相关论文: On the differentiability of $\phi$-projections in …
On metric spaces equipped with doubling measures, we prove that a differentiability theorem holds for Lipschitz functions if and only if the space supports nontrivial (metric) derivations in the sense of Weaver that satisfy an additional…
Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…
In this paper, we study the following problem: Let $D\geq 2$ and let $E\subset \mathbb R^D$ be finite satisfying certain conditions. Suppose that we are given a map $\phi:E\to \mathbb R^D$ with $\phi$ a small distortion on $E$. How can one…
With increasing concerns about security, the need for highly secure physical biometrics-based authentication systems utilizing \emph{cancelable biometric} technologies is on the rise. Because the problem of cancelable template generation…
We prove that admissible functions for Fubini-Study metrics on the complex projective space $P_{m}C$, of complex dimension $m$, invariant by a convenient automorphisms group, are lower bounded by a function going to minus infinity on the…
$\Phi$-intermediate dimensions interpolate between Hausdorff and box-counting dimensions by restricting admissible coverings to scale windows of the form $[\Phi(r),r]$. Using a family of $\Phi$-dependent kernels, we develop a…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…
The convex feasibility problem (CFP) is at the core of the modeling of many problems in various areas of science. Subgradient projection methods are important tools for solving the CFP because they enable the use of subgradient calculations…
Many popular algorithmic fairness measures depend on the joint distribution of predictions, outcomes, and a sensitive feature like race or gender. These measures are sensitive to distribution shift: a predictor which is trained to satisfy…
We present a necessary and sufficient condition for the reachable set, i.e., the set of states reachable from a ball of initial states at some time, of an ordinary differential equation to be convex. In particular, convexity is guaranteed…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of…
We consider the differential entropy of probability measures absolutely continuous with respect to a given $\sigma$-finite reference measure on an arbitrary measurable space. We state the asymptotic equipartition property in this general…
We propose and axiomatize preferences on a product state space in light of uncertainty regarding the dependency of different payoff-relevant factors. Dependence structures allow to decompose probabilities and allow to pin down behavior…
In this article we study exponential dichotomies for noninvertible linear difference equations in finite dimensions. After giving the definition, we study the extent to which the projection $P(k)$ in a dichotomy is unique. For equations on…
In this article we introduce the new modulus $\triangle'_{X,\phi}(\varepsilon)$, for which we prove that in the general case is different from the classical modulus of noncompact convexity. The main result of the paper is showing the…
This article examines differentiability properties of the value function of positioning choice problems, a class of optimisation problems in finite-dimensional Euclidean spaces. We show that positioning choice problems' value function is…
In this paper, we first present a simpler proof of a result on the strict Fr\'echet differentiability of the metric projection operator onto closed balls centered at the origin in Hilbert spaces, which given by Li in \cite{Li24}. Then,…
Linear projections are widely used in the analysis of high-dimensional data. In unsupervised settings where the data harbour latent classes/clusters, the question of whether class discriminatory signals are retained under projection is…