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Determinantal point processes (DPPs) have attracted significant attention as an elegant model that is able to capture the balance between quality and diversity within sets. DPPs are parameterized by a positive semi-definite kernel matrix.…

Machine Learning · Statistics 2019-05-30 Mike Gartrell , Elvis Dohmatob , Jon Alberdi

Symmetric determinantal point processes (DPP's) are a class of probabilistic models that encode the random selection of items that exhibit a repulsive behavior. They have attracted a lot of attention in machine learning, when returning…

Statistics Theory · Mathematics 2018-11-02 Victor-Emmanuel Brunel

Properties of strong mixing have been established for the stationary linear Hawkes process in the univariate case, and can serve as a basis for statistical applications. In this paper, we provide the technical arguments needed to extend the…

Statistics Theory · Mathematics 2023-11-21 Ousmane Boly , Felix Cheysson , Thi Hien Nguyen

We study point processes on $\mathbb S^d$, the $d$-dimensional unit sphere $\mathbb S^d$, considering both the isotropic and the anisotropic case, and focusing mostly on the spherical case $d=2$. The first part studies reduced Palm…

Methodology · Statistics 2016-06-14 Jesper Møller , Ege Rubak

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 offer tractable algorithms…

Machine Learning · Computer Science 2012-02-20 Alex Kulesza , Ben Taskar

Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key…

Machine Learning · Computer Science 2015-10-12 Zelda Mariet , Suvrit Sra

Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product…

Machine Learning · Statistics 2016-08-17 Mike Gartrell , Ulrich Paquet , Noam Koenigstein

Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, we obtain large-time asymptotic expansions in large…

Probability · Mathematics 2019-07-26 Xuefeng Gao , Lingjiong Zhu

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

Determinantal point processes (a.k.a. DPPs) have recently become popular tools for modeling the phenomenon of negative dependence, or repulsion, in data. However, our understanding of an analogue of a classical parametric statistical theory…

Machine Learning · Statistics 2021-11-22 Subhro Ghosh , Philippe Rigollet

We study stochastic motion planning problems which involve a controlled process, with possibly discontinuous sample paths, visiting certain subsets of the state-space while avoiding others in a sequential fashion. For this purpose, we first…

Optimization and Control · Mathematics 2017-11-27 Peyman Mohajerin Esfahani , Debasish Chatterjee , John Lygeros

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

In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…

Probability · Mathematics 2022-02-11 Michael Fleermann , Werner Kirsch

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

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…

Statistics Theory · Mathematics 2008-12-18 François Roueff , Murad S. Taqqu

Determinantal Point Processes (DPPs) have attracted significant interest from the machine-learning community due to their ability to elegantly and tractably model the delicate balance between quality and diversity of sets. DPPs are commonly…

Machine Learning · Computer Science 2019-02-27 Zelda Mariet , Mike Gartrell , Suvrit Sra

We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…

Probability · Mathematics 2022-04-27 Loïc Béthencourt

Determinantal Point Processes (DPPs) provide an elegant and versatile way to sample sets of items that balance the point-wise quality with the set-wise diversity of selected items. For this reason, they have gained prominence in many…

Machine Learning · Statistics 2019-01-09 Zelda Mariet , Yaniv Ovadia , Jasper Snoek

Although the Poisson point process (PPP) has been widely used to model base station (BS) locations in cellular networks, it is an idealized model that neglects the spatial correlation among BSs. The present paper proposes the use of…

Information Theory · Computer Science 2014-12-08 Yingzhe Li , François Baccelli , Harpreet S. Dhillon , Jeffrey G. Andrews

The Probability Hypothesis Density (PHD) filter, which is used for multi-target tracking based on sensor measurements, relies on the propagation of the first-order moment, or intensity function, of a point process. This algorithm assumes…

Probability · Mathematics 2020-12-11 Nicolas Privault , Timothy Teoh