arXiv research

Simplified argument for second order estimate in quaternionic Calabi-Yau problem.

Paper derives estimates for complex Hessian equations on Hermitian manifolds.

Researchers find second-order estimates for $p$-Laplacian in RCD spaces.

Paper proposes an online covariance estimator for sketched Newton methods.

Enhances gradient estimates for Hermitian Monge-Ampère equations.

The study provides interior estimates for $Q_k$-flows and translators in $\mathbb{R}^{n+1}$.

Estimates for complex Hessian equations on Hermitian manifolds.

A first-order model for a stock market assigns to each stock a return parameter and a variance parameter that depend only on the rank of the stock. A second-order model assigns these parameters based on both the rank and the name of the stock. First- and second-order models exhibit stability properties that make them a…

Estimates for harmonic functions in curved spaces.

Second-order economic theory considers new variables to improve price volatility predictions.

Second-order methods fail to fully quantify epistemic uncertainty, leading to biased predictions.

We derive a priori second order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under some very general structure conditions. We treat both equations on closed manifolds, and the Dirichlet problem on manifolds with boundary without any geometric restrictions to the bound…

Improved algorithm finds second-order stationary points in non-convex optimization.

Develops first and second-order pseudo-mirror descent methods for nonnegative function estimation.

Paper proposes a second-order method for faster SVI convergence.

New method improves online covariance estimation for SGD.

AdamNX improves Adam's stability by adjusting its learning rate.

Estimates mass of static vacuum metrics with small Bartnik data.

New technique debiases distributed optimization, improving convergence rate.

This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.

Study shows how macroeconomic news affects intraday price and order flow dynamics.

New SGD algorithm finds critical points faster with second-order corrections.

Gradient descent and its variants are widely used in machine learning. However, oracle access of gradient may not be available in many applications, limiting the direct use of gradient descent. This paper proposes a method of estimating gradient to perform gradient descent, that converges to a stationary point for gene…

We derive a priori $C^2$ estimates for the $χ$-plurisubharmonic solutions of general complex Hessian equations with right-hand side depending on gradients.

Paper develops a TR-SSQP method for noisy optimization with heavy-tailed noise.

In stochastic gradient descent, especially for neural network training, there are currently dominating first order methods: not modeling local distance to minimum. This information required for optimal step size is provided by second order methods, however, they have many difficulties, starting with full Hessian having…

ADAHESSIAN optimizes machine learning models with adaptive second-order methods.

Second-order estimator improves continuous-time policy evaluation.

Study shows Kähler-Einstein metric singularities linked to curvature.

Estimates for complex equations on manifolds derived from a conjecture.

SLEDGE algorithm reduces gradient computation errors in optimization.

We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of solutions up to the portion of the boundary where the operator is degenerate. Degenerat…

New theory allows ICA without assuming non-Gaussian sources.

We derive gradient and second order {\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and existence results.

We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization that employ sampling and sketching of the Hessian. Existing works do not take the…

New methods show sparse portfolios offer no advantage over mean-variance in diversification.

In this paper we consider Yamabe type problem for higher order curvatures on manifolds with totally geodesic boundaries. We prove local gradient and second derivative estimates for solutions to the fully nonlinear elliptic equations associated with the problems.

Policy optimization on high-dimensional continuous control tasks exhibits its difficulty caused by the large variance of the policy gradient estimators. We present the action subspace dependent gradient (ASDG) estimator which incorporates the Rao-Blackwell theorem (RB) and Control Variates (CV) into a unified framework…

Zeroth-order optimization is an important research topic in machine learning. In recent years, it has become a key tool in black-box adversarial attack to neural network based image classifiers. However, existing zeroth-order optimization algorithms rarely extract second-order information of the model function. In this…

New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.

Mini-Hes improves LFA model performance on HDI tasks with missing data.

Proposes second-order Esscher transform for Lévy models in financial markets.

The paper examines $L^p$ gradient and Riesz transform estimates under Ricci lower bounds.

A two-step nonparametric method estimates financial systemic risk.

We consider the local solution to the Calabi flow for C^αinitial metric. We also prove that the Calabi flow on compact Kaehler surfaces can be extended once the metrics along the flow are bounded in L^\infty sense. This can be viewed as obtaining higher order derivative estimates from second order derivatives for a fou…

Smooth solutions found for a curvature problem in hyperbolic space.

Most of the existing approaches focus on specific visual tasks while ignoring the relations between them. Estimating task relation sheds light on the learning of high-order semantic concepts, e.g., transfer learning. How to reveal the underlying relations between different visual tasks remains largely unexplored. In th…

This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window …