Related papers: Hierarchical Low-rank Structure of Parameterized D…
We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on…
We examine the distribution and popularity of different parameters (such as the number of descents, runs, valleys, peaks, right-to-left minima, and more) on the sets of increasing and flattened permutations. For each parameter, we provide…
In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for…
This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…
An access structure is said to be multipartite, if the set of participants is divided into several parts and all participants in the same part play an equivalent role. The search for ideal secret sharing schemes for some special interesting…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…
The lower bound of Cramer and Rao is generalized to pairs of families of probability distributions, one of which is escort to the other. This bound is optimal for certain families, called phi-exponential in the paper. Their dual structure…
In this paper we explore the concept of hierarchy as a quantifiable descriptor of ordered structures, departing from the definition of three conditions to be satisfied for a hierarchical structure: {\em order}, {\em predictability} and {\em…
The statistical distribution of levels of an integrable system is claimed to be a Poisson distribution. In this paper, we numerically generate an ensemble of N dimensional random diagonal matrices as a model for regular systems. We evaluate…
The hierarchical distribution matching (Hi-DM) approach for probabilistic shaping is described. The potential of Hi-DM in terms of trade-off between performance,complexity, and memory is illustrated through three case studies.
In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…
Orthonormal matrices play an important role in reduced-rank matrix approximations and the analysis of matrix-valued data. A matrix Bingham-von Mises-Fisher distribution is a probability distribution on the set of orthonormal matrices that…
We consider hierarchical structures such as Fibonacci sequences and Penrose tilings, and examine the consequences of different choices for the definition of isomorphism. In particular we discuss the role such a choice plays with regard to…
The widespread occurrence of an inverse square relation in the hierarchical distribution of sub-communities within communities (or sub-species within species) has been recently invoked as a signature of hierarchical self-organization within…
This work considers the low-rank approximation of a matrix $A(t)$ depending on a parameter $t$ in a compact set $D \subset \mathbb{R}^d$. Application areas that give rise to such problems include computational statistics and dynamical…
Compound Poisson distributions and signed compound Poisson measures are used for approximation of the Markov binomial distribution. The upper and lower bound estimates are obtained for the total variation, local and Wasserstein norms. In a…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
We show that certain families of sets in $\mathbb{R}^2$ (or $\mathbb{R}^n$) which are neither definable nor have bounded VC-dimension are nonetheless uniformly approximately definable in the real field, an o-minimal structure.
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…