A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Establishes a concavity property for positive Hessian quotient operators.
Heat flow fails to preserve concavity in curved spaces.
We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a concavity maximum principle argument to the corresponding level set f…
Study properties of contact structures on symplectic disk bundles with concave boundaries.
The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing an additional mathematical property. For this, we introduce the notion of a conca…
We provide new results for noise-tolerant and sample-efficient learning algorithms under -concave distributions. The new class of -concave distributions is a broad and natural generalization of log-concavity, and includes many important additional distributions, e.g., the Pareto distribution and -distribution.…
This work studies the location estimation problem for a mixture of two rotation invariant log-concave densities. We demonstrate that Least Squares EM, a variant of the EM algorithm, converges to the true location parameter from a randomly initialized point. We establish the explicit convergence rates and sample complex…
Two important goals of high-dimensional modeling are prediction and variable selection. In this article, we consider regularization with combined and concave penalties, and study the sampling properties of the global optimum of the suggested method in ultra-high dimensional settings. The -penalty provides th…
Gradient methods converge exponentially in concave network games.
New framework for managing medical risks using convex responses.
The Links-Gould invariant of alternating links has log-concave coefficients.
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamenta…
New Orlicz Brunn-Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical log-concavity properties of intrinsic volumes and generalize seminal results of Lutwak and others. Two different approaches which refine previously employed techniques are…
Zigzag sampling algorithm efficiently samples from strongly log-concave distributions with low computational cost.
We analyze the classical model of compound interest with a constant per-period payment and interest rate. We examine the outstanding balance function as well as the periodic payment function and show that the outstanding balance function is not generally concave in the interest rate, but instead may be initially convex…
We explore the tan-concavity of the Lagrangian phase operator for the study of the deformed Hermitian Yang-Mills (dHYM) metrics. This new property compensates for the lack of concavity of the Lagrangian phase operator as long as the metric is almost calibrated. As an application, we introduce the tangent Lagrangian pha…
The paper extends risk measures to two-step approximations and studies log-concave distributions.
Paper improves performance guarantees for Rademacher projections.
The curvature of almost Fuchsian immersions is concave in their Hopf differentials.
Study concavity of solutions to elliptic equations under conformal deformations.
In this paper we study the smooth convex-concave saddle point problem. Specifically, we analyze the last iterate convergence properties of the Extragradient (EG) algorithm. It is well known that the ergodic (averaged) iterates of EG converge at a rate of (Nemirovski, 2004). In this paper, we show that the last…
Study proves estimate for Hessian quotient equations on 2D Riemannian manifolds.
Improves SGM convergence bounds in W2-distance without strict assumptions.
New method for modeling densities on Riemannian manifolds with symmetries.
The paper analyzes how optimization algorithms affect the generalization of minimax models.
Gradient Descent Ascent converges to von-Neumann solution in hidden zero-sum games.
As has been observed by Morse \cite{Mo}, any generic vector field on a compact smooth manifold with boundary gives rise to a stratification of the boundary $\d X$ by compact submanifolds $\{\d_j^\pm X(v)\}_{1 \leq j \leq \dim(X)}$, where $\textup{codim}(\d_j^\pm X(v))= j$. Our main observation is that this stra…
In the first part Busemann concavity as non-negative curvature is introduced and a bi-Lipschitz splitting theorem is shown. Furthermore, if the Hausdorff measure of a Busemann concave space is non-trivial then the space is doubling and satisfies a Poincaré condition and the measure contraction property. Using a compari…
Decision maker's preferences are often captured by some choice functions which are used to rank prospects. In this paper, we consider ambiguity in choice functions over a multi-attribute prospect space. Our main result is a robust preference model where the optimal decision is based on the worst-case choice function fr…
New proof of trapezoidal property for Alexander polynomials of special alternating links.
In the field of optimal transport theory, an optimal map is known to be a gradient map of a potential function satisfying cost-convexity. In this paper, the Jacobian determinant of a gradient map is shown to be log-concave with respect to a convex combination of the potential functions when the underlying manifold is t…
Complex performance measures, beyond the popular measure of accuracy, are increasingly being used in the context of binary classification. These complex performance measures are typically not even decomposable, that is, the loss evaluated on a batch of samples cannot typically be expressed as a sum or average of losses…
This article provides a simple explanation of the asymptotic concavity of the price impact of a meta-order via the microstructural properties of the market. This explanation is made more precise by a model in which the local relationship between the order flow and the fundamental price (i.e. the local price impact) is …
Study on a metric space derived from Kähler manifolds.
These are notes of a talk given at the Mathematische Arbeitstagung 2005 in Bonn. Following ideas of Ozbagci-Stipsicz, a proof based on contact Dehn surgery is given of Eliashberg's concave filling theorem for contact 3-manifolds. The role of that theorem in the Kronheimer-Mrowka proof of property P for nontrivial knots…
The paper establishes conditions for strict power concavity in convolutions.
Developing a non-symmetric strainer theory for spaces with non-negative curvature beyond Alexandrov geometry.
New algorithms solve DR-submodular maximization with faster convergence.
High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular classes of convex ones and concave ones. A long debate has been on whether one class dominates the other, an important question both in theory and to practitioners. In this pape…
The paper studies stability of mean-field variational inference for log-concave distributions.
Minimal graph level sets are concave if boundary is concave.
This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a finite time set and finite sample space, we find natural risk-transfer and time-co…
For sampling from a log-concave density, we study implicit integrators resulting from -method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the resulting sampling methods for and a range of step sizes are established. Ou…
Most content-based image retrieval systems consider either one single query, or multiple queries that include the same object or represent the same semantic information. In this paper we consider the content-based image retrieval problem for multiple query images corresponding to different image semantics. We propose a…
Proves log-concavity of cluster algebra coefficients for type .
Study improves sampling from non-log-concave distributions using Fisher information.
An online learning framework for survival analysis with real-time adaptation.
Established concavity principle for curved spaces.