempesta logarithms for machine learning.
problem Optimization in machine learning with tailored hyperparameters.
method Developed Mirror Descent algorithms using Tempesta multi-parametric logarithms.
result Wide and flexible family of Mirror Descent and mirror-less updates.
Develops a simple method for creating private confidence intervals.
problem Creating private confidence intervals for parametric estimation.
method Parametric bootstrap approach to construct confidence intervals.
result The parametric bootstrap provides consistent and effective confidence intervals.
Study shows improper learning can outperform proper learning in misspecified models.
problem Misspecification in probabilistic prediction models.
method Investigates the performance of proper and improper learning strategies in misspecified models.
result Improper learning can achieve lower regret compared to proper learning, especially in high-dimensional settings.
DPPS uses DP priors for Bayesian non-parametric multi-arm bandits.
problem Optimizing multi-arm bandit environments with prior beliefs.
method Bayesian non-parametric algorithm based on Dirichlet Process priors.
result DPPS provides principled incorporation of prior beliefs and is optimal in Bayesian regret setup.
Continuous Sweep improves binary quantifier performance.
problem Estimating class prevalence in datasets.
method Parametric binary quantifier inspired by Median Sweep, using parametric class distributions and mean of Adjusted Count estimates.
result Continuous Sweep outperforms other quantifiers in simulations and empirical data analysis.
New Bregman chord divergences simplify distance selection in machine learning.
problem Selecting appropriate distances for machine learning tasks.
method Extend Bregman divergences with two scalar parameters.
result Simplified distance selection with asymptotic generalization of Bregman divergences.
Optimizes prediction error method for time-varying models.
problem Achieving optimal prediction error rates for time-varying models.
method Nonlinear least squares method for time-varying parametric models.
result First rate-optimal non-asymptotic analysis for time-varying models.
Motivated by families of formal moduli problems, in this note we generalize the notion of L-infinity space by allowing sheaves of L-infinity algebras over any (reasonable) nilpotent dg manifold. We discuss various examples including those coming from Lie algebroids. Given a Lie algebroid, we show that there is an L-inf…
A contractible simplicial complex is constructed that parametrizes different ways of representing a fixed one-dimensional homology class in a closed orientable surface by isotopy classes of systems of disjoint oriented simple closed curves. This is a variant on an earlier construction of Bestvina-Bux-Margalit.
Neural networks trained with backpropagation often struggle to identify classes that have been observed a small number of times. In applications where most class labels are rare, such as language modelling, this can become a performance bottleneck. One potential remedy is to augment the network with a fast-learning non…
PGF kernels analyze spherical data using generalized RBF kernels.
problem Analysis of spherical data.
method Introduced PGF kernels and a semi-parametric learning algorithm.
result PGF kernels generalize RBF kernels for spherical data.
Researchers classify cmc surfaces using Jacobi elliptic functions.
problem Classifying rotational cmc surfaces in non-Euclidean space forms.
method Lie sphere geometric description of rotational linear Weingarten surfaces.
result Explicit parametrizations of cmc surfaces in hyperbolic space.
Study compares non-parametric models for predicting medical insurance reimbursement delays.
problem Estimating the time-lapse between medical insurance reimbursement.
method Comparative study of four non-parametric regression models (KNNs, SVMs, Decision Trees, Random Forests) using R-squared metric.
result Each model's performance varies with training data size, feature space, and hyperparameters.