We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the simplest type of LSVMs called Local Linear Support Vector Machines (LLSVMs). For…
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48 results for “local formulæ”
New optimization for federated learning with local models.
problem Training models with private data from multiple devices.
method Proposes a new optimization formulation and efficient SGD variants.
result Local steps can improve communication for heterogeneous data.
Formula for sections on complex manifolds with non-isolated components.
problem Localization of sections on complex manifolds with non-isolated zero varieties.
method Logarithmic Bott localization formula, current-theoretic formulation.
result Established a formula for sections on compact complex manifolds with non-isolated components.
We formulate the theory of nearly autoparallel maps (generalizing conformal transforms) of locally anisotropic spaces and define the nearly autoparallel integration as the inverse operation to both covariant derivation and deformation of connections by nearly autoparallel maps. By using this geometric formalism we cons…
It is well known that mean-variance portfolio selection is a time-inconsistent optimal control problem in the sense that it does not satisfy Bellman's optimality principle and therefore the usual dynamic programming approach fails. We develop a time- consistent formulation of this problem, which is based on a local not…
Developed a new symmetric hyperbolic formulation for Einstein-Yang-Mills system.
problem Future stability of solutions of the Einstein-Yang-Mills system with arbitrary dimension.
method Tensorial symmetric hyperbolic formulation and local well-posedness for Cauchy problem.
result Established local well-posedness for the Cauchy problem of EYM equations in the temporal gauge.
The notion of local equivalence relation on a topological space is generalised to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation of a monodromy principle on the extendibility of local Lie morphisms.
We formulate a conjectural Lefschetz formula for locally symmetric spaces of finite volume. The formula can be verified in the compact case and for Riemann surfaces.
Our main aim is to associate a holonomy Lie groupoid to the connective structure of an abelian gerbe. The construction has analogies with a procedure for the holonomy Lie groupoid of a foliation, in using a locally Lie groupoid and a globalisation procedure. We show that path connections and 2-holonomy on line bundles …
Gaussian process regression loses locality in high dimensions, affecting molecular energy surface fitting.
problem Loss of locality in high-dimensional Gaussian process regression.
method Analysis of Matern family kernels and multi-zeta basis functions.
result The property of locality disappears in high dimensions, impacting regression quality.
We extend Dupire's formula for stochastic interest rates and local volatility.
problem Deriving formulas for stochastic interest rates and local volatility.
method Generalizations of Dupire's formula for stochastic drift and local volatility.
result Validated the limits of the generalized Dupire formulae for specific cases.
This paper proposes an in-depth re-thinking of neural computation that parallels apparently unrelated laws of physics, that are formulated in the variational framework of the least action principle. The theory holds for neural networks that are also based on any digraph, and the resulting computational scheme exhibits …
A general approach to formulation of supergravity in higher order anisotropic superspaces (containing as particular cases different supersymmetric extensions and prolongations of Riemann, Finsler, Lagrange and Kaluza--Klein spaces) is given. We analyze three models of locally anisotropic supergravity.
We define Radon transform and its inverse on the two-dimensional anti-de Sitter space over local fields using a novel construction through a quadratic equation over the local field. We show that the holographic bulk reconstruction of quantum fields in this space can be formulated as the inverse Radon transform, general…
The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the knowledge of vanilla option prices for a continuum of strikes and maturities that…
The problem of multi-speaker localization is formulated as a multi-class multi-label classification problem, which is solved using a convolutional neural network (CNN) based source localization method. Utilizing the common assumption of disjoint speaker activities, we propose a novel method to train the CNN using synth…
We prove that the results regarding the Isoperimetric inequality and Cheeger constant formulated in terms of the Minkowski content, obtained by the authors in previous papers in the framework of essentially non-branching metric measure spaces verifying the local curvature dimension condition, also hold in the stronger …
We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to the case of regular local realizations. A reasonable classification problem for general realizations is rigorously formulated and an algori…
A new dynamical formulation of log-PCA captures local principal modes of geodesic variations.
problem Learning principal variations of random probability measures under Wasserstein geometry.
method Introducing a new dynamical formulation of log-PCA as a variational approach.
result Deriving a general statistical convergence rate for empirical WT-PCA.
In this paper, we study a semi-martingale optimal transport problem and its application to the calibration of Local-Stochastic Volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial and final time, we optimise our cost function given the prices of a finite number…
This paper surveys recent progress on issues related to the Bartnik quasi-local mass . In addition, we formulate a number of new problems and conjectures regarding foundational properties of the mass . This work is dedicated with pleasure to Robert Bartnik in honor of his 60th birthday.
Unified federated learning via GTV minimization.
problem Training local models for decentralized datasets with network structure.
method Formulated federated learning as GTV minimization, developed a decentralized algorithm.
result Upper bound on local model parameters deviation, revealing conditions for pooling homogeneous datasets.
Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.
problem Deriving and generalizing the Selberg trace formula.
method Supersymmetric localization principle and path integral derivation.
result Derives Selberg trace formula on arbitrary compact Riemann surfaces and generic compact locally symmetric spaces.
On Local Heat Kernelmath-ph
The paper studies local heat kernel properties on smooth manifolds.
problem Understanding heat kernel properties in open convex sets of smooth Riemannian manifolds.
method Utilizes path integral formulation to investigate properties like uniqueness, symmetry, and asymptotics.
result Uniqueness and symmetry of Seeley-DeWitt coefficients are established.
Study examines how Lorentz transformations affect foliations in spacetime.
problem Understanding foliations and their relation to observers under Lorentz transformations.
method Exploration of kinematic characteristics of timelike congruences (observers) and their relation to foliations.
result Local Lorentz transformations impact the existence of transversal foliations.
Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FBSDEs. In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives, including options and swaptions, with XVA under the flexible dynamics of a local…
Paper proposes a new method for joint feature selection and graph learning.
problem Previous methods suffer from neglecting joint formulation and lack of graph learning.
method Formulates multi-view feature selection with orthogonal decomposition, incorporates cross-space locality preservation, and uses a unified objective function for simultaneous learning.
result Demonstrates superior performance in multi-view feature selection and graph learning tasks.
Localized big bang singularities found without background solutions.
problem Proving localized big bang formation without proximity to background solutions.
method Introducing a new foliation by spacelike hypersurfaces and a time function to synchronize and stabilize the singularity.
result Maximally globally hyperbolic developments have local quiescent big bang singularities with curvature blow-up.
Extends partitioned local depth concept with probabilistic considerations.
problem Uncertain, variable, and conflicting information in data.
method Partitioned local depth with probabilistic concepts of local relevance and support division.
result Extends original ideas to handle uncertain data.
We present a local formulation for 2D Discrete Exterior Calculus (DEC) similar to that of the Finite Element Method (FEM), which allows a natural treatment of material heterogeneity (element by element). It also allows us to deduce, in a robust manner, anisotropic fluxes and the DEC discretization of the pullback of 1-…
Proposes a new optimization method for local graph clustering.
problem Local graph clustering and community detection.
method Convex optimization with p-norm network flow.
result Achieves quadratic approximation of conductance for p=2 and constant factor approximation for p→∞.
We formulate simple assumptions, implying the Robbins-Monro conditions for the -learning algorithm with the local learning rate, depending on the number of visits of a particular state-action pair (local clock) and the number of iteration (global clock). It is assumed that the Markov decision process is communicatin…
This paper is the third of the series concerning the localization of the index of Dirac-type operators. In our previous papers we gave a formulation of index of Dirac-type operators on open manifolds under some geometric setting, whose typical example was given by the structure of a torus fiber bundle on the ends of th…
The aim of this note is to improve upon our earlier result which translates Weyl's (curvature) formulation of Chern character of a smooth vector bundle into the language of residues. The dualized Chern character is the functional on smooth differential forms on M. In our previous paper, this functional has been express…
New classifier combines locally linear kernels for fast and accurate non-linear classification.
problem Developing a fast and accurate non-linear classifier.
method Combines locally linear classifiers using a Multiple Kernel Learning (MKL) problem with scalable MKL training for streaming kernels.
result The resulting classifier achieves high accuracy with fast inference time.
Field Theories in Physics can be formulated giving a local Lagrangian density. Locality is imposed using the infinite jet bundle. That bundle is viewed as a pro-finite dimensional smooth manifold and that point of view has been compared to different topological and Frechét structures on it. A category of local (insular…
Robust VB framework handles contamination using min-max median aggregation.
problem Handling contamination and outliers in datasets.
method Partition data into subsets, formulate robust optimization problem, use min-max median KL divergence.
result Min-max median formulation improves robustness and statistical rates.
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.
Improved local feature attributions using neighbourhood reference distributions.
problem Misleading results from global population in local model behaviour.
method Formulation of neighbourhood reference distributions and self-normalised importance sampling.
result Neighbourhood Shapley values provide meaningful sparse feature attributions.
Paper presents a new port-Hamiltonian model for vehicle manipulators.
problem Complex mechanical systems' energy flow and conservation.
method Derives port-Hamiltonian dynamics from Hamiltonian reduction theory.
result Establishes mathematical equivalence with existing formulations.
The goal of this note is to give an introduction to locally conformally symplectic and Kähler geometry. In particular, Sections 1 and 3 aim to provide the reader with enough mathematical background to appreciate this kind of geometry. The reference book for locally conformally Kähler geometry is "Locally conformal Kähl…
Develops model-free methods for event history analysis and efficient covariate adjustment.
problem Estimating treatment effects while accounting for confounding and understanding event history.
method Model-free prediction techniques, Local Covariance Measure (LCM), Debiased Outcome-adapted Propensity Estimator (DOPE), Aalen Covariance Measure (ACM).
result Demonstrates the effectiveness and robustness of the proposed methods in various settings.
Efron et al. (2001) proposed empirical Bayes formulation of the frequentist Benjamini and Hochbergs False Discovery Rate method (Benjamini and Hochberg,1995). This article attempts to unify the `two cultures' using concepts of comparison density and distribution function. We have also shown how almost all of the existi…
Paper develops a new local convexity condition for non-isolated minima in non-convex optimization.
problem Lack of theory for non-isolated minima in non-convex optimization.
method Formulates a new local convexity condition and studies SGD convergence under this condition.
result Shows SGD can converge locally under the new condition.
Investigate AR-Finsler metrics for local dual flatness and projective flatness.
problem Locally dually and projectively flat AR-Finsler metrics
method Derive necessary and sufficient conditions and a compatibility relation.
result Establish a rigidity result for AR-Finsler metrics.
We study a geometric flow where the motion of a set is driven by the mean curvature of its boundary and the normal derivative of its capacity potential. We establish local well-posedness and propose two possible weak formulations that exist after singularities.
This thesis proposes a global geometric formulation of Extended Field Theories.
problem Global understanding of Extended Field Theories remains an open problem.
method Introducing an atlas for the principal infinity-bundle, unifying metric and higher gauge field.
result Global abelian T-duality and Poisson-Lie T-duality are automatically recovered.
Local mass perspective on Bayesian inference
problem Measuring distributional discrepancy in Bayesian inference
method Introducing Mass Index and Regularised Extended KL
result Proving inequalities for comparing local small-ball masses