相关论文: On the differentiability of $\phi$-projections in …

The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…

In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…

The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…

Learning-based models for fluid dynamics often operate in unconstrained function spaces, leading to physically inadmissible, unstable simulations. While penalty-based methods offer soft regularization, they provide no structural guarantees,…

We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two…

We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…

We study an extreme scenario of the Mastrand projection theorem for which a fractal has the property that its orthogonal projection is the same as the orthogonal projection of its convex hull. We extend results in current literature and…

Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…

A local projection model is defined by a set of linear regressions that account for the associations between exogenous variables and an endogenous variable observed at different time points. While it is standard practice to separately…

For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…

We show that the variational representations for f-divergences currently used in the literature can be tightened. This has implications to a number of methods recently proposed based on this representation. As an example application we use…

We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…

The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue…

In a recent paper, Pertti Mattila asked which gauge functions $\phi$ have the property that for any planar Borel set $A$ with positive Hausdorff measure in gauge $\phi$, the projection of $A$ to almost every line has positive length. We…

Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…

The extremal dependence structure of a regularly varying $d$-dimensional random vector can be described by its angular measure. The standard nonparametric estimator of this measure is the empirical measure of the observed angles of the $k$…

Consider the projection of an $n$-dimensional random vector onto a random $k_n$-dimensional basis, $k_n \leq n$, drawn uniformly from the Haar measure on the Stiefel manifold of orthonormal $k_n$-frames in $\mathbb{R}^n$, in three different…

Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…

We recently characterized the separated determinantal point processes $\Lambda_\phi$ associated with Fock spaces $\mathcal F_\phi$ in the plane with doubling weight $\phi$. We also showed that, as expected, a more restrictive condition is…

This paper considers projection and convolution operations for integrally convex functions, which constitute a fundamental function class in discrete convex analysis. It is shown that the class of integrally convex functions is stable under…