arXiv research

PPO-B improves sampling efficiency by using a logarithmic barrier method.

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, base…

We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlappin…

Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their asymmetric generalizations. Properties of these estimators depend on the choice of pena…

Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space complexity by leveraging regularity and bounded-input bounded-output stability. T…

We describe a novel binary classification technique called Banded SVM (B-SVM). In the standard C-SVM formulation of Cortes et al. (1995), the decision rule is encouraged to lie in the interval [1, \infty]. The new B-SVM objective function contains a penalty term that encourages the decision rule to lie in a user specif…

This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundar…

The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and variance. Recently, a different approach to linear system identification has been…

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's metho…

New manifolds found without interior conjugate points.

New formula simplifies interior polynomial calculation.

Develops consistent approximations for composite optimization problems.

Estimates for special Lagrangian curvature equations in critical and convex cases.

The interior polynomial is an invariant of bipartite graphs, and a part of the HOMFLY polynomial of a special alternating link coincides with the interior polynomial of the Seifert graph of the link. We extend the interior polynomial to signed bipartite graphs, and we show that, in the planar case, it is equal to a par…

We establish interior $C^2$ estimates for convex solutions of scalar curvature equation and $σ_2$-Hessian equation. We also prove interior curvature estimate for isometrically immersed hypersurfaces $(M^n,g)\subset \mathbb R^{n+1}$ with positive scalar curvature. These estimates are consequences of an interior estimate…

Paper proves interior regularity estimates for complex Monge-Ampère solutions.

Study interior estimates for solutions of Poisson equation on Riemann surfaces.

This paper compiles formulas involving differential operators and interior products.

Proves interior singular set dimension for area-minimizing currents in smooth submanifolds.

This paper reverses a construction by merging boundary critical points into an interior one.

Real analytic solutions found for special Lagrangian equation.

The study provides interior curvature estimates for convex graphs satisfying a specific quotient equation.

The interior polynomial is an invariant of (signed) bipartite graphs, and the interior polynomial of a plane bipartite graph is equal to a part of the HOMFLY polynomial of a naturally associated link. The HOMFLY polynomial $P_L(v,z)$ is a famous link invariant with many known properties. For example, the HOMFLY polynom…

The paper explores nonconvex penalties for deep learning regularization.

Interior $C^{2}$ estimates for sum Hessian quotient equations on Riemannian manifolds

New interior-point method tackles Wasserstein barycenter problem efficiently.

We prove a priori interior C2 estimate for σ_2 = f in R3, which generalizes Warren-Yuan's result.

We give a maximum principle proof of interior derivative estimates for the Kähler-Ricci flow, assuming local uniform bounds on the metric.

We study a generalized Abreu Equation in $n$-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform $K$-stability.

We use elementary methods to construct a minimal lamination of the interior of a positive cone in R3.

In this paper we prove the interior regularity for the solution to the Abreu equation in any dimension assuming the existence of the $C^0$ estimate.

We study the Abreu's equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform K-stability.

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

IPO optimizes reinforcement learning with constraints for better performance.

The study calculates best Sobolev constants with sharp Hardy terms in Euclidean and hyperbolic spaces.

3-manifolds and handlebody interiors with nonnegative scalar curvature are topologically rigid.

Gradient penalty improves GAN performance by inducing a large-margin classifier.

New examples show flat singular sets can be arbitrarily complex.

Study examines insider trading with penalties, finding optimal penalties increase quickly for small orders.

In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.

One-bit measurements widely exist in the real world, and they can be used to recover sparse signals. This task is known as the problem of learning halfspaces in learning theory and one-bit compressive sensing (1bit-CS) in signal processing. In this paper, we propose novel algorithms based on both convex and nonconvex s…

The paper studies robust risk measures with linear penalties under uncertain distributions.

The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited…

Paper introduces a new SVR model using a combined reward and penalty loss function.

The study confirms conjectures about normals to convex polytopes in 3D space.

The notions of the interior and truncated connections of a nonholonomic manifold are introduced. A class of extended truncated connections is distinguished. For the case of a contact space with a Finsler metric, it is shown that there exists a unique extended truncated connection that satisfies additional properties. T…

The paper studies fully nonlinear equations on Hermitian manifolds, proving existence and interior estimates.

New sparse penalty improves biclustering for gene expression data.