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Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes [article]

Nima Anari, Shayan Oveis Gharan, Alireza Rezaei
2016 arXiv   pre-print
We show that the "natural" Monte Carlo Markov Chain (MCMC) is rapidly mixing in the support of a homogeneous strongly Rayleigh distribution.  ...  As a byproduct, our proof implies Markov chains can be used to efficiently generate approximate samples of a k-determinantal point process.  ...  Since determinantal point processes are special cases of strongly Rayleigh measures, our result implies that the same Markov chain efficiently generates random samples of a k-determinantal point process  ... 
arXiv:1602.05242v3 fatcat:stw6mvlzubfrfhozeustanuszi

Fast Sampling for Strongly Rayleigh Measures with Application to Determinantal Point Processes [article]

Chengtao Li, Stefanie Jegelka, Suvrit Sra
2016 arXiv   pre-print
As an important corollary, we obtain a fast mixing Markov Chain sampler for Determinantal Point Processes.  ...  In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures.  ...  We sample from π via a Markov Chain Monte Carlo method (MCMC), i.e., we run a Markov Chain with state space 2 V (the power set of V). All the chains discussed here are ergodic.  ... 
arXiv:1607.03559v1 fatcat:ohtcpoyhy5conirrqjwqaj6wye

Fixed-Size Determinantal Point Processes Sampling For Species Phylogeny

Diala Wehbe, Nicolas Wicker, Baydaa Al-Ayoubi, Luc Moulinier
2021 MathematicS in Action  
Determinantal point processes (DPPs) are popular tools that supply useful information for repulsiveness.  ...  They provide coherent probabilistic models when negative correlations arise and also represent new algorithms for inference problems like sampling, marginalization and conditioning.  ...  Thompson for careful reading of the manuscript and English language correction.  ... 
doi:10.5802/msia.13 fatcat:lezkimjydnfvneywnjpg3lpel4

Discrete Sampling using Semigradient-based Product Mixtures [article]

Alkis Gotovos, Hamed Hassani, Andreas Krause, Stefanie Jegelka
2018 arXiv   pre-print
Locally-moving Markov chain Monte Carlo algorithms, such as the Gibbs sampler, are commonly used for inference in such models, but their convergence is, at times, prohibitively slow.  ...  These encompass a range of well-known models in machine learning, such as determinantal point processes and Ising models.  ...  Acknowledgements This work was partially supported by ERC Starting Grant 307036, NSF CAREER award 1553284, and the Simons Institute for the Theory of Computing.  ... 
arXiv:1807.01808v2 fatcat:xeuzzt72xnf2bjdre46vrctohq

Determinantal Point Processes in Randomized Numerical Linear Algebra

Michał Dereziński, Michael W. Mahoney
2021 Notices of the American Mathematical Society  
We would like to acknowledge DARPA, NSF (via the TRIPODS program), and ONR (via the BRC on RandNLA) for providing partial support for this work.  ...  Also, extensions of intermediate sampling exist for classes of distributions beyond DPPs, including all Strongly Rayleigh measures [21] . 5.4. DPPs: Monte Carlo sampling.  ...  A completely different approach of (approximately) sampling from a DPP was proposed by [3] , who showed that a simple fastmixing Monte Carlo Markov chain (MCMC) algorithm has a cardinality constrained  ... 
doi:10.1090/noti2202 fatcat:h5xetz2udbhndguu2glukp3k4m

Determinantal Point Processes in Randomized Numerical Linear Algebra [article]

Michał Dereziński, Michael W. Mahoney
2020 arXiv   pre-print
Determinantal Point Processes (DPPs), a seemingly unrelated topic in pure and applied mathematics, is a class of stochastic point processes with probability distribution characterized by sub-determinants  ...  sense, an optimal randomized algorithm for the Nystr\"om method; and a RandNLA technique called leverage score sampling can be derived as the marginal distribution of a DPP.  ...  Acknowledgements We would like to acknowledge DARPA, NSF (via the TRIPODS program), and ONR (via the BRC on RandNLA) for providing partial support for this work.  ... 
arXiv:2005.03185v1 fatcat:6z64xgo5x5bkfgwucyj3ysyhum

Modified log-Sobolev Inequalities for Strongly Log-Concave Distributions

Mary Cryan, Heng Guo, Giorgos Mousa
2019 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)  
We show that the modified log-Sobolev constant for a natural Markov chain which converges to an r-homogeneous strongly log-concave distribution is at least 1/r.  ...  As a consequence, we obtain an asymptotically optimal mixing time bound for this chain. Applications include the bases-exchange random walk in a matroid.  ...  Monte Carlo Markov chain algorithms for sampling strongly Rayleigh distributions and determinantal point processes.  ... 
doi:10.1109/focs.2019.00083 dblp:conf/focs/Cryan0M19 fatcat:ihrgvm6wsbgkrey3ia3ichfcrm

Sampling from a k-DPP without looking at all items [article]

Daniele Calandriello, Michał Dereziński, Michal Valko
2020 arXiv   pre-print
Determinantal point processes (DPPs) are a useful probabilistic model for selecting a small diverse subset out of a large collection of items, with applications in summarization, stochastic optimization  ...  Existing k-DPP sampling algorithms require an expensive preprocessing step which involves multiple passes over all n items, making it infeasible for large datasets.  ...  Monte carlo markov chain algorithms for sampling strongly rayleigh distributions and determinantal point processes.  ... 
arXiv:2006.16947v1 fatcat:v4nuxiebpfaepd6ououm673k6m

Fair and Diverse DPP-based Data Summarization [article]

L. Elisa Celis, Vijay Keswani, Damian Straszak, Amit Deshpande, Tarun Kathuria, Nisheeth K. Vishnoi
2018 arXiv   pre-print
Coming up with efficient algorithms to sample from these constrained determinantal distributions, however, suffers from a complexity barrier and we present a fast sampler that is provably good when the  ...  We work with a well-studied determinantal measure of diversity and corresponding distributions (DPPs) and present a framework that allows us to incorporate a general class of fairness constraints into  ...  Another possible approach for sampling from DPPs is the Markov Chain Monte Carlo method.  ... 
arXiv:1802.04023v1 fatcat:3oym4zzcpzg6bos3mkfd45dfha

Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds [article]

Jordan T. Ash, Chicheng Zhang, Akshay Krishnamurthy, John Langford, Alekh Agarwal
2020 arXiv   pre-print
Our algorithm, Batch Active learning by Diverse Gradient Embeddings (BADGE), samples groups of points that are disparate and high-magnitude when represented in a hallucinated gradient space, a strategy  ...  We design a new algorithm for batch active learning with deep neural network models.  ...  Monte carlo markov chain algorithms for sampling strongly rayleigh distributions and determinantal point processes. In Conference on Learning Theory, 2016.  ... 
arXiv:1906.03671v2 fatcat:tuotj3rrnnhjbfduqketynkjvu

Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD [article]

Remi Bardenet, Subhro Ghosh, Meixia Lin
2021 arXiv   pre-print
In particular, experimental evidence suggests drawing minibatches from determinantal point processes (DPPs), distributions over minibatches that favour diversity among selected items.  ...  Moreover, our estimators are amenable to a recent algorithm that directly samples linear statistics of DPPs (i.e., the gradient estimator) without sampling the underlying DPP (i.e., the minibatch), thereby  ...  Monte Carlo integration of smooth functions.  ... 
arXiv:2112.06007v1 fatcat:7zr3zigelzgzla6pzeqtkwjknu

Learning Signed Determinantal Point Processes through the Principal Minor Assignment Problem [article]

Victor-Emmanuel Brunel
2018 arXiv   pre-print
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 diverse sets of items is sought for. Sampling and learning these symmetric DPP's is pretty well understood.  ...  For symmetric kernels, sampling a DPP can be done using a spectral decomposition of the kernel [18, Section 2.4.4] or a Markov chain Monte Carlo method, relying on the fact that DPP(K) is a strongly  ... 
arXiv:1811.00465v1 fatcat:rdpvapqwr5bwnesbrtoulfpmnu

SPADE: Sequential-clustering Particle Annihilation via Discrepancy Estimation [article]

Sihong Shao, Yunfeng Xiong
2020 arXiv   pre-print
One factor measures the irregularity of point distributions and reflects their discrete nature. The other relies on the variation of test function and is influenced by the continuity.  ...  In this paper, we propose an algorithm for PA in high-dimensional Euclidean space based on hybrid of clustering and matching, dubbed the Sequential-clustering Particle Annihilation via Discrepancy Estimation  ...  YX is partially supported by The Elite Program of Computational and Applied Mathematics for PhD Candidates in Peking University.  ... 
arXiv:2005.05129v2 fatcat:vyslobmxvzaa7aalfcjzrre7zi

Asteroseismology: Data Analysis Methods and Interpretation for Space and Ground-based Facilities [article]

T. L. Campante
2014 arXiv   pre-print
M\'ario Jo\~ao Monteiro at the Centro de Astrof\'isica da Universidade do Porto and Dr. Hans Kjeldsen at the Institut for Fysik og Astronomi, Aarhus Universitet.  ...  The chapter ends with a description of the implementation of a pipeline for mode parameter analysis of Kepler data.  ...  The OAPS is plotted for three values of the large separations (54, 55, and 56 μHz), and they are superimposed.  ... 
arXiv:1405.3145v1 fatcat:sehn5sck35gxhflko47yfja7sy

Computational Physics: An Introduction to Monte Carlo Simulations of Matrix Field Theory [article]

Badis Ydri
2016 arXiv   pre-print
Sample codes as well as sample key solutions are also provided for convenience and completness. An appendix containing an executive arabic summary of the first part is added at the end of the book.  ...  The second part is much more advanced and deals with the problem of how to set up working Monte Carlo simulations of matrix field theories which involve finite dimensional matrix regularizations of noncommutative  ...  Hybrid Monte Carlo Algorithm The hybrid Monte Carlo algorithm can be summarized as follows: • 1) Choose P (0) such that P (0) is distributed according to the Gaussian probability distribution exp(− 1 2  ... 
arXiv:1506.02567v2 fatcat:mbtpkxbbmrcwrbvpazr77we5a4
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