Finite frames, frame potentials and determinantal point processes on the sphere
نویسندگان
چکیده
Herein, we address the expectations of frame potentials three types determinantal point processes(DPPs) on d-dimensional unit sphere: (i) spherical ensembles 2-dimensional sphere; (ii) harmonic sphere and (iii) jittered sampling processes sphere. The random configurations generated by such DPPs converge more rapidly towards finite norm tight frames(FUNTFs) than Poisson
منابع مشابه
Determinantal point process models on the sphere
We consider determinantal point processes on the d-dimensional unit sphere Sd. These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified by a so-called kernel which we assume is a complex covariance function defined on Sd× Sd. We review the appealing properties of such processes, including their specific ...
متن کاملNotes on Determinantal Point Processes
In these notes we review the main concepts about Determinantal Point Processes. Determinantal point processes are of considerable current interest in Probability theory and Mathematical Physics. They were first introduced by Macchi ([8]) and they arise naturally in Random Matrix theory, non-intersecting paths, certain combinatorial and stochastic growth models and representation theory of large...
متن کاملMarkov Determinantal Point Processes
A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y . For example, we might use a DPP to display a set of news headlines that are relevant to a user’s interests while covering a variety of topics. Suppose, however, th...
متن کاملStructured Determinantal Point Processes
We present a novel probabilistic model for distributions over sets of structures— for example, sets of sequences, trees, or graphs. The critical characteristic of our model is a preference for diversity: sets containing dissimilar structures are more likely. Our model is a marriage of structured probabilistic models, like Markov random fields and context free grammars, with determinantal point ...
متن کاملLearning Determinantal Point Processes
Determinantal point processes (DPPs), which arise in random matrix theory and quantum physics, are natural models for subset selection problems where diversity is preferred. Among many remarkable properties, DPPs other tractable algorithms for exact inference, including computing marginal probabilities and sampling; however, an important open question has been how to learn a DPP from labeled tr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Statistics & Probability Letters
سال: 2021
ISSN: ['1879-2103', '0167-7152']
DOI: https://doi.org/10.1016/j.spl.2021.109129