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The Multiple Quantile Graphical Model 16

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The Multiple Quantile Graphical Model

Annual Conference on Neural Information Processing Systems

作者： Alnur Ali J. Zico Kolter Ryan J. Tibshirani Machine Learning Department Carnegie Mellon University Computer Science Department Carnegie Mellon University Department of Statistics Carnegie Mellon University

ISBN: (纸本)9781510838819

We introduce the Multiple Quantile Graphical Model (MQGM), which extends the neighborhood selection approach of Meinshausen and Buehlmann for learning sparse graphical models. The latter is defined by the basic subproblem of modeling the conditional mean of one variable as a sparse function of all others. Our approach models a set of conditional quantiles of one variable as a sparse function of all others, and hence offers a much richer, more expressive class of conditional distribution estimates. We establish that, under suitable regularity conditions, the MQGM identifies the exact conditional independencies with probability tending to one as the problem size grows, even outside of the usual homoskedastic Gaussian data model. We develop an efficient algorithm for fitting the MQGM using the alternating direction method of multipliers. We also describe a strategy for sampling from the joint distribution that underlies the MQGM estimate. Lastly, we present detailed experiments that demonstrate the flexibility and effectiveness of the MQGM in modeling hetereoskedastic non-Gaussian data.

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BIISQ: Bayesian nonparametric discovery of Isoforms and Individual Specific Quantification

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arXiv

arXiv 2017年

作者： Aguiar, Derek Cheng, Li-Fang Dumitrascu, Bianca Mordelet, Fantine Pai, Athma A. Engelhardt, Barbara E. Department of Computer Science Princeton University PrincetonNJ United States Department of Electrical Engineering Princeton University PrincetonNJ United States Lewis Sigler Institute Princeton University PrincetonNJ United States Institute for Genome Sciences and Policy Duke University DurhamNC United States Department of Biology Massachusetts Institute of Technology CambridgeMA United States Center for Statistics and Machine Learning Princeton University PrincetonNJ United States

Most human protein-coding genes can be transcribed into multiple possible distinct mRNA isoforms. These alternative splicing patterns encourage molecular diversity and dysregulation of isoform expression plays an important role in disease etiology. However, isoforms are difficult to characterize from short-read RNA-seq data because they share identical subsequences and exist in tissue- and sample-specific frequencies. Here, we develop BIISQ, a Bayesian nonparametric model to discover Isoforms and Individual Specific Quantification from RNA-seq data. BIISQ does not require known isoform reference sequences but instead estimates isoform composition directly with an isoform catalog shared across samples. We develop a stochastic variational inference approach for efficient and robust posterior inference and demonstrate superior precision and recall for short read RNA-seq simulations and simulated short read data from PacBio long read sequencing when compared to state-of-the-art isoform reconstruction methods. BIISQ achieves the most significant gains for longer (in terms of exons) isoforms and isoforms that are lowly expressed (over 500% more transcripts correctly inferred at low coverage in simulations). Finally, we estimate isoforms in the GEUVADIS RNA-seq data, identify genetic variants that regulate transcript ratios, and demonstrate variant enrichment in functional elements related to mRNA splicing regulation. Copyright © 2017, The Authors. All rights reserved.

关键词： RNA

Simple, robust and optimal ranking from pairwise comparisons

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The Journal of machine learning Research 2017年第1期18卷

作者： Nihar B. Shah Martin J. Wainwright Machine Learning Department and Computer Science Department Carnegie Mellon University Pittsburgh PA Department of Electrical Engineering and Computer Sciences and Department of Statistics University of California Berkeley CA

We consider data in the form of pairwise comparisons of n items, with the goal of identifying the top k items for some value of k < n, or alternatively, recovering a ranking of all the items. We analyze the Borda counting algorithm that ranks the items in order of the number of pairwise comparisons won, and show it has three attractive features: (a) it is an optimal method achieving the information-theoretic limits up to constant factors; (b) it is robust in that its optimality holds without imposing conditions on the underlying matrix of pairwise-comparison probabilities, in contrast to some prior work that applies only to the BTL parametric model; and (c) its computational efficiency leads to speedups of several orders of magnitude. We address the problem of exact recovery, and for the top-k recovery problem we also extend our results to obtain sharp guarantees for approximate recovery under the Hamming distortion metric, and more generally, to any arbitrary error requirement that satisfies a simple and natural monotonicity condition. In doing so, we introduce a general framework that allows us to treat a variety of problems in the literature in an unified manner.

关键词： approximate recovery borda count occam's razor pairwise comparisons permutation-based models ranking set recovery

learning instrumental variables with structural and non-gaussianity assumptions

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The Journal of machine learning Research 2017年第1期18卷

作者： Ricardo Silva Shohei Shimizu Department of Statistical Science and Centre for Computational Statistics and Machine Learning University College London UK The Center for Data Science Education and Research Shiga University Shiga Japan and The Institute of Scientific and Industrial Research Osaka University Japan

learning a causal effect from observational data requires strong assumptions. One possible method is to use instrumental variables, which are typically justified by background knowledge. It is possible, under further assumptions, to discover whether a variable is structurally instrumental to a target causal effect X → Y. However, the few existing approaches are lacking on how general these assumptions can be, and how to express possible equivalence classes of solutions. We present instrumental variable discovery methods that systematically characterize which set of causal effects can and cannot be discovered under local graphical criteria that define instrumental variables, without reconstructing full causal graphs. We also introduce the first methods to exploit non-Gaussianity assumptions, highlighting identifiability problems and solutions. Due to the difficulty of estimating such models from finite data, we investigate how to strengthen assumptions in order to make the statistical problem more manageable.

关键词： causal discovery causality instrumental variables

Generalized póya urn for time-varying pitman-yor processes

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The Journal of machine learning Research 2017年第1期18卷

作者： François Caron Willie Neiswanger Frank Wood Arnaud Doucet Manuel Davy Department of Statistics University of Oxford Oxford UK Machine Learning Department Carnegie Mellon University Pittsburgh Department of Engineering Science University of Oxford Oxford UK VEKIA Lille France

This article introduces a class of first-order stationary time-varying Pitman-Yor processes. Subsuming our construction of time-varying Dirichlet processes presented in (Caron et al., 2007), these models can be used for time-dynamic density estimation and clustering. Our intuitive and simple construction relies on a generalized Pólya urn scheme. Significantly, this construction yields marginal distributions at each time point that can be explicitly characterized and easily controlled. Inference is performed using Markov chain Monte Carlo and sequential Monte Carlo methods. We demonstrate our models and algorithms on epidemiological and video tracking data.

关键词： Bayesian nonparametrics clustering dynamic models mixture models particle Markov chain Monte Carlo sequential Monte Carlo

Scalable Adaptive Stochastic Optimization Using Random Projections 16

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Scalable Adaptive Stochastic Optimization Using Random Proje...

Annual Conference on Neural Information Processing Systems

作者： Gabriel Krummenacher Brian Mc Williams Yannic Kilcher Joachim M. Buhmann Nicolai Meinshausen Institute for Machine Learning Department of Computer Science ETH Zurich Switzerland Disney Research Zurich Switzerland Seminar for Statistics Department of Mathematics ETH Zurich Switzerland

ISBN: (纸本)9781510838819

Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by accumulating past gradients which are used to tune the step size adaptively. In certain situations the full-matrix variant of AdaGrad is expected to attain better performance, however in high dimensions it is computationally impractical. We present Ada-lr and RadaGrad two computationally efficient approximations to full-matrix AdaGrad based on randomized dimensionality reduction. They are able to capture dependencies between features and achieve similar performance to full-matrix AdaGrad but at a much smaller computational cost. We show that the regret of Ada-lr is close to the regret of full-matrix AdaGrad which can have an up-to exponentially smaller dependence on the dimension than the diagonal variant. Empirically, we show that Ada-lr and RadaGrad perform similarly to full-matrix AdaGrad. On the task of training convolutional neural networks as well as recurrent neural networks, RadaGrad achieves faster convergence than diagonal AdaGrad.

关键词： Regret dimensionality reduction gradient methods step size dimensions Stochastic Diagonal Self tuning Scalability Neural network Diagonal matrix

Adaptive randomized dimension reduction on massive data

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The Journal of machine learning Research 2017年第1期18卷

作者： Gregory Darnell Stoyan Georgiev Sayan Mukherjee Barbara E. Engelhardt Lewis-Sigler Institute Princeton University Princeton NJ Google Palo Alto CA Departments of Statistical Science Mathematics and Computer Science Duke University Durham NC Department of Computer Science Center for Statistics and Machine Learning Princeton University Princeton NJ

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In this paper, we develop an approach for dimension reduction that exploits the assumption of low rank structure in high dimensional data to gain both computational and statistical advantages. We adapt recent randomized low-rank approximation algorithms to provide an efficient solution to principal component analysis (PCA), and we use this efficient solver to improve estimation in large-scale linear mixed models (LMM) for association mapping in statistical genomics. A key observation in this paper is that randomization serves a dual role, improving both computational and statistical performance by implicitly regularizing the covariance matrix estimate of the random effect in an LMM. These statistical and computational advantages are highlighted in our experiments on simulated data and large-scale genomic studies.

关键词： Krylov subspace methods dimension reduction generalized eigendecompositon genomics linear mixed models low-rank random projections randomized algorithms supervised

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 Antwerp, Belgium. 15-20 July 2017 Abstracts

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BMC NEUROscience 2017年第SUPPL 1期18卷 95-176页

作者： [Anonymous] Department of Neuroscience Yale University New Haven CT 06520 USA Department Physiology & Pharmacology SUNY Downstate Brooklyn NY 11203 USA NYU School of Engineering 6 MetroTech Center Brooklyn NY 11201 USA Departament de Matemàtica Aplicada Universitat Politècnica de Catalunya Barcelona 08028 Spain Institut de Neurobiologie de la Méditerrannée (INMED) INSERM UMR901 Aix-Marseille Univ Marseille France Center of Neural Science New York University New York NY USA Aix-Marseille Univ INSERM INS Inst Neurosci Syst Marseille France Laboratoire de Physique Théorique et Modélisation CNRS UMR 8089 Université de Cergy-Pontoise 95300 Cergy-Pontoise Cedex France Department of Mathematics and Computer Science ENSAT Abdelmalek Essaadi’s University Tangier Morocco Laboratory of Natural Computation Department of Information and Electrical Engineering and Applied Mathematics University of Salerno 84084 Fisciano SA Italy Department of Medicine University of Salerno 84083 Lancusi SA Italy Dipartimento di Fisica Università degli Studi Aldo Moro Bari and INFN Sezione Di Bari Italy Data Analysis Department Ghent University Ghent Belgium Coma Science Group University of Liège Liège Belgium Cruces Hospital and Ikerbasque Research Center Bilbao Spain BIOtech Department of Industrial Engineering University of Trento and IRCS-PAT FBK 38010 Trento Italy Department of Data Analysis Ghent University Ghent 9000 Belgium The Wellcome Trust Centre for Neuroimaging University College London London WC1N 3BG UK Department of Electronic Engineering NED University of Engineering and Technology Karachi Pakistan Blue Brain Project École Polytechnique Fédérale de Lausanne Lausanne Switzerland Departement of Mathematics Swansea University Swansea Wales UK Laboratory for Topology and Neuroscience at the Brain Mind Institute École polytechnique fédérale de Lausanne Lausanne Switzerland Institute of Mathematics University of Aberdeen Aberdeen Scotland UK Department of Integrativ

Reply to Brown and Behrmann, Cox, et al., and Kessler et al.: data and code sharing is the way forward for fMRI

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Proceedings of the National Academy of sciences of the United States of America 2017年第17期114卷 E3374-E3375页

作者： Anders Eklund Thomas E Nichols Hans Knutsson Division of Medical Informatics Department of Biomedical Engineering Linköping University S-581 85 Linköping Sweden anders.eklund@liu.se. Division of Statistics and Machine Learning Department of Computer and Information Science Linköping University S-581 83 Linköping Sweden. Center for Medical Image Science and Visualization Linköping University S-581 83 Linköping Sweden. Department of Statistics University of Warwick Coventry CV4 7AL United Kingdom. WMG University of Warwick Coventry CV4 7AL United Kingdom. Division of Medical Informatics Department of Biomedical Engineering Linköping University S-581 85 Linköping Sweden.