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Related papers: Kronecker Determinantal Point Processes

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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

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

Determinantal Point Processes (DPPs) were introduced by Macchi as a model for repulsive (fermionic) particle distributions. But their recent popularization is largely due to their usefulness for encouraging diversity in the final stage of a…

Numerical Analysis · Mathematics 2021-04-28 Jack Poulson

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures $\Xi$ on a space $S$ with measure $\lambda$, whose correlation functions are all given by determinants specified by an integral kernel…

Probability · Mathematics 2021-09-08 Makoto Katori , Tomoyuki Shirai

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…

Sequential recommendation is a popular task in academic research and close to real-world application scenarios, where the goal is to predict the next action(s) of the user based on his/her previous sequence of actions. In the training…

Information Retrieval · Computer Science 2022-04-26 Yuli Liu , Christian Walder , Lexing Xie

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

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

Stochastic gradient descent (SGD) is a cornerstone of machine learning. When the number N of data items is large, SGD relies on constructing an unbiased estimator of the gradient of the empirical risk using a small subset of the original…

Machine Learning · Statistics 2021-12-14 Remi Bardenet , Subhro Ghosh , Meixia Lin

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 random configurations of points with tunable negative dependence. Because sampling is tractable, DPPs are natural candidates for subsampling tasks, such as minibatch selection or coreset…

Machine Learning · Statistics 2024-11-04 Rémi Bardenet , Subhroshekhar Ghosh , Hugo Simon-Onfroy , Hoang-Son Tran

The Nystr\"om method has long been popular for scaling up kernel methods. Its theoretical guarantees and empirical performance rely critically on the quality of the landmarks selected. We study landmark selection for Nystr\"om using…

Machine Learning · Computer Science 2016-05-31 Chengtao Li , Stefanie Jegelka , Suvrit Sra

We introduce new families of determinantal point processes (DPPs) on a complex plane ${\mathbb{C}}$, which are classified into seven types following the irreducible reduced affine root systems, $R_N=A_{N-1}$, $B_N$, $B^{\vee}_N$, $C_N$,…

Mathematical Physics · Physics 2020-08-04 Makoto Katori

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

Semi-parametric regression models are used in several applications which require comprehensibility without sacrificing accuracy. Typical examples are spline interpolation in geophysics, or non-linear time series problems, where the system…

Machine Learning · Computer Science 2021-03-10 Michaël Fanuel , Joachim Schreurs , Johan A. K. Suykens

Understanding how subsets of items are chosen from offered sets is critical to assortment planning, wireless network planning, and many other applications. There are two seemingly unrelated subset choice models that capture dependencies…

Machine Learning · Computer Science 2023-02-23 Sander Aarts , David B. Shmoys , Alex Coy

Determinantal point processes (DPPs) have recently proved to be a useful class of models in several areas of statistics, including spatial statistics, statistical learning and telecommunications networks. They are models for repulsive (or…

Statistics Theory · Mathematics 2016-06-07 Christophe Ange Napoléon Biscio , Frédéric Lavancier

Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient…

Artificial Intelligence · Computer Science 2020-06-30 Honghua Zhang , Steven Holtzen , Guy Van den Broeck

By using the framework of Determinantal Point Processes (DPPs), some theoretical results concerning the interplay between diversity and regularization can be obtained. In this paper we show that sampling subsets with kDPPs results in…

Machine Learning · Computer Science 2021-07-22 Joachim Schreurs , Michaël Fanuel , Johan A. K. Suykens

Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find…

Discrete Mathematics · Computer Science 2017-06-15 Insu Han , Prabhanjan Kambadur , Kyoungsoo Park , Jinwoo Shin