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Related papers: Determinantal point process models on the sphere

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Determinantal Point Processes (DPPs) are probabilistic models that arise in quantum physics and random matrix theory and have recently found numerous applications in computer science. DPPs define distributions over subsets of a given ground…

Data Structures and Algorithms · Computer Science 2017-04-25 L. Elisa Celis , Amit Deshpande , Tarun Kathuria , Damian Straszak , Nisheeth K. Vishnoi

This paper concerns space-sphere point processes, that is, point processes on the product space of $\mathbb R^d$ (the $d$-dimensional Euclidean space) and $\mathbb S^k$ (the $k$-dimen\-sional sphere). We consider specific classes of models…

We discuss the use of the determinantal point process (DPP) as a prior for latent structure in biomedical applications, where inference often centers on the interpretation of latent features as biologically or clinically meaningful…

Methodology · Statistics 2017-02-28 Yanxun Xu , Peter Mueller , Donatello Telesca

A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…

Machine Learning · Computer Science 2019-06-19 Bartłomiej Błaszczyszyn , Paul Keeler

Determinantal point processes (DPPs) are popular probabilistic models of diversity. In this paper, we investigate DPPs from a new perspective: property testing of distributions. Given sample access to an unknown distribution $q$ over the…

Machine Learning · Computer Science 2020-08-11 Khashayar Gatmiry , Maryam Aliakbarpour , Stefanie Jegelka

Continuous determinantal point processes (DPPs) are a class of repulsive point processes on $\mathbb{R}^d$ with many statistical applications. Although an explicit expression of their density is known, it is too complicated to be used…

Statistics Theory · Mathematics 2022-01-24 Arnaud Poinas , Frédéric Lavancier

We propose a novel diverse feature selection method based on determinantal point processes (DPPs). Our model enables one to flexibly define diversity based on the covariance of features (similar to orthogonal matching pursuit) or…

Machine Learning · Computer Science 2014-11-25 Nematollah Kayhan Batmanghelich , Gerald Quon , Alex Kulesza , Manolis Kellis , Polina Golland , Luke Bornn

A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main…

Probability · Mathematics 2015-06-26 Alexander I. Bufetov

Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly…

Data Structures and Algorithms · Computer Science 2020-05-08 Michał Dereziński , Michael W. Mahoney

Determinantal point processes (DPPs) are a class of repulsive point processes, popular for their relative simplicity. They are traditionally defined via their marginal distributions, but a subset of DPPs called "L-ensembles" have tractable…

Statistics Theory · Mathematics 2022-06-01 Nicolas Tremblay , Simon Barthelmé , Konstantin Usevich , Pierre-Olivier Amblard

A determinantal point process (DPP) is an elegant model that assigns a probability to every subset of a collection of $n$ items. While conventionally a DPP is parameterized by a symmetric kernel matrix, removing this symmetry constraint,…

Machine Learning · Computer Science 2022-07-04 Insu Han , Mike Gartrell , Elvis Dohmatob , Amin Karbasi

We study expected Riesz s-energies and linear statistics of some determinantal processes on the sphere. In particular, we compute the expected Riesz and logarithmic energies of the determinantal processes given by the reproducing kernel of…

Classical Analysis and ODEs · Mathematics 2016-10-21 Carlos Beltrán , Jordi Marzo , Joaquim Ortega-Cerdà

It is known that determinantal point processes have an intimate relation to operator algebras. In the paper, we extend this relationship to encompass dynamical aspects. Especially, we delve into two types of determinantal point processes.…

Operator Algebras · Mathematics 2023-09-06 Ryosuke Sato

We review how to simulate continuous determinantal point processes (DPPs) and improve the current simulation algorithms in several important special cases as well as detail how certain types of conditional simulation can be carried out.…

Methodology · Statistics 2023-08-23 Frédéric Lavancier , Ege Rubak

For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…

Probability · Mathematics 2016-05-05 Alexander I. Bufetov

Determinantal consensus clustering is a promising and attractive alternative to partitioning about medoids and k-means for ensemble clustering. Based on a determinantal point process or DPP sampling, it ensures that subsets of similar…

Computation · Statistics 2021-02-09 Serge Vicente , Alejandro Murua

We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the…

Machine Learning · Statistics 2020-01-03 Ayoub Belhadji , Rémi Bardenet , Pierre Chainais

For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a…

Classical Analysis and ODEs · Mathematics 2018-10-17 Rafaela N. Bonfim , Jean C. Guella , Valdir A. Menegatto

Goldman [7] proved that the distribution of a stationary determinantal point process (DPP) $\Phi$ can be coupled with its reduced Palm version $\Phi^{0,!}$ such that there exists a point process $\eta$ where $\Phi = \Phi^{0,!} \cup \eta$ in…

Probability · Mathematics 2018-07-26 François Baccelli , Eliza O'Reilly

We present a new class of cluster point process models, which we call determinantal shot noise Cox processes (DSNCP), with repulsion between cluster centres. They are the special case of generalized shot noise Cox processes where the…

Methodology · Statistics 2022-05-31 Jesper Møller , Ninna Vihrs