Determinantal Point Processes for Machine Learning

Kulesza, Alex; Taskar, Ben

doi:10.1561/9781601986290

Cited by 248 publications

(102 citation statements)

References 119 publications

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“…Determinantal Point Processes (DPPs) have been used in subset selection tasks such as product recommendation [28], text summarization [29], web search [30], and graph sampling [31]. As shown in Equation 2, a point process is a probabilistic measure for one instantiation Y of a set Y.…”

Section: Background a Determinantal Point Processesmentioning

confidence: 99%

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A New Many-Objective Evolutionary Algorithm Based on Determinantal Point Processes

Zhang

et al. 2021

IEEE Trans. Evol. Computat.

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To handle different types of Many-Objective Optimization Problems (MaOPs), Many-Objective Evolutionary Algorithms (MaOEAs) need to simultaneously maintain convergence and population diversity in the high-dimensional objective space. In order to balance the relationship between diversity and convergence, we introduce a Kernel Matrix and probability model called Determinantal Point Processes (DPPs). Our Many-Objective Evolutionary Algorithm with Determinantal Point Processes (MaOEADPPs) is presented and compared with several state-of-the-art algorithms on various types of MaOPs with different numbers of objectives. The experimental results demonstrate that MaOEADPPs is competitive.

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Section: Background a Determinantal Point Processesmentioning

confidence: 99%

“…Here P r denotes the probability, whereas P L (Y = Y) is a probability measure. In [29], it is shown that when sampling from DPPs, the probability of an element i from Y, is given by…”

Section: Background a Determinantal Point Processesmentioning

confidence: 99%

A New Many-Objective Evolutionary Algorithm Based on Determinantal Point Processes

Zhang

et al. 2021

IEEE Trans. Evol. Computat.

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“…for M = C(I + C) −1 (Kulesza and Taskar, 2012), where M A is a submatrix of M. Equation (4) defines a DPP on a finite state space S. Every L-ensemble is a DPP. But not every DPP is an L-ensemble.…”

Section: Definitionmentioning

confidence: 99%

“…For singular (I − M) we can define (4), but not (3). A good review of DPP models for finite state spaces, including the derivation of the normalizing constant in (3) appears in Kulesza and Taskar (2012). For a continuous state space S ⊆ D , we define an Lensemble by a density f (X) with respect to the unit rate Poisson process as…”

Section: Definitionmentioning

confidence: 99%

“…Again, an independent prior on the cluster-specific parameters μ h complicates a meaningful interpretation of posterior inference on the random partition s. In this article we argue for an alternative model that replaces the independent prior on μ h by the repulsive DPP (Macchi, 1975). Recent reviews of the DPP appear in Lavancier et al (2015) and, specifically for finite state spaces, in Kulesza and Taskar (2012). The use of the DPP as a prior for statistical inference in mixture models, we believe, is first discussed in Affandi et al (2013).…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Inference for Latent Biologic Structure With Determinantal Point Processes (DPP)

Müller

Telesca³

2016

Biometrics

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Summary 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 structure. Typical examples include mixture models, when the terms of the mixture are meant to represent clinically meaningful subpopulations (of patients, genes, etc.). Another class of examples are feature allocation models. We propose the DPP prior as a repulsive prior on latent mixture components in the first example, and as prior on feature-specific parameters in the second case. We argue that the DPP is in general an attractive prior model for latent structure when biologically relevant interpretation of such structure is desired. We illustrate the advantages of DPP prior in three case studies, including inference in mixture models for magnetic resonance images (MRI) and for protein expression, and a feature allocation model for gene expression using data from The Cancer Genome Atlas. An important part of our argument are efficient and straightforward posterior simulation methods. We implement a variation of reversible jump Markov chain Monte Carlo simulation for inference under the DPP prior, using a density with respect to the unit rate Poisson process.

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Design of monitoring networks using k‐determinantal point processes

Casquilho‐Resende

Zidek

et al. 2017

Environmetrics

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In this paper, we introduce a design strategy based on k-determinantal point processes (k-DPPs). The k-DPP design is a flexible design scheme that is able to yield spatially balanced designs while also imposing diversity of the selected locations based on extra sources of information known to be related to the underlying process of interest. The methodology is able to handle both the designing and the redesigning of a monitoring network. In particular, we discuss how a k-DPP design can be used as a randomized alternative for the space-filling designs when the objective is to provide a good spatial coverage of the region of interest. Furthermore, we discuss how the k-DPP optimal design objective is remarkably similar to that of entropy design for Gaussian fields. Because the optimization for entropy designs is a NP-hard problem, we explore an approximate solution based on a k-DPP sampling design strategy. Through a case study of augmentation of a network for monitoring temperatures, we illustrate how a k-DPP sampling design strategy can yield an approximation for the entropy solution.

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Determinantal Point Processes for Machine Learning

Cited by 248 publications

References 119 publications

A New Many-Objective Evolutionary Algorithm Based on Determinantal Point Processes

A New Many-Objective Evolutionary Algorithm Based on Determinantal Point Processes

Bayesian Inference for Latent Biologic Structure With Determinantal Point Processes (DPP)

Design of monitoring networks using k‐determinantal point processes

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