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The Journal of Machine Learning Research 2017年第1期18卷

作者： Ardavan Saeedi Tejas D. Kulkarni Vikash K. Mansinghka Samuel J. Gershman Computer Science & Artificial Intelligence Laboratory Massachusetts Institute of Technology Cambridge MA DeepMind London Department of Brain & Cognitive Sciences Massachusetts Institute of Technology Cambridge MA Department of Psychology and Center for Brain Science Harvard University Cambridge MA

Approximate inference in high-dimensional, discrete probabilistic models is a central problem in computational statistics and machine learning. This paper describes discrete particle variational inference (DPVI), a new approach that combines key strengths of Monte Carlo, variational and search-based techniques. DPVI is based on a novel family of particle-based variational approximations that can be fit using simple, fast, deterministic search techniques. Like Monte Carlo, DPVI can handle multiple modes, and yields exact results in a well-defined limit. Like unstructured mean-field, DPVI is based on optimizing a lower bound on the partition function; when this quantity is not of intrinsic interest, it facilitates convergence assessment and debugging. Like both Monte Carlo and combinatorial search, DPVI can take advantage of factorization, sequential structure, and custom search operators. This paper defines DPVI particle-based approximation family and partition function lower bounds, along with the sequential DPVI and local DPVI algorithm templates for optimizing them. DPVI is illustrated and evaluated via experiments on lattice Markov Random Fields, nonparametric Bayesian mixtures and block-models, and parametric as well as non-parametric hidden Markov models. Results include applications to real-world spike-sorting and relational modeling problems, and show that DPVI can offer appealing time/accuracy trade-offs as compared to multiple alternatives.

关键词： Bayesian inference dirichlet process mixture model hidden Markov model infinite relational model ising model variational methods

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Improved Algorithms for Two Energy-Optimal Routing Problems in Ad-Hoc Wireless Networks

Improved Algorithms for Two Energy-Optimal Routing Problems ...

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IEEE International Conference on Big Data and Cloud Computing (BdCloud)

作者： Samuel Baugh Gruia Calinescu David Rincon-Cruz Kan Qiao University of Chicago Chicago USA Department of Computer Science Illinois Institute of Technology Chicago USA Knox College USA Google Inc. USA

ISBN: (纸本)9781509039371

We study two problems of assigning transmission power to the nodes of ad hoc wireless networks to minimize total power consumption while satisfying certain connectivity constraints. The first problem requires to establish k node-disjoint paths from a given source to a given destination. Our new algorithm works for the most general cost model, and returns an optimal solution in time O(n 3 ) (where n is the number of nodes), improving the running time over the previously published algorithm by a factor of k. The second problem assumes that the power requirement between any two nodes is symmetric, and that there are exactly two possible power levels, one of which is negligible. A source is given and all the nodes in the network must be reachable from the source (unidirectional links allowed for broadcast). We obtain a (4 + ln n)-approximation algorithm, while the best published approximation ratio is 2 (1+ln(n-1)). It was also known that no approximation ratio better than O(ln n) is possible unless P = NP.

关键词： Approximation algorithms Ad hoc networks Computational modeling Routing Wireless networks Complexity theory

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First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole

arXiv

引用

arXiv 2019年

作者： Akiyama, Kazunori Alberdi, Antxon Alef, Walter Asada, Keiichi Azulay, Rebecca Baczko, Anne-Kathrin Ball, David Baloković, Mislav Barrett, John Bintley, Dan Blackburn, Lindy Boland, Wilfred Bouman, Katherine L. Bower, Geoffrey C. Bremer, Michael Brinkerink, Christiaan D. Brissenden, Roger Britzen, Silke Broderick, Avery E. Broguiere, Dominique Bronzwaer, Thomas Byun, Do-Young Carlstrom, John E. Chael, Andrew Chan, Chi-kwan Chatterjee, Shami Chatterjee, Koushik Chen, Ming-Tang Chen, Yongjun Cho, Ilje Christian, Pierre Conway, John E. Cordes, James M. Crew, Geoffrey B. Cui, Yuzhu Davelaar, Jordy de Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dexter, Jason Doeleman, Sheperd S. Eatough, Ralph P. Falcke, Heino Fish, Vincent L. Fomalont, Ed Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Gómez, José L. Galison, Peter Gammie, Charles F. García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco Gold, Roman Gu, Minfeng Gurwell, Mark Hada, Kazuhiro Hecht, Michael H. Hesper, Ronald Ho, Luis C. Ho, Paul Honma, Mareki Huang, Chih-Wei L. Huang, Lei Hughes, David H. Ikeda, Shiro Inoue, Makoto Issaoun, Sara James, David J. Jannuzi, Buell T. Janssen, Michael Jeter, Britton Jiang, Wu Johnson, Michael D. Jorstad, Svetlana Jung, Taehyun Karami, Mansour Karuppusamy, Ramesh Kawashima, Tomohisa Keating, Garrett K. Kettenis, Mark Kim, Jae-Young Kim, Junhan Kim, Jongsoo Kino, Motoki Koay, Jun Yi Koch, Patrick M. Koyama, Shoko Kramer, Michael Kramer, Carsten Krichbaum, Thomas P. Kuo, Cheng-Yu Lauer, Tod R. Lee, Sang-Sung Li, Yan-Rong Li, Zhiyuan Lindqvist, Michael Liu, Kuo Liuzzo, Elisabetta Lo, Wen-Ping Lobanov, Andrei P. Loinard, Laurent Lonsdale, Colin Lu, Ru-Sen MacDonald, Nicholas R. Mao, Jirong Markoff, Sera Marrone, Daniel P. Marscher, Alan P. Martí-Vidal, Iván Matthews, Lynn D. Medeiros, Lia Matsushita, Satoki Menten, Karl M. Mizuno, Yosuke Mizuno, Izumi Moran, James M. Moriyama, Kotaro Moscibrodzka, Monika Müller, Cornelia Nagai, Hiroshi Nagar, Neil M. Nakamura, Masanori National Radio Astronomy Observatory 520 Edgemont Rd CharlottesvilleVA22903 United States Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Black Hole Initiative at Harvard University 20 Garden Street CambridgeMA02138 United States Instituto de Astrofísica de Andalucía–CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd Taipei10617 Taiwan Departament d’Astronomia i Astrofísica Universitat de València C. Dr. Moliner 50 Burjassot ValènciaE-46100 Spain Observatori Astronòmic Universitat de València C. Catedrático José Beltrán 2 PaternaValènciaE-46980 Spain Steward Observatory and Department of Astronomy University of Arizona 933 N. Cherry Ave. TucsonAZ85721 United States Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States East Asian Observatory 660 N. A’ohoku Pl. HiloHI96720 United States PO Box 9513 Leiden2300 RA Netherlands California Institute of Technology 1200 East California Boulevard PasadenaCA91125 United States Institute of Astronomy and Astrophysics Academia Sinica 645 N. A’ohoku Place HiloHI96720 United States Institut de Radioastronomie Millimétrique 300 rue de la Piscine Saint Martin d’HèresF-38406 France Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Perimeter Institute for Theoretical Physics 31 Caroline Street North WaterlooONN2L 2Y5 Canada Department of Physics and Astronomy University of Waterloo 200 University Avenue West WaterlooONN2L 3G1 Canada Waterloo Centre for Astrophysics University of Waterloo WaterlooONN2L 3G1 Canada Korea Astronomy and Space Science Institute Daedeok-daero 776 Yuseon

We present the first Event Horizon Telescope (EHT) images of M87, using observations from April 2017 at 1.3 mm wavelength. These images show a prominent ring with a diameter of ∼40 μas, consistent with the size and shape of the lensed photon orbit encircling the "shadow" of a supermassive black hole. The ring is persistent across four observing nights and shows enhanced brightness in the south. To assess the reliability of these results, we implemented a two-stage imaging procedure. In the first stage, four teams, each blind to the others’ work, produced images of M87 using both an established method (CLEAN) and a newer technique (regularized maximum likelihood). This stage allowed us to avoid shared human bias and to assess common features among independent reconstructions. In the second stage, we reconstructed synthetic data from a large survey of imaging parameters and then compared the results with the corresponding ground truth images. This stage allowed us to select parameters objectively to use when reconstructing images of M87. Across all tests in both stages, the ring diameter and asymmetry remained stable, insensitive to the choice of imaging technique. We describe the EHT imaging procedures, the primary image features in M87, and the dependence of these features on imaging assumptions. Copyright © 2019, The Authors. All rights reserved.

关键词： Image reconstruction

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Scalable inuence maximization for multiple products in continuous-time diffusion networks

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2017年第1期18卷

作者： Nan Du Yingyu Liang Maria-Florina Balcan Manuel Gomez-Rodriguez Hongyuan Zha Le Song Google Research Mountain View CA Department of Computer Science Princeton University Princeton NJ School of Computer Science Carnegie Mellon University Pittsburgh PA MPI for Software Systems Kaiserslautern Germany College of Computing Georgia Institute of Technology Atlanta GA

A typical viral marketing model identifies influential users in a social network to maximize a single product adoption assuming unlimited user attention, campaign budgets, and time. In reality, multiple products need campaigns, users have limited attention, convincing users incurs costs, and advertisers have limited budgets and expect the adoptions to be maximized soon. Facing these user, monetary, and timing constraints, we formulate the problem as a submodular maximization task in a continuous-time diffusion model under the intersection of one matroid and multiple knapsack constraints. We propose a randomized algorithm estimating the user inuence in a network (|V| nodes, |E| edges) to an accuracy of ε with n = O(1/ε2) randomizations and O (n|E|+n|V|) computations. By exploiting the influence estimation algorithm as a subroutine, we develop an adaptive threshold greedy algorithm achieving an approximation factor ka/(2 + 2k) of the optimal when ka out of the k knapsack constraints are active. Extensive experiments on networks of millions of nodes demonstrate that the proposed algorithms achieve the state-of-the-art in terms of effectiveness and scalability.

关键词： continuous-time diffusion influence estimation influence maximization knapsack matroid model

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OpenFermion: The electronic structure package for quantum computers

arXiv

引用

arXiv 2017年

作者： McClean, Jarrod R. Sung, Kevin J. Kivlichan, Ian D. Cao, Yudong Dai, Chengyu Schuyler Fried, E. Gidney, Craig Gimby, Brendan Gokhale, Pranav Häner, Thomas Hardikar, Tarini Havlíček, Vojtěch Higgott, Oscar Huang, Cupjin Izaac, Josh Jiang, Zhang Liu, Xinle McArdle, Sam Neeley, Matthew O'Brien, Thomas O'Gorman, Bryan Ozfidan, Isil Radin, Maxwell D. Romero, Jhonathan Rubin, Nicholas Sawaya, Nicolas P.D. Setia, Kanav Sim, Sukin Steiger, Damian S. Steudtner, Mark Sun, Qiming Sun, Wei Wang, Daochen Zhang, Fang Babbush, Ryan Google Inc. VeniceCA90291 United States Department of Electrical Engineering and Computer Science University of Michigan Ann ArborMI48109 United States Department of Physics Harvard University CambridgeMA02138 United States Department of Chemistry and Chemical Biology Harvard University CambridgeMA02138 United States Zapata Computing Inc. Cambridge02138 United States Department of Physics University of Michigan Ann ArborMI48109 United States Rigetti Computing BerkeleyCA94710 United States Google Inc. Santa BarbaraCA93117 Department of Computer Science University of Chicago ChicagoIL60637 United States Theoretische Physik ETH Zurich Zurich8093 Switzerland Department of Physics Dartmouth College HanoverNH03755 United States Department of Computer Science Oxford University OxfordOX1 3QD United Kingdom Department of Physics and Astronomy University College London Gower Street LondonWC1E 6BT United Kingdom Xanadu 372 Richmond St W TorontoM5V 1X6 Canada QuAIL NASA Ames Research Center Moffett FieldCA94035 Google Inc. Mountain ViewCA94043 United States Department of Materials University of Oxford Parks Road OxfordOX1 3PH United Kingdom Instituut-Lorentz Universiteit Leiden Leiden2300 RA Netherlands BQIC University of California BerkeleyCA94720 United States D-Wave Systems Inc. BurnabyBC Canada Materials Department University of California Santa Barbara Santa BarbaraCA93106 United States QuTech Delft University of Technology Lorentzweg 1 Delft2628 CJ Netherlands Division of Chemistry and Chemical Engineering California Institute of Technology PasadenaCA91125 United States Joint Center for Quantum Information and Computer Science University of Maryland College ParkMD20742 United States

Quantum simulation of chemistry and materials is predicted to be an important application for both near-term and fault-tolerant quantum devices. However, at present, developing and studying algorithms for these problems can be difficult due to the prohibitive amount of domain knowledge required in both the area of chemistry and quantum algorithms. To help bridge this gap and open the field to more researchers, we have developed the OpenFermion software package (***). OpenFermion is an open-source software library written largely in Python under an Apache 2.0 license, aimed at enabling the simulation of fermionic and bosonic models and quantum chemistry problems on quantum hardware. Beginning with an interface to common electronic structure packages, it simplifies the translation between a molecular specification and a quantum circuit for solving or studying the electronic structure problem on a quantum computer, minimizing the amount of domain expertise required to enter the field. The package is designed to be extensible and robust, maintaining high software standards in documentation and testing. This release paper outlines the key motivations behind design choices in OpenFermion and discusses some basic OpenFermion functionality which we believe will aid the community in the development of better quantum algorithms and tools for this exciting area of research. Copyright © 2017, The Authors. All rights reserved.

关键词： Electronic structure

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A Large Probabilistic Semantic Network Based Approach to Compute Term Similarity

引用

IEEE Transactions on Knowledge and Data Engineering 2015年第10期27卷 2604-2617页

作者： Li, Peipei Wang, Haixun Zhu, Kenny Q. Wang, Zhongyuan Hu, Xuegang Wu, Xindong School of Computer Science and Information Engineering Hefei University of Technology Hefei Anhui Province230009 China Google Research Mountain ViewCA94043 United States Department of Computer Science Shanghai Jiao Tong University Shanghai200240 China Renmin University of China Microsoft Research Asia Beijing China Department of Computer Science University of Vermont BurlingtonVT05405 United States

Measuring semantic similarity between two terms is essential for a variety of text analytics and understanding applications. Currently, there are two main approaches for this task, namely the knowledge based and the corpus based approaches. However, existing approaches are more suitable for semantic similarity between words rather than the more general multi-word expressions (MWEs), and they do not scale very well. Contrary to these existing techniques, we propose an efficient and effective approach for semantic similarity using a large scale semantic network. This semantic network is automatically acquired from billions of web documents. It consists of millions of concepts, which explicitly model the context of semantic relationships. In this paper, we first show how to map two terms into the concept space, and compare their similarity there. Then, we introduce a clustering approach to orthogonalize the concept space in order to improve the accuracy of the similarity measure. Finally, we conduct extensive studies to demonstrate that our approach can accurately compute the semantic similarity between terms of MWEs and with ambiguity, and significantly outperforms 12 competing methods under Pearson Correlation Coefficient. Meanwhile, our approach is much more efficient than all competing algorithms, and can be used to compute semantic similarity in a large scale. © 2015 IEEE.

关键词： Semantics

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Differential privacy for bayesian inference through posterior sampling

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2017年第1期18卷

作者： Christos Dimitrakakis Blaine Nelson Zuhe Zhang Aikaterini Mitrokotsa Benjamin I. P. Rubinstein University of Lille SEAS Harvard University Cambridge MA and DIT Chalmers University of Technology Gothenburg Sweden Google Inc. Mountain View CA School of Mathematics & Statistics The University of Melbourne Parkville VIC Australia Department of Computer Science & Engineering Chalmers University of Technology Gothenburg Sweden School of Computing & Information Systems The University of Melbourne Parkville VIC Australia

Differential privacy formalises privacy-preserving mechanisms that provide access to a database. Can Bayesian inference be used directly to provide private access to data? The answer is yes: under certain conditions on the prior, sampling from the posterior distribution can lead to a desired level of privacy and utility. For a uniform treatment, we define differential privacy over arbitrary data set metrics, outcome spaces and distribution families. This allows us to also deal with non-i.i.d or non-tabular data sets. We then prove bounds on the sensitivity of the posterior to the data, which delivers a measure of robustness. We also show how to use posterior sampling to provide differentially private responses to queries, within a decision-theoretic framework. Finally, we provide bounds on the utility of answers to queries and on the ability of an adversary to distinguish between data sets. The latter are complemented by a novel use of Le Cam's method to obtain lower bounds on distinguishability. Our results hold for arbitrary metrics, including those for the common definition of differential privacy. For specific choices of the metric, we give a number of examples satisfying our assumptions.

关键词： Bayesian inference adversarial learning differential privacy robustness

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First M87 event horizon telescope results. I. The shadow of the supermassive black hole

arXiv

引用

arXiv 2019年

作者： Akiyama, Kazunori Alberdi, Antxon Alef, Walter Asada, Keiichi Azulay, Rebecca Baczko, Anne-Kathrin Ball, David Baloković, Mislav Barrett, John Bintley, Dan Blackburn, Lindy Boland, Wilfred Bouman, Katherine L. Bower, Geoffrey C. Bremer, Michael Brinkerink, Christiaan D. Brissenden, Roger Britzen, Silke Broderick, Avery E. Broguiere, Dominique Bronzwaer, Thomas Byun, Do-Young Carlstrom, John E. Chael, Andrew Chan, Chi-kwan Chatterjee, Shami Chatterjee, Koushik Chen, Ming-Tang Chen, Yongjun Cho, Ilje Christian, Pierre Conway, John E. Cordes, James M. Crew, Geoffrey B. Cui, Yuzhu Davelaar, Jordy de Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dexter, Jason Doeleman, Sheperd S. Eatough, Ralph P. Falcke, Heino Fish, Vincent L. Fomalont, Ed Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Gómez, José L. Galison, Peter Gammie, Charles F. García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco Gold, Roman Gu, Minfeng Gurwell, Mark Hada, Kazuhiro Hecht, Michael H. Hesper, Ronald Ho, Luis C. Ho, Paul Honma, Mareki Huang, Chih-Wei L. Huang, Lei Hughes, David H. Ikeda, Shiro Inoue, Makoto Issaoun, Sara James, David J. Jannuzi, Buell T. Janssen, Michael Jeter, Britton Jiang, Wu Johnson, Michael D. Jorstad, Svetlana Jung, Taehyun Karami, Mansour Karuppusamy, Ramesh Kawashima, Tomohisa Keating, Garrett K. Kettenis, Mark Kim, Jae-Young Kim, Junhan Kim, Jongsoo Kino, Motoki Koay, Jun Yi Koch, Patrick M. Koyama, Shoko Kramer, Michael Kramer, Carsten Krichbaum, Thomas P. Kuo, Cheng-Yu Lauer, Tod R. Lee, Sang-Sung Li, Yan-Rong Li, Zhiyuan Lindqvist, Michael Liu, Kuo Liuzzo, Elisabetta Lo, Wen-Ping Lobanov, Andrei P. Loinard, Laurent Lonsdale, Colin Lu, Ru-Sen National Radio Astronomy Observatory 520 Edgemont Road CharlottesvilleVA22903 United States Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observator of Ja an 2-21-1 Osawa Mitaka Tok o Ja an181-8588 Japan Black Hole Initiative at Harvard Universit 20 Garden Street Cambrid eMA02138 United States Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd Taipei10617 Taiwan Departament d’Astronomia i Astrofísica Universitat de València C. Dr. Moliner 50 Burjassot ValènciaE-46100 Spain Observatori Astronòmic Universitat de València C. Catedrático José Beltrán 2 Paterna ValènciaE-46980 Spain Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave TucsonAZ85721 United States Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States East Asian Observatory 660 N. A’ohoku Pl. HiloHI96720 United States PO Box 9513 Leiden2300 RA Netherlands California Institute of Technolo 1200 East California Boulevard PasadenaCA91125 United States Institute of Astronom Astro h sics Academia Sinica 645 N A’ohoku Place HiloHI96720 United States Institut de Radioastronomie Millimétri ue 300 rue de la Piscine Saint Martin d’HèresF-38406 France Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Perimeter Institute for Theoretical Ph sics 31 Caroline Street North WaterlooONN2L 2Y5 Canada De artment of Ph sics Universit of Waterloo 200 Universit Avenue West WaterlooONN2L 3G1 Canada Waterloo Centre for Astrophysics University of Waterloo WaterlooONN2L 3G1 Canada Korea Astronomy and Space Science Institute Daedeok-daero 776 Yuseong-gu Daejeon34055 Korea

When surrounded by a transparent emission region, black holes are expected to reveal a dark shadow caused by gravitational light bending and photon capture at the event horizon. To image and study this phenomenon, we have assembled the Event Horizon Telescope, a global very long baseline interferometry array observing at a wavelength of 1.3 mm. This allows us to reconstruct event-horizon-scale images of the supermassive black hole candidate in the center of the giant elliptical galaxy M87. We have resolved the central compact radio source as an asymmetric bright emission ring with a diameter of 42 ± 3 μas, which is circular and encompasses a central depression in brightness with a flux ratio 10:1. The emission ring is recovered using different calibration and imaging schemes, with its diameter and width remaining stable over four different observations carried out in different days. Overall, the observed image is consistent with expectations for the shadow of a Kerr black hole as predicted by general relativity. The asymmetry in brightness in the ring can be explained in terms of relativistic beaming of the emission from a plasma rotating close to the speed of light around a black hole. We compare our images to an extensive library of ray-traced general-relativistic magnetohydrodynamic simulations of black holes and derive a central mass of M = (6.5 ± 0.7) × 109 Me. Our radio-wave observations thus provide powerful evidence for the presence of supermassive black holes in centers of galaxies and as the central engines of active galactic nuclei. They also present a new tool to explore gravity in its most extreme limit and on a mass scale that was so far not accessible. Copyright © 2019, The Authors. All rights reserved.

关键词： Gravitation

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Neural autoregressive distribution estimation

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2016年第1期17卷

作者： Kevin Murphy Bernhard Schölkopf Benigno Uria Marc-Alexandre Côté Karol Gregor Iain Murray Hugo Larochelle Google MPI for Intelligent Systems Google DeepMind London UK Department of Computer Science Université de Sherbrooke Sherbrooke QC Canada School of Informatics University of Edinburgh Edinburgh UK Twitter Cambridge MA

We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a weight sharing scheme inspired from restricted Boltzmann machines, to yield an estimator that is both tractable and has good generalization performance. We discuss how they achieve competitive performance in modeling both binary and real-valued observations. We also present how deep NADE models can be trained to be agnostic to the ordering of input dimensions used by the autoregressive product rule decomposition. Finally, we also show how to exploit the topological structure of pixels in images using a deep convolutional architecture for NADE.

关键词： deep learning density modeling neural networks unsupervised learning

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Structure discovery in Bayesian networks by sampling partial orders

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2016年第1期17卷

作者： Kevin Murphy Bernhard Schölkopf Teppo Niinimäki Pekka Parviainen Mikko Koivisto Google MPI for Intelligent Systems Helsinki Institute for Information Technology Department of Computer Science University of Helsinki Finland Helsinki Institute for Information Technology Department of Computer Science Aalto Finland

We present methods based on Metropolis-coupled Markov chain Monte Carlo (MC3) and annealed importance sampling (AIS) for estimating the posterior distribution of Bayesian networks. The methods draw samples from an appropriate distribution of partial orders on the nodes, continued by sampling directed acyclic graphs (DAGs) conditionally on the sampled partial orders. We show that the computations needed for the sampling algorithms are feasible as long as the encountered partial orders have relatively few down-sets. While the algorithms assume suitable modularity properties of the priors, arbitrary priors can be handled by dividing the importance weight of each sampled DAG by the number of topological sorts it has|we give a practical dynamic programming algorithm to compute these numbers. Our empirical results demonstrate that the presented partial-order-based samplers are superior to previous Markov chain Monte Carlo methods, which sample DAGs either directly or via linear orders on the nodes. The results also suggest that the convergence rate of the estimators based on AIS are competitive to those of MC3. Thus AIS is the preferred method, as it enables easier large-scale parallelization and, in addition, supplies good probabilistic lower bound guarantees for the marginal likelihood of the model.

关键词： Markov chain Monte Carlo annealed importance sampling directed acyclic graph fast zeta transform linear extension

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