This paper introduces a family of local feature aggregation functions and a novel method to estimate their parameters, such that they generate optimal representations for classification (or any task that can be expressed as a cost function minimization problem). To achieve that, we compose the local feature aggregation…
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48 results for “functional localization”
New method calibrates local volatility models to marginal distributions.
problem Calibrating local volatility models to specific marginal distributions.
method Inspired by volatility interpolation, constructs time-homogeneous or continuous local volatility functions.
result Efficient numerical algorithms for constructing local volatility functions.
Local gap theorem for Ricci shrinkers ensures flatness if certain functionals are close to zero.
problem Understanding the global geometry of Ricci shrinkers from local information.
method Proving a local gap theorem using the local -functional.
result Ricci shrinkers are flat if the local -functional is close to zero.
Deep neural networks perform well on local tasks but struggle with global tasks.
problem Understanding the limitations of overparameterized deep neural networks in learning global functions.
method Introduced -local and -global functions to study the interplay between depth and function locality.
result Depth is beneficial for learning local functions but detrimental to learning global functions.
New GP model estimates piecewise continuous functions.
problem Piecewise continuous regression functions in scientific and engineering applications.
method Local Gaussian process model with partitioned local data and joint estimation of boundaries.
result Superior performance over conventional GP models in estimating piecewise regression functions.
funLOCI identifies clusters in functional data.
problem Identifying similar behavior in functional data.
method Divisive hierarchical clustering with additive model.
result funLOCI reduces the number of local clusters.
This paper describes another extension of the Local Variance Gamma model originally proposed by P. Carr in 2008, and then further elaborated on by Carr and Nadtochiy, 2017 (CN2017), and Carr and Itkin, 2018 (CI2018). As compared with the latest version of the model developed in CI2018 and called the ELVG (the Expanded …
Local gluingmath.SG
Local gluing connects flow lines in finite time intervals.
problem Connecting flow lines in finite time intervals.
method Functional analytic approach to define local gluing map.
result Explicit construction of local gluing map in Euclidean case; intricate construction in non-Euclidean case.
Locally Sasakian Manifoldsmath.DG
We show that every Sasakian manifold in dimension is locally generated by a free real function of variables. This function is a Sasakian analogue of the Kähler potential for Kähler geometry. It is also shown that every locally Sasakian-Einstein manifold in dimensions is generated by a locally Kähler-…
Localized diffusion models reduce training complexity by exploiting low-dimensional structure.
problem Training diffusion models is computationally expensive due to the curse of dimensionality.
method Localized neural networks and localized score matching loss to estimate low-dimensional score functions.
result Localized diffusion models can circumvent the curse of dimensionality with reduced sample complexity.
This study improves estimation of locally stationary functional time series using NW method.
problem Accurately capturing time-dependence in locally stationary functional time series with time-varying covariates.
method Nadaraya-Watson (NW) estimation procedure for the conditional distribution of LSFTS.
result Established convergence rates of NW estimator for LSFTS with respect to Wasserstein distance.
The paper finds local minimizers for obstacle avoidance on curved spaces.
problem Finding optimal paths on curved spaces avoiding obstacles.
method Minimizing an action functional with bi-Jacobi fields and biconjugate points.
result Local minimizers are classified into two categories with local uniqueness results.
Paper introduces P-sensitive functions and their applications in robust optimization and financial models.
problem Developing robust models for financial and optimization problems under uncertainty.
method Introducing P-sensitive functions and their localization representations, applying to optimization and financial models.
result P-sensitive functions are precisely those that can be localized, providing a new perspective on robust modeling.
We give a proof of Ilmanen's lemma, which asserts that between a locally semi-convex and a locally semi-concave function it is possible to find a C function.
Universal locally univalent functions and universal conformal metrics with constant curvaturemath.CV
We prove Runge-type theorems and universality results for locally univalent holomorphic and meromorphic functions. Refining a result of M. Heins, we also show that there is a universal bounded locally univalent function on the unit disk. These results are used to prove that on any hyperbolic simply connected plane doma…
We study local Lie algebras of pairs of functions which generate infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds.
Global optimization finds applications in a wide range of real world problems. The multi-start methods are a popular class of global optimization techniques, which are based on the ideas of conducting local searches at multiple starting points. In this work we propose a new multi-start algorithm where the starting poin…
We study the Selberg zeta and the theta function associated to bundles over even-dimensional locally symmetric spaces of rank one.
Classifies Kähler metrics with constant holomorphic curvature.
problem Classifying Kähler metrics with constant holomorphic sectional curvature.
method Exploiting the geometry of the bundle of 1-jets of holomorphic functions.
result Local classification of Kähler metrics with constant holomorphic sectional curvature.
The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian …
Using the reformulation in divergence form of the Euler-Lagrange equation for the Willmore functional as it was developed in "Analysis of the Willmore Functional" by T. Riviere (Invent. Math. 174), we study the limit of a local Palais-Smale sequence of weak Willmore immersions with locally square-integrable second fund…
Zeta functions for non-unitary twists are shown to have analytic continuation.
problem Analytic continuation of zeta functions for non-unitary twists.
method Analytic continuation for compact locally-symmetric spaces with non-unitary twists.
result Zeta functions admit analytic continuation as meromorphic functions.
We study the local volatility function in the Foreign Exchange market where both domestic and foreign interest rates are stochastic. This model is suitable to price long-dated FX derivatives. We derive the local volatility function and obtain several results that can be used for the calibration of this local volatility…
The paper details local forms of morphisms in colored supermanifolds.
problem Understanding local forms of morphisms in colored supermanifolds.
method Detailed account of -differential calculus and local theorems.
result Detailed insights into local forms of morphisms in colored supermanifolds.
We construct infinite families of closed hyperbolic surfaces that are local maxima for the systole function on their respective moduli spaces. The systole takes values along a linearly divergent sequence at these local maxima. The only surface corresponding to is the Bolza surface i…
It is shown that locally conformally flat Lorentzian gradient Ricci solitons are locally isometric to a Robertson-Walker warped product, if the gradient of the potential function is non null, and to a plane wave, if the gradient of the potential function is null. The latter gradient Ricci solitons are necessarily stead…
Study examines surfaces with bounded fractional mean curvature, proving control over local parametrization.
problem Understanding surfaces with bounded fractional mean curvature.
method Investigates bounded L^p-norm of fractional mean curvature, proving control over local parametrization.
result Proves control over local parametrization, leading to lower Ahlfors-regularity, weak Michael-Simon type inequality, and stability application.
LSH methods extend to function spaces for efficient similarity search.
problem Efficient similarity search in function spaces.
method Locality-sensitive hashing (LSH) extended to spaces using function approximation or Monte Carlo techniques.
result An LSH family for Wasserstein distance over continuous probability distributions.
Proves regularity of extremal function on compact Kähler manifolds.
problem Regularity of extremal function on compact Kähler manifolds.
method Local property analysis and equivalence of continuity and Hölder continuity.
result Equivalence of classical notions of local -regularity and locally Hölder continuous property.
Constructs a map with prescribed local Lipschitz constants on a subset of a manifold.
problem Creating a Lipschitz map with specific local Lipschitz constants on a subset of a manifold.
method Constructs a Lipschitz map that matches a given map on a subset and has a local Lipschitz constant defined by a continuous function.
result A Lipschitz map can be constructed with a local Lipschitz constant prescribed by a continuous function.
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
problem Creating an arbitrage-free interpolation for option pricing models.
method Generalizing the local variance gamma model to a piecewise quadratic local variance function.
result The quadratic model results in an arbitrage-free interpolation of class C3, reducing knots and computational cost.
Relative cup-length defined for non-Morse functions on manifolds.
problem Defining a lower bound on critical points of non-Morse functions.
method Using local Morse cohomology and cohomology of isolating neighborhoods.
result A lower bound on critical points stronger than absolute cup-length.
Rationality of conformally invariant local correlation functions on compactified Minkowski spacehep-th
Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification o…
Gradients help find global optima in complex functions.
problem Finding global optima in functions with many local minima.
method A principle for generating search directions from non-local quadratic approximants based on gradients.
result The proposed algorithm and CMA-ES perform better than random reinitialized BFGS.
Develops a functional generalization of Eldan's stochastic localization for optimization and privacy.
problem Sampling under non-Euclidean geometries and optimization in differential privacy.
method Functional generalization of Eldan's stochastic localization, incorporating log-Laplace transform.
result Improves query complexities in zeroth-order differential private convex optimization.
Localized transfer learning improves nonparametric regression performance.
problem Improving nonparametric regression performance on target tasks.
method Localized transfer learning framework that models heterogeneity and partition covariate space into cells.
result Sharp minimax rates show local transfer mitigates the curse of dimensionality.
The existence of negatively curved metrics on locally conformally flat manifolds with boundarymath.DG
Constructs metrics with negative curvature on specific manifold types.
problem Creating negatively curved metrics on locally conformally flat manifolds.
method Using Morse functions to construct conformal metrics.
result Successfully constructs conformal metrics with negative sectional curvature.
Establishes refined singularity estimate for nonnegative n-superharmonic functions in locally conformally flat manifolds.
problem Analyzing volume growth and verifying Cohn-Vossen inequality in locally conformally flat manifolds.
method Refined singularity estimate and characterization of volume growth.
result Analytically characterizes volume growth and verifies Cohn-Vossen inequality.
Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and its function value, repeating these two procedures: (i) modeling a surrogate function; (ii) maximizing an acquisition funct…
In this paper we study the gradient estimate for positive solutions of Schrodinger equations on locally finite graph. Then we derive Harnack's inequality for positive solutions of the Schrodinger equations. We also set up some results about Green functions of the Laplacian equation on locally finite graph. Interesting …
We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions between locally convex spaces to ensure that the induced functio…
Extends Lipschitz functions while preserving local constants.
problem Extending Lipschitz functions on metric spaces while maintaining local constants.
method Extends Lipschitz functions on metric spaces while locally preserving the asymptotic Lipschitz constant.
result Sobolev spaces on metric measure spaces are invariant under isomorphism of mm-structures.
Complex valued analytic torsion and dynamical zeta function studied on locally symmetric spaces.
problem Analyzing the Ruelle dynamical zeta function on locally symmetric spaces with flat vector bundles.
method Meromorphic extension and regularisation of the dynamical zeta function, relating it to the complex valued analytic torsion.
result The leading term of the dynamical zeta function at zero is related to the regularised determinant of the flat Laplacian.
Large bundles of myelinated axons, called white matter, anatomically connect disparate brain regions together and compose the structural core of the human connectome. We recently proposed a method of measuring the local integrity along the length of each white matter fascicle, termed the local connectome. If communicat…
The paper introduces a method to learn local maxima from unlabeled data.
problem Learning local maxima from unlabeled data.
method Two functions are learned: a set indicator c and a comparator function h. Loss terms ensure all points are local maxima.
result The method provides a more efficient alternative to conventional classification and outperforms one-class classification in anomaly detection.
New subharmonicity concept proves conjecture on Riemannian manifolds.
problem Proving positivity of solutions to a specific PDE on Riemannian manifolds.
method Introducing local -shift defectivity and studying it on locally smoothing spaces.
result Proof of Braverman, Milatovic, Shubin conjecture on positivity of solutions.
This work is a further study on the Generalized Constraint Neural Network (GCNN) model [1], [2]. Two challenges are encountered in the study, that is, to embed any type of prior information and to select its imposing schemes. The work focuses on the second challenge and studies a new constraint imposing scheme for equa…
The paper develops predictors for functional data on manifolds.
problem Functional data prediction on time-varying manifolds.
method Least-squares local linear Fréchet curve predictor and weighted Fréchet mean approach.
result Asymptotical optimality of the proposed predictors.