arXiv research

RATE metrics evaluate treatment prioritization rules, subsuming existing methods.

Study on convergence rate of Bergman metrics on Kähler manifolds.

Study on convergence rate of weighted Yamabe flow.

Paper introduces new metrics for evaluating model accuracy.

Sharp bounds on neural network approximation rates and widths.

New Calabi-Yau metrics converge polynomially to Calabi model space.

Prototype rules simplify multiclass classification in metric spaces, achieving consistency and reduced complexity.

In this paper, a metric with G$_2$ holonomy and slow rate of convergence to the cone metric is constructed on a ball inside the cone over the flag manifold.

Unified framework for comparing classification metrics across different imbalance rates.

The paper tightens the regret rate for linear bandit problems.

Study on Kähler-Einstein metrics with polynomial convergence rates.

We study the minimax optimal rate for estimating the Wasserstein-$1$ metric between two unknown probability measures based on $n$ i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability measures, is not significantly easier than estimating the probability measures u…

Study provides obstructions for Q-curvature on complete metrics in n-space.

Study improves the exponential rate of metric difference in Higgs bundles.

Quantizes symplectic fibrations to analyze vector bundles and metrics.

The Weil-Petersson metric for the moduli space of Riemann surfaces has negative sectional curvature. Surfaces represented in the complement of a compact set in the moduli space have short geodesics. At such surfaces the Weil-Petersson metric is approximately a product metric. An almost product metric has sections with …

This paper develops a new method for eliciting more flexible metrics, improving fairness and applicability.

In this paper, we consider a CscK metric defined away from divisor and with metric upper bound and lower bound going to zero in certain rate. And we'll prove that this "nicely" behaved metric is a smooth CscK metric across the divisor.

Rating platforms enable large-scale collection of user opinion about items (products, other users, etc.). However, many untrustworthy users give fraudulent ratings for excessive monetary gains. In the paper, we present FairJudge, a system to identify such fraudulent users. We propose three metrics: (i) the fairness of …

Polynomial networks converge to Gaussian processes at a rate of O(n^(-1/2)).

We consider a family of manifolds with a class of degenerating warped product metrics $g_ε=ρ(ε,t)^{2a}dt^2 +ρ(ε,t)^{2b}ds_M^2$, with $M$ compact, $ρ$ homogeneous degree one, $a \le -1$ and $b > 0$. We study the Laplace operator acting on $L^{2}$ differential $p$-forms and give sharp accumulation rates for eigenvalues n…

A new method for optimizing non-decomposable metrics with constraints.

The paper improves convergence rates of curvature approximations using Regge elements.

The paper shows how contracting elements in groups lead to large quotients with specific growth rates.

We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure or G-mean, and constrained training problems where the classifier needs to sati…

Sharp lower bounds on shallow neural networks' approximation rates are derived.

We study the asymptotics of the natural $L^2$ metric on the Hitchin moduli space with group $G = \mathrm{SU}(2)$. Our main result, which addresses a detailed conjectural picture made by Gaiotto, Neitzke and Moore \cite{gmn13}, is that on the regular part of the Hitchin system, this metric is well-approximated by the se…

We define and study certain hyperkaehler manifolds which capture the asymptotic behaviour of the SU(2)-monopole metric in regions where monopoles break down into monopoles of lower charges. The rate at which these new metrics approximate the monopole metric is exponential, as for the Gibbons-Manton metric.

We study the one-parameter family of twisted Kahler Taub-NUT metrics (discovered by Donaldson), along with two exceptional Taub-NUT-like instantons, and understand them to the extend that should be sufficient for blow-up and gluing arguments. In particular we parametrize their geodesics from the origin, determine curva…

Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional data has low intrinsic dimension (e.g. a manifold). We show that k-NN regression is also adaptive to intrinsic dimension. …

Tian and Yau constructed a complete Ricci-flat Kähler metric on the complement of an ample and smooth anticanonical divisor. We inquire into the behaviour of this metric towards the boundary divisor and prove a slow decay rate of the difference to an appropriate explicitely given referential metric.

The paper analyzes how GANs converge using dual metric flows.

Paper analyzes convergence of proximal algorithm in metric spaces without geodesic convexity.

AdaS adapts SGD learning rate based on knowledge gain metrics.

Paper discusses binary classification with metric space predictors, privacy constraints, and convergence rates.

We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on $n$ independent samples from them. Curiously, we show that estimating the IPM itself between probability measures, is not significantly easier than estimating the probabili…

Square metrics $F=\frac{(α+β)^2}α$ are a special class of Finsler metrics. It is the rate kind of metric category to be of excellent geometrical properties. In this paper, we discuss the so-called singular square metrics $F=\frac{(bα+β)^2}α$. A characterization for such metrics to be of vanishing Douglas curvature is p…

Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and upper-bounds showing that the sample complexity scales with the representation di…

This work evaluates deep generative models using RD curves, providing a more comprehensive quality assessment.

Study exact minimax rates for density estimation over convex classes, extending previous work.

Solves large-scale metric constrained problems using Project and Forget algorithm.

LxCIM metric improves binary classification performance evaluation.

We introduce the \emph{metric spectrum}, which measures the exponential rate of approximation to an isolated invariant set of points starting in its stable set, and relate it to the Lyapunov spectrum. We determine the metric spectrum of each Morse component of the finest Morse decomposition of a linear induced flow on …

Addressing a question of Gromov, we give a rate in Pansu's theorem about the convergence in Gromov-Hausdorff metric of a finitely generated nilpotent group equipped with a left-invariant word metric scaled by a factor 1/n towards its asymptotic cone. We show that due to the possible presence of abnormal geodesics in th…

We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number theory on sets of integers with no three-term arithmetic progressions. We also carr…

Score based learning (SBL) is a promising approach for learning Bayesian networks in the discrete domain. However, when employing SBL in the continuous domain, one is either forced to move the problem to the discrete domain or use metrics such as BIC/AIC, and these approaches are often lacking. Discretization can have …

We prove exponential growth rate of contractible closed geodesics for an arbitrary bumpy metric on manifolds of the form X#Y, where the fundamental group of X has a subgroup of finite index at least 3 and Y is simply connected and not a homotopy sphere.

New findings on flatness of certain metrics with fast decay.