arXiv research

Study expands classical harmonic function results to Riemannian manifolds.

We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Tail Value at Risk and the Entropic Risk Measure in a unified way. We then investigate the fundamental propert…

The study extends classical results on harmonic functions to Riemannian manifolds with non-tangential boundary limits.

The second boundary value problem of the prescribed affine mean curvature equation is a nonlinear, fourth order, geometric partial differential equation. It was introduced by Trudinger and Wang in 2005 in their investigation of the affine Plateau problem in affine geometry. The previous works of Trudinger-Wang, Chau-We…

A new permutation method improves two-sample testing power.

The paper generalizes a mean value theorem for solutions of the ultrahyperbolic equation.

The paper proves conditions for smooth convergence of hyperkaehler 4-manifolds with boundary.

New graph properties inherited by Frechet mean and median.

We study properties of the mean curvature one-form and its holomorphic and antiholomorphic cousins on a transverse Kähler foliation. If the mean curvature of the foliation is automorphic, then there are some restrictions on basic cohomology similar to that on Kähler manifolds, such as the requirement that the odd basic…

The asymptotic pseudo-trajectory approach to stochastic approximation of Benaim, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of a…

One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some known examples coming from the theory of metric measured spaces and also from oscill…

Let (M,g) be a non-compact and complete Riemannian manifold with minimal horospheres and infinite injectivity radius. We prove that bounded functions on (M,g) satisfying the mean-value property are constant. We extend thus a result of A. Ranjan and H. Shah who proved a similar result for bounded harmonic functions on h…

We introduce a geometric evolution equation of hyperbolic type, which governs the evolution of a hypersurface moving in the direction of its mean curvature vector. The flow stems from a geometrically natural action containing kinetic and internal energy terms. As the mean curvature of the hypersurface is the main drivi…

The study proves a new inequality and formula for manifolds with non-negative Ricci curvature.

New algorithms exploit mean bounds to improve bandit problem performance.

Generalizes Fenchel conjugation to nonlinear functions on arbitrary sets.

We describe the range of a restricted spherical mean transform, which sends a function supported inside a closed ball in a hyperbolic space to its mean values on the geodesics spheres centered at the boundary of the ball. The description resembles that of the same transform on the Euclidean spaces obtained by Mark Agra…

Study submersions with definite folds on manifolds with boundary into Euclidean spaces.

Proves properties of neural network basins of attraction and their expressiveness.

The paper analyzes Karcher means on restricted PSD matrices with statistical guarantees.

A new framework for robust risk measurement and portfolio optimization.

New method calibrates probabilistic regression models without restrictive assumptions.

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct a push-forward map in differential equivariant K-theory. Finally, we construct …

We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a martingale equation of a new type and characterize the optimal strategy in terms of the solution of this equ…

This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It…

We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal…

This work analyzes centered binary Restricted Boltzmann Machines (RBMs) and binary Deep Boltzmann Machines (DBMs), where centering is done by subtracting offset values from visible and hidden variables. We show analytically that (i) centering results in a different but equivalent parameterization for artificial neural …

In the Compressed Sensing community, it is well known that given a matrix $X \in \mathbb R^{n\times p}$ with $\ell_2$ normalized columns, the Restricted Isometry Property (RIP) implies the Null Space Property (NSP). It is also well known that a small Coherence $μ$ implies a weak RIP, i.e. the singular values of $X_T$ l…

Proposes debiasing strategy for ill-posed regression problems.

We prove that every closed, smooth $n$-manifold $X$ admits a Riemannian metric together with a smooth, transversely oriented CMC foliation if and only if its Euler characteristic is zero, where by CMC foliation we mean a codimension-one, transversely oriented foliation with leaves of constant mean curvature and where t…

Axiomatizes $Λ$-quantiles, a generalization of quantiles.

In this paper, we study the complete bounded $λ$-hypersurfaces in weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded $λ$-hypersurfaces with $|A|\leqα$ and get some applications of the volume comparison theorem. Secondly, we consider the relation amo…

This paper optimizes off-policy evaluation in reinforcement learning with function approximation.

Extends diameter bounds for submanifolds with boundary and minor curvature restrictions.

Interestingness measures provide information that can be used to prune or select association rules. A given value of an interestingness measure is often interpreted relative to the overall range of the values that the interestingness measure can take. However, properties of individual association rules restrict the val…

Universal approximation for ODENet and ResNet with a single activation function.

This article is concerned with the Bridge Regression, which is a special family in penalized regression with penalty function $\sum_{j=1}^{p}|β_j|^q$ with $q>0$, in a linear model with linear restrictions. The proposed restricted bridge (RBRIDGE) estimator simultaneously estimates parameters and selects important varia…

The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary tim…

Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message pas…

J. Nash proved that the geometry of any Riemannian manifold M imposes no restrictions to be embedded isometrically into a (fixed) ball B_{\mathbb{R}^{N}}(1) of the Euclidean space R^N. However, the geometry of M appears, to some extent, imposing restrictions on the mean curvature vector of the embedding.

Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is critical to the interpretability of a learned model. Much of the current literature…

Paper explores RKHS properties for derivative and integral operators.

Study solves utility maximization in a transient price impact market.

We prove a chord arc bound for disks embedded in $\mathbb{R}^3$ with constant mean curvature. This bound does not depend on the value of the mean curvature. It is inspired by and generalizes the work of Colding and Minicozzi in [2] for embedded minimal disks. Like in the minimal case, this chord arc bound is a fundamen…

Value-at-Risk can be superadditive for sufficiently heavy-tailed losses.

Develops a TL framework for estimating RMST difference in clinical trials.

This paper connects Wasserstein distances to MMD norms for compressive statistical learning.

New method improves estimation of complex models from conditional moment restrictions.