Flexible links have symplectic representatives in complex projective space.
problem Existence of symplectic representatives for flexible links.
method Construction of a symplectic surface invariant under complex conjugation.
result No obstructions to finding symplectic representatives beyond classical topology.
New method for flexible tubes and structures, enabling rigid-foldability.
problem Creating flexible tubes with rigid-foldability.
method Discrete, semi-discrete, and smooth construction of surfaces (T-hedra and profile-affine surfaces).
result Unified treatment of continuous flexible structures composed of tubes.
Study on choosing points on cubic curves, answering some questions about their flexibility.
problem Determining if algebraic structures can continuously choose points on cubic plane curves.
method Analyzing the flex points and sextatic points of cubic plane curves.
result Affirmative answer for n=9 and 18, negative for infinitely many n. A new clustering method uses nonparametric smoothing to estimate cluster membership functions.
problem Clustering with flexible, nonparametric estimation.
method Nonparametric smoothing to estimate cluster membership functions without explicit modelling assumptions.
result The method automatically determines the number of clusters and level of flexibility.
Researchers relax the CVF's smoothness requirement to create more flexible flow models.
problem Challenges in constructing flexible density models due to the CVF's smoothness requirement.
method Introduce L-diffeomorphisms as generalized transformations that may violate smoothness on zero Lebesgue-measure sets. result The relaxation allows for the use of non-smooth activation functions like ReLU in residual flows.
Extends h-principle to stratified spaces using sheaf and jet theories.
problem Applying h-principle to stratified spaces.
method Developed new sheaf and bundle theories for stratified spaces, and proved the h-principle.
result Stratified continuous sheaves and homotopy fiber sheaves lead to the parametric h-principle.
New method finds smooth isometric immersions for low regularity metrics, achieving full flexibility.
problem Finding smooth isometric immersions for metrics with low Hölder regularity.
method Techniques of convex integration to find isometric immersions of low regularity.
result Achieves full flexibility, reaching C1,1− for Cr,β metrics. Dropout improves regularization in flexible models for rare features.
problem Understanding theoretical properties of dropout in generalized linear models.
method Theoretical analysis and application to adaptive smoothing with B-splines.
result Dropout prefers rare features in mean and dispersion parameters.
Improved analysis for nonconvex SGD methods with flexible sampling.
problem Finding approximately stationary points of nonconvex functions with gradient evaluations.
method Generalized SPIDER and PAGE algorithms with flexible sampling mechanisms.
result Sharper complexity bounds for optimal SGD methods in smooth nonconvex settings.
Smooth neural TPPs using B-splines for better efficiency and accuracy.
problem Efficiently modeling sequences of events in continuous time with neural networks.
method Directly parametrize the CIF as a non-negative combination of B-spline basis functions, predicting coefficients with a neural network.
result Improved computational efficiency and predictive accuracy compared to existing methods.
Identifies smooth curves for financial models.
problem Consistent term structures with flexible diffusion.
method Analyzes manifolds of curves for Heath-Jarrow-Morton models.
result Term structures cannot be affine but must be linear-rational.
Given a flexible n-gon with generic side lengths, the moduli space of its configurations in R2 as well as in R3 is a smooth manifold. It is equipped with n \textit{tautological} line bundles whose definition is motivated by M. Kontsevich's tautological bundles over M0,n. We st…
We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative procedure is developed to recover both the important covariates and the regress…
Paper develops fast low-rank approximation for smoothing splines.
problem Computational infeasibility of fitting cubic smoothing splines to large datasets.
method Low-rank approximation using eigensystem truncation.
result The method provides accurate, fast estimates with error bounds.
The paper explores rigidity and flexibility of isometric extensions with critical Hölder exponent.
problem The critical Hölder exponent in isometric extensions and its implications.
method Convex integration and construction of isometric extensions.
result The Hölder exponent $θ_0= rac12$ is critical, with extensions violating the tangential connection for $θ< rac12$.
New neural network smoothness constraints improve model performance.
problem Improving model sensitivity to input changes for better generalization and robustness.
method Exploring current smoothness constraints and proposing new flexible definitions.
result Current smoothness constraints lack flexibility and understanding of data, tasks, and learning.
Consider a smooth closed surface M of fixed genus ⩾2 with a hyperbolic metric σ of total area A. In this article, we study the behavior of geometric and dynamical characteristics (e.g., diameter, Laplace spectrum, Gaussian curvature and entropies) of nonpositively curved smooth metrics with total area …
Method approximates Lipschitz domains with smoother shapes.
problem Approximating bounded Lipschitz domains.
method Sequence of smooth, bounded domains with weak curvatures.
result Uniform isocapacitary estimates for approximating sets.
A winning method for day-ahead electricity demand forecasting during and after the COVID-19 pandemic.
problem Day-ahead electricity demand forecasting during and after the COVID-19 pandemic.
method Online forecast combination of multiple point prediction models with a holiday adjustment procedure and smoothed Bernstein Online Aggregation (BOA).
result Excellent forecasting performance, particularly due to the holiday adjustment procedure and fully adaptive smoothed BOA approach.
DNAMite creates interpretable, calibrated survival analysis models.
problem Limited interpretability in survival analysis models, especially for healthcare applications.
method Feature discretization and kernel smoothing in embedding module for flexible shape functions.
result DNAMite produces calibrated shape functions interpretable as contributions to cumulative incidence function.
Rational neural networks approximate functions more efficiently with less depth.
problem Choosing optimal nonlinear activation functions in neural networks.
method Rational activation functions with optimal bounds and efficiency proofs.
result Rational neural networks approximate smooth functions more efficiently than ReLU networks with exponentially smaller depth.
Study nonconcave portfolio choice with smooth ambiguity and Bayesian learning.
problem Nonconcave portfolio choice under smooth ambiguity and Bayesian learning.
method Developed a general framework for dynamic, non-concave asset allocation.
result Dynamic consistency achieved through a robust representation.
SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.
problem Sampling partially known densities or using gradients in probabilistic models.
method Smoothed Particle Hydrodynamics (SPH) for modeling fluid dynamics to approximate target densities.
result SPH-ParVI provides fast, flexible, scalable, and deterministic sampling for Bayesian inference and generative models.
We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach provides a flexible framework for incorporating feature similarity or temporal information present in data sets, via non-parametric kernel sm…
Classifies nets with area-preserving transformations into two types.
problem Classifying nets with area-preserving transformations.
method Classification using Combescure transformations and isotropic metric duality.
result Found two classes of nets: cone nets and Koenigs nets.
Flexible spatial models improve predictive performance over nonstationary alternatives.
problem Improving predictive performance in nonstationary spatial modeling.
method Introduces a modular parametric covariance function that extends nonstationary spatial models.
result The proposed covariance function outperforms nonparametric methods in predictive performance.
The Serre-Swan theorem in differential geometry establishes an equivalence between the category of smooth vector bundles over a smooth compact manifold and the category of finitely generated projective modules over the unital ring of smooth functions. This theorem is here generalized to manifolds of bounded geometry. I…
Develops wavelet-based neural network approximation theory.
problem Analyzing neural network approximation capabilities over various activation functions.
method Wavelet frame theory on spaces of homogeneous type, sufficient conditions for approximation, error estimates.
result Derives sufficient conditions for neural networks to approximate any functions in a given space, including non-smooth activations.
We present power low rank ensembles (PLRE), a flexible framework for n-gram language modeling where ensembles of low rank matrices and tensors are used to obtain smoothed probability estimates of words in context. Our method can be understood as a generalization of n-gram modeling to non-integer n, and includes standar…
Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.
problem Efficiently solving ordinary differential equations (ODEs) with reduced computational cost.
method Formulated a parallel-in-time probabilistic numerical ODE solver using time-parallel formulation of iterated extended Kalman smoothers.
result Reduces span cost from linear to logarithmic in the number of time steps.
Riemannian flows model curved spaces better.
problem Normalizing flows misspecified on curved spaces.
method Riemannian continuous normalizing flows using ODE solutions.
result Improves modeling on spheres, torii, and hyperbolic spaces.
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly incorporates row and column features, smoothing kernels, and other sources of sid…
Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable models of time series and to forecast future values. Despite its popularity, expon…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired ma…
A new method constructs smooth, arbitrage-free option surfaces efficiently.
problem Creating smooth, arbitrage-free option surfaces efficiently.
method Non-parametric approach using strictly positive 'discrete local volatility' variables.
result First construction of smooth, strictly arbitrage-free option price surfaces.
Researchers describe isometric deformations of T-hedra and T-surfaces.
problem Understanding the isometric deformations of discrete and smooth T-surfaces.
method Synthetic and analytic descriptions of T-hedra and T-surfaces, providing parametrizations of isometric deformations.
result Explicit parametrization of isometric deformations of T-hedra and T-surfaces.
Improved sampling guarantees for underdamped Langevin Monte Carlo without restrictive assumptions.
problem Sampling from unnormalized densities with improved guarantees and acceleration.
method Novel analysis relaxing assumptions on log-Sobolev inequality and Hessian smoothness, using Rényi discretization bounds.
result First KL divergence guarantees for ULMC without Hessian smoothness under strong log-concavity.
Forest-guided smoothing uses random forest outputs for interpretable local smoothers.
problem Creating interpretable local smoothers from complex random forest outputs.
method Uses random forest outputs to define spatially adaptive bandwidth matrices for a linear smoother.
result Improves interpretability and applicability of random forest outputs for various analyses.
Flexible framework for transfer learning with optimal rates.
problem Inference about a target population using related source data.
method Adaptive transfer learning framework allowing covariate-dependent relationships.
result Achieves minimax optimal rates of convergence by adapting to transfer relationship.
Smoothing graphons improve link prediction in Bayesian SBM without increasing computational complexity.
problem Accurate modeling of exchangeable relational data with flexible and computationally efficient graphons.
method Introducing smoothing procedures to piecewise-constant graphons to create smoothing graphons, which allow continuous intensity values for relations.
result Smoothing graphons improve AUC and precision for link prediction in real-world data sets.
NAS-X improves inference and model learning for SLVMs.
problem Challenges in analytic inference and model learning for flexible SLVMs.
method NAS-X combines reweighted wake-sleep and smoothing sequential Monte Carlo.
result NAS-X provides low-bias and low-variance gradient estimates.
GPCDL uses Gaussian Processes to learn smooth templates from data.
problem Lack of smoothness in learned templates leads to overfitting and poor predictive performance.
method GPCDL incorporates Gaussian Process priors to enforce smoothness in the learned templates.
result GPCDL outperforms unregularized CDL in accuracy and predictive performance across various SNRs and applications.
We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed algorithm is adjustable to various levels of communication cost, delays, machines compu…
Neural ODEs extended to manifolds for flexible sampling.
problem Sampling from complex multimodal distributions on non-trivial topologies.
method Extending Neural ODEs to smooth manifolds using vector fields.
result A general methodology for building normalizing flows on manifolds.
The paper examines Gaussian process means under misspecified likelihoods and smoothness.
problem Accuracy of Gaussian process approximations under misspecified smoothness and likelihood.
method Analysis of Gaussian process properties under misspecified conditions.
result The accuracy of Gaussian process approximations is influenced by experimental design and kernel choice.
Multiple generalized additive models (GAMs) are a type of distributional regression wherein parameters of probability distributions depend on predictors through smooth functions, with selection of the degree of smoothness via L2 regularization. Multiple GAMs allow finer statistical inference by incorporating explana…
In this paper, we focus on solving an important class of nonconvex optimization problems which includes many problems for example signal processing over a networked multi-agent system and distributed learning over networks. Motivated by many applications in which the local objective function is the sum of smooth but po…
Researchers prove spaces of positive scalar curvature metrics are contractible with symmetry.
problem Contractibility of spaces of invariant positive scalar curvature metrics.
method Combining equivariant Morse theory with conformal deformations and local flexibility properties.
result Spaces of invariant positive scalar curvature metrics are contractible.