相关论文: Klee sets and Chebyshev centers for the right Breg…

Deep metric learning techniques have been used for visual representation in various supervised and unsupervised learning tasks through learning embeddings of samples with deep networks. However, classic approaches, which employ a fixed…

An $\mathcal{O}(N(\log N)^2/\log\!\log N)$ algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev…

Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…

Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods.…

We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…

Trace estimators allow to approximate thermodynamic equilibrium observables with astonishing accuracy. A prominent representative is the finite-temperature Lanczos method (FTLM) which relies on a Krylov space expansion of the exponential…

In this work we investigate the relationship between Bregman distances and regularized Logistic Regression model. We present a detailed study of Bregman Distance minimization, a family of generalized entropy measures associated with convex…

A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true…

In this work, we investigate the problem of learning distance functions within the query-based learning framework, where a learner is able to pose triplet queries of the form: ``Is $x_i$ closer to $x_j$ or $x_k$?'' We establish formal…

Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…

We study three possible definitions of the notion of CR functions at CR singular points, their extension to a fixed-neighborhood of the singular point, and analogues of the Baouendi--Tr\`eves approximation in a fixed neighborhood. In…

Deep Bregman divergence measures divergence of data points using neural networks which is beyond Euclidean distance and capable of capturing divergence over distributions. In this paper, we propose deep Bregman divergences for contrastive…

Analytic expressions for the Fourier transforms of the Chebyshev and Legendre polynomials are derived, and the latter is used to find a new representation for the half-order Bessel functions. The numerical implementation of the so-called…

We propose a general deep architecture for learning functions on multiple permutation-invariant sets. We also show how to generalize this architecture to sets of elements of any dimension by dimension equivariance. We demonstrate that our…

We present a method for calculating the complex Green function $G_{ij} (\omega)$ at any real frequency $\omega$ between any two sites $i$ and $j$ on a lattice. Starting from numbers of walks on square, cubic, honeycomb, triangular, bcc,…

We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard loss function for the analysis of parameter estimation in…

Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear,…

The aim of this article is to generalize the notion of the cut locus and to get the structure theorem for it. For this purpose, we first introduce a class of 1-Lipschitz functions, each member of which is called an {\it almost distance…

We systematically study the local single-valuedness of the Bregman proximal mapping and local smoothness of the Bregman--Moreau envelope of a nonconvex function under relative prox-regularity - an extension of prox-regularity - which was…

The Chebyshev set of a bounded set $K$ in a normed space is the set of centers of all minimal enclosing balls of $K$. We use the concept of ball intersection and ball hull operators to derive new properties of Chebyshev sets in normed…