arXiv research

A test confirms if a local maximum is globally optimal in imaging problems.

The study finds a unique systole maximum in non-hyperelliptic surfaces.

Researchers examine global properties of a scalar curvature functional to solve the prescribed Ricci curvature problem.

Proves a principle for one-phase Bernoulli problem minimizers.

Postprocessing reduces Bayesian optimization steps for global optima.

The economy globalization measure problem is discussed. Four macroeconomic indices of twenty among the "richest" countries are examined. Four types of "distances" are calculated.Two types of networks are next constructed for each distance measure definition. It is shown that the globalization process can be best charac…

The paper studies global Yamabe flow on AF manifolds, preserving ADM mass.

Optimizes MMD learning for generative models with theoretical guarantees.

Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference, however, even for this restricted class, is in #P. We prove new formulations of deriv…

We will generalize a Maximum Principle at Infinity in the parabolic case given by De Lima [Ann. Global Anal. Geom. ${\bf 20}$, 325-343 2001] and De Lima and Meeks [Indiana Univ. Math. Journal ${\bf 53}$ 5, 1211-1223 2004], for disjoints hypersurfaces of $\mathbb{R}^{n+1}$ with bounded mean curvature without restriction…

EM algorithm converges to global max in latent Gaussian tree models.

The so called "globalization" process (i.e. the inexorable integration of markets, currencies, nation-states, technologies and the intensification of consciousness of the world as a whole) has a behavior exactly equivalent to a system that is tending to a maximum entropy state. This globalization process obeys a collec…

This paper demonstrates the usefulness and importance of the concept of honest times to financial modeling. It studies a financial market with asset prices that follow jump-diffusions with negative jumps. The central building block of the market model is its growth optimal portfolio (GOP), which maximizes the growth ra…

Study compares nodal sets of solutions to the Allen-Cahn equation.

Paper proposes quantum methods for optimizing machine learning functions.

New method improves MMD estimation without convexity assumptions.

We prove a Lorentzian splitting theorem with weakened curvature conditions.

Chow and Liu (1968) studied the problem of learning a maximumlikelihood Markov tree. We generalize their work to more complexMarkov networks by considering the problem of learning a maximumlikelihood Markov network of bounded complexity. We discuss howtree-width is in many ways the appropriate measure of complexity and…

There are a number of examples of variations of Hodge structure of maximum dimension. However, to our knowledge, those that are global on the level of the period domain are totally geodesic subspaces that arise from an orbit of a subgroup of the group of the period domain. That is, they are defined by Lie theory rather…

Study improves adversarial classification using distributionally robust models.

Bayesian networks with latent variables are characterized and their likelihoods compared.

Study proposes curvature flow model for Drosophila dorsal closure.

We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a…

Clustering stocks reduces estimation error in global minimum variance portfolio.

Gradient flow for MMD converges to optimal solution, with regularization.

Gradient descent on MMD GAN parameter space converges globally to target distribution.

The paper uses graph Laplacians and maximum principles to study learning problems on unknown manifolds.

Bayesian Optimization (BO) has become a core method for solving expensive black-box optimization problems. While much research focussed on the choice of the acquisition function, we focus on online length-scale adaption and the choice of kernel function. Instead of choosing hyperparameters in view of maximum likelihood…

The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved that if the Cauchy problem has a local solution, this solution has a unique maximal…

Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial configurations and fails to find the global optimum. On the other hand, in the field …

Study on Cheeger constant in specific hyperbolic 3-manifolds.

Closed-form solutions derived for perpetual options under insider models.

New method finds points for approximating distributions faster.

Although both systems analyzed are described through two theories apparently different (quantum mechanics and game theory) it is shown that both are analogous and thus exactly equivalents. The quantum analogue of the replicator dynamics is the von Neumann equation. Quantum mechanics could be used to explain more correc…

A new gradient flow for MMD with closed-form implementation.

New method certifies global robustness of neural networks efficiently.

MQF$^2$ forecasts multivariate quantiles globally.

This paper optimizes Bayesian acquisition functions in Gaussian Processes for better optimization.

In this paper we extend to non-compact Riemannian manifolds with boundary the use of two important tools in the geometric analysis of compact spaces, namely, the weak maximum principle for subharmonic functions and the integration by parts. The first one is a new form of the classical Ahlfors maximum principle whereas …

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance matrix, which can be computationally intensive in large dimensions. Approximate infer…

The paper solves complex control problems using neural networks.

The study identifies assets with local balance deviating from global balance to mitigate financial risk.

Global optimization approach for MAP clustering under Gaussian mixtures.

Study on ratio of intrinsic to extrinsic metrics and its relation to surface area.

Framework learns to transform majority to minority samples for balanced classification.

Emulator speeds up landslide run-out modeling sensitivity analysis.

In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and typically attains an order of magnitude or better improvement in optimization pe…

Recent results on the maximization of the charged-particle action I in a globally hyperbolic spacetime are discussed and generalized. We focus on the maximization of I over a given causal homotopy class C of curves connecting two causally related events x_0 <= x_1. Action I is proved to admit a maximum on C, and also o…