arXiv research

The paper finds upper limits for the first eigenvalue of the p-Laplacian on Riemannian manifolds.

The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the…

Estimates higher-order Poincaré constants for weighted manifolds.

Estimating and assessing the risk of a large portfolio is an important topic in financial econometrics and risk management. The risk is often estimated by a substitution of a good estimator of the volatility matrix. However, the accuracy of such a risk estimator for large portfolios is largely unknown, and a simple ine…

ACP-UCB1 ranks arms based on upper-tail performance, improving stochastic bandit algorithms.

We estimate risk measures in Markov cost processes with lower and upper bounds.

This paper provides fast estimates for complex option types.

In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser's iteration. As an application, we will obtain an upper bound estimate for the heat kernel under the flow.

The paper tackles estimating optimal policy value in linear bandits with general context distributions.

New upper diameter estimate for manifolds with positive Bakry-Émery Ricci curvature.

Bounds on Hessian of heat equation coupled with Ricci flow.

Paper finds the best way to estimate neural net distance from samples.

New method makes robust estimators work without knowing corruption levels.

Paper estimates upper bound of analytic torsion under Arakelov metric.

In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.

This paper introduces a set of algorithms for Monte-Carlo Bayesian reinforcement learning. Firstly, Monte-Carlo estimation of upper bounds on the Bayes-optimal value function is employed to construct an optimistic policy. Secondly, gradient-based algorithms for approximate upper and lower bounds are introduced. Finally…

The paper develops estimators for variance in graph structures using fused lasso.

New formulas estimate life insurance benefits with less computation.

Paper proposes a new UCB approach for estimating maximum mean.

Estimates volume of convex Alexandrov spaces with boundary.

In this paper, we consider low rank matrix estimation using either matrix-version Dantzig Selector $\hat{A}_λ^d$ or matrix-version LASSO estimator $\hat{A}_λ^L$. We consider sub-Gaussian measurements, $i.e.$, the measurements $X_1,\ldots,X_n\in\mathbb{R}^{m\times m}$ have $i.i.d.$ sub-Gaussian entries. Suppose $\textrm…

We consider a complete noncompact smooth Riemannian manifold $M$ with a weighted measure and the associated drifting Laplacian. We demonstrate that whenever the $q$-Bakry-Émery Ricci tensor on $M$ is bounded below, then we can obtain an upper bound estimate for the heat kernel of the drifting Laplacian from the upper b…

We prove an asymptotic analog of the classical Hurewicz theorem on mappings which lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As a…

Upper bounds for essential spectrum of minimal submanifolds linked to volume growth.

Upper bounds for Steklov eigenvalues of warped products are derived.

Improved estimator for least squares using random projections achieves smaller error.

Upper diameter bound for manifolds with positive scalar curvature.

Upper bounds for surface-links in the Yoshikawa table are estimated.

In the first part, we derive a sharp gradient estimate for the log of Dirichlet heat kernel and Poisson heat kernel on domains, and a sharpened local Li-Yau gradient estimate that matches the global one. In the second part, without explicit curvature assumptions, we prove a global upper bound for the fundamental soluti…

The study proves stability of quermassintegral inequalities in hyperbolic space.

The study establishes risk bounds for distributional regression estimators.

Paper compares two hedging strategies for Lévy models.

Locally private mechanisms' output divergence bounds derived.

Proposes CLUB for reliable MI minimization in high dimensions.

Upper bound found for Steklov eigenvalues counting function.

Sharp upper bounds found for solutions of a specific equation on Riemannian manifolds.

The paper studies heat kernels on modified manifolds and bounds their properties.

The paper estimates matrix-valued functions with low rank using penalized estimators.

We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.

Smooth conic Kähler metrics with uniform curvature bound.

The study estimates the expressiveness of GCNs with bounds on the number of linear regions.

Sharp upper bound for vertices with positive curvature in planar graphs.

We establish a uniform estimate for the injectivity radius of the past null cone of a point in a general Lorentzian manifold foliated by spacelike hypersurfaces and satisfying an upper curvature bound. Precisely, our main assumptions are, on one hand, upper bounds on the null curvature of the spacetime and the lapse fu…

TAKDE optimizes kernel density estimation for real-time dynamic processes.

Let $M^n$ be an $n$-dimensional Riemannian manifold with boundary $\partial M$. Assume that Ricci curvature is bounded from below by $(n-1)k$, for $k\in \RR$, we give a sharp estimate of the upper bound of $ρ(x)=\dis(x, \partial M)$, in terms of the mean curvature bound of the boundary. When $\partial M$ is compact, th…

Upper bounds for CV errors apply to lasso and other models.

Estimates mass of static vacuum metrics with small Bartnik data.

Inequalities for Riemannian manifolds with upper sectional curvature bounds.