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Expectation-Maximization for Learning Determinantal Point Processes [article]

Jennifer Gillenwater, Alex Kulesza, Emily Fox, Ben Taskar
2014 arXiv   pre-print
A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix.  ...  Thus, previous work has instead focused on more restricted convex learning settings: learning only a single weight for each row of the kernel matrix, or learning weights for a linear combination of DPPs  ...  Determinantal point processes (DPPs) offer one way to model this tradeoff; a DPP defines a distribution over all possible subsets of a ground set, and the mass it assigns to any given set is a balanced  ... 
arXiv:1411.1088v1 fatcat:7kln6xs5jnaptoyq7rd2qkndcy

Determinantal thinning of point processes with network learning applications [article]

Bartłomiej Błaszczyszyn, Paul Keeler
2018 arXiv   pre-print
Models based on determinantal point processes are also well suited for statistical (supervised) learning techniques, allowing the models to be fitted to observed network patterns with some particular geometric  ...  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  ...  We call this point process a determinantally-thinned Poisson point process or, for brevity, a determintantal Poisson process.  ... 
arXiv:1810.08672v2 fatcat:a6zw4evd2ze4hmml5dvnojfj3q

Priors for Diversity in Generative Latent Variable Models

James Y. Zou, Ryan P. Adams
2012 Neural Information Processing Systems  
In this work, we revisit these independence assumptions for probabilistic latent variable models, replacing the underlying i.i.d. prior with a determinantal point process (DPP).  ...  Probabilistic latent variable models are one of the cornerstones of machine learning.  ...  The determinantal point process is a convenient statistical tool for constructing a tractable point process with repulsive interaction.  ... 
dblp:conf/nips/ZouA12 fatcat:ym7r7p7ex5df7mxgojaz2r5fme

Exact Sampling from Determinantal Point Processes [article]

Philipp Hennig, Roman Garnett
2018 arXiv   pre-print
Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics.  ...  We point out that, for many settings of relevance to machine learning, it is also possible to draw exact samples from DPPs on continuous domains.  ...  Acknowledgements The authors are grateful to Lucy Kuncheva and Joseph Courtney for (separately) pointing out a nontrivial typo in Eq. (12) in an earlier version of this manuscript.  ... 
arXiv:1609.06840v2 fatcat:xjnhn2occ5eexhlraovv5r7nru

A Determinantal Point Process Latent Variable Model for Inhibition in Neural Spiking Data

Jasper Snoek, Richard S. Zemel, Ryan Prescott Adams
2013 Neural Information Processing Systems  
We develop a novel model based on a determinantal point process over latent embeddings of neurons that effectively captures and helps visualize complex inhibitory and competitive interaction.  ...  However, the most common neural point process models, the Poisson process and the gamma renewal process, do not capture interactions and correlations that are critical to modeling populations of neurons  ...  Determinantal Point Processes The determinantal point process is an elegant distribution over configurations of points in space that tractably models repulsive interactions.  ... 
dblp:conf/nips/SnoekZA13 fatcat:olhd2e5gfzhylggryb4tvxut6m

Learning Determinantal Point Processes [article]

Alex Kulesza, Ben Taskar
2012 arXiv   pre-print
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 for exact inference, including computing marginal probabilities and sampling; however, an important open question has been how to learn  ...  This process is computation- We showed how determinantal point processes can be ally expensive, but it provides a point of comparison applied to subset selection tasks like extractive sum- for  ... 
arXiv:1202.3738v1 fatcat:xjlrvrzsgbbhlfs6v5m2rcmghm

Diversity Networks: Neural Network Compression Using Determinantal Point Processes [article]

Zelda Mariet, Suvrit Sra
2017 arXiv   pre-print
We introduce Divnet, a flexible technique for learning networks with diverse neurons. Divnet models neuronal diversity by placing a Determinantal Point Process (DPP) over neurons in a given layer.  ...  We present experimental results to corroborate our claims: for pruning neural networks, Divnet is seen to be notably superior to competing approaches.  ...  Neuronal diversity via Determinantal Point Processes DPPs are probability measures over subsets of a ground set of items.  ... 
arXiv:1511.05077v6 fatcat:l4laul3l7vfdleqthpqq3fmh64

Practical Nonisotropic Monte Carlo Sampling in High Dimensions via Determinantal Point Processes

Krzysztof Choromanski, Aldo Pacchiano, Jack Parker-Holder, Yunhao Tang
2020 International Conference on Artificial Intelligence and Statistics  
reduce the variance of the estimator via determinantal point processes.  ...  We successfully apply DPPMCs to highdimensional problems involving nonisotropic distributions arising in guided evolution strategy (GES) methods for reinforcement learning (RL), CMA-ES techniques and trust  ...  via learned or nonadaptive determinantal point processes (DPPs, Kulesza and Taskar (2012) ; Gartrell et al. (2017) ).  ... 
dblp:conf/aistats/ChoromanskiPPT20 fatcat:7fpqauzavzbkjky34m32bo5a7y

Learning Determinantal Point Processes by Corrective Negative Sampling [article]

Zelda Mariet, Mike Gartrell, Suvrit Sra
2019 arXiv   pre-print
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  ...  While fitting observed sets well, MLE for DPPs may also assign high likelihoods to unobserved sets that are far from the true generative distribution of the data.  ...  A model that offers an elegant, tractable way to achieve this balance is a Determinantal Point Process (DPP).  ... 
arXiv:1802.05649v4 fatcat:4q4jqfpjxvgabgfwq7pepcvxim

Diverse Sequential Subset Selection for Supervised Video Summarization

Boqing Gong, Wei-Lun Chao, Kristen Grauman, Fei Sha
2014 Neural Information Processing Systems  
To this end, we propose the sequential determinantal point process (seqDPP), a probabilistic model for diverse sequential subset selection.  ...  Meanwhile, seqDPP retains the power of modeling diverse subsets, essential for summarization.  ...  We are grateful to Jiebo Luo for providing the Kodak dataset [32] .  ... 
dblp:conf/nips/GongCGS14 fatcat:q2sjg3ugu5f2ta2bjx4ldywuu4

Coverage probability in wireless networks with determinantal scheduling [article]

Bartek Błaszczyszyn, Antoine Brochard, H. Paul Keeler
2020 arXiv   pre-print
developed for statistical learning with determinantal processes.  ...  The idea is to use (discrete) determinantal point processes (subsets) to randomly assign medium access to various repulsive subsets of potential transmitters.  ...  i )] , (34) where the expectation E ! xi is taken with respect to the reduced Palm distribution of the (determinantal) point process Ψ.  ... 
arXiv:2006.05038v1 fatcat:rrjzsgd73rddtgf3l4obpdicy4

Diverse Trajectory Forecasting with Determinantal Point Processes [article]

Ye Yuan, Kris Kitani
2019 arXiv   pre-print
To learn the parameters of the DSF, the diversity of the trajectory samples is evaluated by a diversity loss based on a determinantal point process (DPP).  ...  While generative models such as variational autoencoders (VAEs) have been shown to be a powerful tool for learning a distribution over future trajectories, randomly drawn samples from the learned implicit  ...  To this end, we make use of determinantal point processes (DPPs) to model the diversity within a set.  ... 
arXiv:1907.04967v2 fatcat:cby7thunhbcexlyn4dqab3wsf4

Approximately Optimal Subset Selection for Statistical Design and Modelling [article]

Yu Wang, Nhu D. Le, James V. Zidek
2019 arXiv   pre-print
We establish an efficient polynomial-time algorithm using Determinantal Point Process for approximating the optimal solution to the problem.  ...  In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix that characterizes the chosen subset.  ...  [7, 26] Algorithm 2 Genetic Algorithm Determinantal Point Processes for Approximating The Optimum Determinantal point processes are probabilistic models that capture negative correlation with respect  ... 
arXiv:1709.00151v3 fatcat:l4wklblstzepzn2fdpsbuadlau

Learning Detection with Diverse Proposals

Samaneh Azadi, Jiashi Feng, Trevor Darrell
2017 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
To predict a set of diverse and informative proposals with enriched representations, this paper introduces a differentiable Determinantal Point Process (DPP) layer that is able to augment the object detection  ...  In contrast, our trainable DPP layer, allowing for Learning Detection with Diverse Proposals (LDDP), considers both label-level contextual information and spatial layout relationships between proposals  ...  Learning with Diverse Proposals Determinantal Point Processes (DPPs) are natural models for diverse subset selection problems [10] .  ... 
doi:10.1109/cvpr.2017.779 dblp:conf/cvpr/AzadiFD17 fatcat:urxtetpyijhvdcswka6rtulwge

Learning Determinantal Point Processes in Sublinear Time [article]

Christophe Dupuy
2016 arXiv   pre-print
We propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items.  ...  new class to modelling text documents as sampling a DPP of sentences, and propose a conditional maximum likelihood formulation to model topic proportions, which is made possible with no approximation for  ...  Acknowledgements We would like to thank Patrick Perez for helpful discussions related to this work.  ... 
arXiv:1610.05925v1 fatcat:ukd5zaljx5clngxgnia2todxzy
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