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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

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

We present the conditional determinantal point process (DPP) approach to obtain new (mostly Fredholm determinantal) expressions for various eigenvalue statistics in random matrix theory. It is well-known that many (especially $\beta=2$)…

Mathematical Physics · Physics 2023-10-23 Alan Edelman , Sungwoo Jeong

Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…

Numerical Analysis · Mathematics 2021-08-04 Fredrik Fryklund , Ludvig af Klinteberg , Anna-Karin Tornberg

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

This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…

Machine Learning · Computer Science 2015-09-16 Corinna Cortes , Prasoon Goyal , Vitaly Kuznetsov , Mehryar Mohri

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

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

Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…

Numerical Analysis · Mathematics 2022-01-20 Fredrik Fryklund , Ludvig af Klinteberg , Anna-Karin Tornberg

Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing…

Machine Learning · Computer Science 2018-04-18 Philipp Hennig , Roman Garnett

A fundamental task in kernel methods is to pick nodes and weights, so as to approximate a given function from an RKHS by the weighted sum of kernel translates located at the nodes. This is the crux of kernel density estimation, kernel…

Machine Learning · Statistics 2020-02-25 Ayoub Belhadji , Rémi Bardenet , Pierre Chainais

The kernel herding algorithm is used to construct quadrature rules in a reproducing kernel Hilbert space (RKHS). While the computational efficiency of the algorithm and stability of the output quadrature formulas are advantages of this…

Numerical Analysis · Mathematics 2022-07-18 Kazuma Tsuji , Ken'ichiro Tanaka

Determinantal point processes (DPP) serve as a practicable modeling for many applications of repulsive point processes. A known approach for simulation was proposed in \cite{Hough(2006)}, which generate the desired distribution point wise…

Probability · Mathematics 2013-11-06 Laurent Decreusefond , Ian Flint , Kah Choon Low

Unstructured neural network pruning algorithms have achieved impressive compression rates. However, the resulting - typically irregular - sparse matrices hamper efficient hardware implementations, leading to additional memory usage and…

Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…

Computation · Statistics 2026-05-19 Edoardo Bandoni , Christian Robert , Julien Stoehr

We consider mixture models where location parameters are a priori encouraged to be well separated. We explore a class of determinantal point process (DPP) mixture models, which provide the desired notion of separation or repulsion. Instead…

Methodology · Statistics 2017-05-16 Ilaria Bianchini , Alessandra Guglielmi , Fernando A. Quintana

Determinantal Point Processes (DPPs) are popular models for point processes with repulsion. They appear in numerous contexts, from physics to graph theory, and display appealing theoretical properties. On the more practical side of things,…

Statistics Theory · Mathematics 2018-08-22 Simon Barthelmé , Pierre-Olivier Amblard , Nicolas Tremblay

Differentiating through the solution of a quadratic program (QP) is a central problem in differentiable optimization. Most existing approaches differentiate through the Karush--Kuhn--Tucker (KKT) system, but their computational cost and…

Machine Learning · Computer Science 2026-03-04 Yuxuan Linghu , Zhiyuan Liu , Qi Deng

We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…

Probability · Mathematics 2026-03-03 Hugo Jaquard , Nicolas Keriven

Subset selection problems ask for a small, diverse yet representative subset of the given data. When pairwise similarities are captured by a kernel, the determinants of submatrices provide a measure of diversity or independence of items…

Data Structures and Algorithms · Computer Science 2016-07-07 Tarun Kathuria , Amit Deshpande