arXiv research

CV inference can be invalid for relatively unstable model comparisons.

A new comparison theorem for geometric spaces.

Paper compares absolute and relative real analytic torsion forms over fibrations.

Paper compares Ricci flow volume changes and applies to Kähler-Ricci flow.

Paper improves volume comparisons and entropy estimates for integral Ricci curvature.

An algorithm learns a kernel matrix from relative-distance constraints for semi-supervised clustering.

In this thesis we describe how minimal surface techniques can be used to prove the Penrose inequality in general relativity for two classes of 3-manifolds. We also describe how a new volume comparison theorem involving scalar curvature for 3-manifolds follows from these same techniques.

Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution comparison such as outlier detection, transfer learning, and two-sample homogeneity…

We consider an infinitesimal version of the Bishop-Gromov relative volume comparison condition as generalized notion of Ricci curvature bounded below for Alexandrov spaces. We prove a Laplacian comparison theorem for Alexandrov spaces under the condition. As an application we prove a topological splitting theorem.

New method improves prediction accuracy in comparison data.

Algorithm learns item qualities from noisy comparisons, scaling with graph resistance.

Sharp inequality for compactifying Poincaré-Einstein manifolds.

Proves volume comparison and monotonicity for Bakry-Émery Ricci curvature.

Survey on a nonlinear d'Alembertian from general relativity.

Study compares six feature sets and three baselines for time-series classification.

On Kahler manifolds with Ricci curvature lower bound, assuming the real analyticity of the metric, we establish a sharp relative volume comparison theorem for small balls. The model spaces being compared to are complex space forms, i.e, Kahler manifolds with constant holomorphic sectional curvature. Moreover, we give a…

The study compares and characterizes different notions of relative combinatorial asphericity.

Meta-learning improves relative density-ratio estimation from limited data.

Paper compares feature selection methods using GCM and LOCO, showing GCM methods generally outperform LOCO.

Motivated by recent work of Choquet-Bruhat, Chrusciel, and Martin-Garcia, we prove monotonicity properties and comparison results for the area of slices of the null cone of a point in a Lorentzian manifold. We also prove volume comparison results for subsets of the null cone analogous to the Bishop-Gromov relative volu…

Paper compares total quotient curvature and proves bounds for Einstein metric.

Study geometric and topological properties of Finsler manifolds with weighted Ricci curvature bounds.

Given a compact Alexadrov $n$-space $Z$ with curvature curv $\ge κ$, and let $f: Z\to X$ be a distance non-increasing onto map to another Alexandrov $n$-space with curv $\ge κ$. The relative volume rigidity conjecture says that if $X$ achieves the relative maximal volume i.e. $vol(Z)=vol(X)$, then $X$ is isometric to $…

This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise comparisons. We are interested in natural situations in which relationships among the o…

New tests measure model goodness of fit with interpretable features.

Paper proves a sharp weighted Isoperimetric inequality for substatic manifolds.

New algorithm reduces dueling bandit regret, efficiently recommending winning arms.

It was proved by Mineyev and Yaman that, if $(Γ, Γ')$ is a relatively hyperbolic pair, the comparison map $H_b^k(Γ, Γ'; V) \to H^k(Γ, Γ'; V)$ is surjective for every $k \ge 2$, and any bounded $Γ$--module $V$. By exploiting results of Groves and Manning, we give another proof of this result. Moreover, we prove the …

In this paper we discuss an extension of Perelman's comparison for quadrangles. Among applications of this new comparison theorem, we study the equidistance evolution of hypersurfaces in Alexandrov spaces with non-negative curvature. We show that, in certain cases, the equidistance evolution of hypersurfaces become tot…

Unified framework for robust ordinal embedding from contaminated comparisons.

New method targets relative risk heterogeneity in clinical trials.

A new framework evaluates HTE estimators using relative error.

Under an infinitesimal version of the Bishop-Gromov relative volume comparison condition for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger-Gromoll type. As a corollary, we prove an isometric splitting theorem for Riemannian manifolds with singularities of nonnegative (Bakry-Emery…

Study reveals how people perceive their carbon footprint.

Paper tackles noisy comparison oracle for robust clustering algorithms.

We give a survey of various rigidity results involving scalar curvature. Many of these results are inspired by the positive mass theorem in general relativity. In particular, we discuss the recent solution of Min-Oo's Conjecture for the hemisphere (cf. [13]). We also analyze the case of equality in Bray's volume compar…

On Kahler manifolds with Ricci curvature bounded from below, we establish some theorems which are counterparts of some classical theorems in Riemannian geometry, for example, Bishop-Gromov's relative volume comparison, Bonnet-Meyers theorem, and Yau's gradient estimate for positive harmonic functions. The tool is a Boc…

Unified estimate for complex Monge-Ampère equations on Kähler manifolds.

We study the $K$-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. We introduce a tight asymptotic regret lower bound that is based on the information divergence. An algorithm that is inspired by the Deterministic…

Paper tackles ranking items with a semi-random comparison graph and a monotone adversary.

The paper develops a method to estimate consumer preferences from observed rankings.

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

New model for pairwise comparisons without stochastic transitivity.

Paper proposes using pairwise feature comparisons to infer modification costs for user recourse.

New methods estimate probabilities from pairwise comparisons, adapting to difficulty.

Einstein's philosophy uses differential identities to derive GR field equations.

In this article a relation between curvature functionals for surfaces in the Euclidean space and area functionals in relative differential geometry will be given. Relative differential geometry can be described as the geometry of surfaces in the affine space, endowed with a distinguished "relative normal vector field" …

Bispectral OT improves dataset comparison by preserving intrinsic coherence.