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Hierarchical Mixtures-of-Experts for Exponential Family Regression Models with Generalized Linear Mean Functions: A Survey of Approximation and Consistency Results [article]

Wenxin Jiang, Martin A. Tanner
2013 arXiv   pre-print
We investigate a class of hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form psi(ga+fx^Tfgb) are mixed.  ...  Suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form psi(h(fx)) where h(...)in W_2^infty (a Sobolev class over  ...  Acknowledgments The authors wish to thank the referees for helpful comments in improving the presentation of this pa per. Martin A. Tanner was supported in part by NIH Grant CA35464.  ... 
arXiv:1301.7390v1 fatcat:ph3ifloosfal5i5y3mhfdpshyy

Performance of variable and function selection methods for estimating the non-linear health effects of correlated chemical mixtures: a simulation study [article]

Nina Lazarevic, Luke D. Knibbs, Peter D. Sly, Adrian G. Barnett
2019 arXiv   pre-print
Statistical methods for identifying harmful chemicals in a correlated mixture often assume linearity in exposure-response relationships.  ...  Penalised regression methods that assume linearity, such as lasso, may not be suitable for studies of environmental chemicals hypothesised to have non-monotonic relationships with outcomes.  ...  @p rior Γ q: (e r , g r ), where 4 . is an exponential-family distributed response for individual / (/ = 1, … , 1), ℎ(•) is a known generalised linear model link function, and ö . = ö c + õ .ú ù ú + ∑  ... 
arXiv:1908.01583v1 fatcat:gvsnohqkmbfrnjzq3ezrnmxwoa

Bayesian Generalized Two-way ANOVA Modeling for Functional Data Using INLA

Yu Yue, David Bolin, Havard Rue, Xiao-Feng Wang
2019 Statistica sinica  
A class of highly flexible Gaussian Markov random fields (GMRF) are taken as priors on the functions in the model, which allows us to model various types of functional effects, such as (discrete or continuous  ...  Functional analysis of variance (ANOVA) modeling has been proved particularly useful to investigate the dynamic changes of functional data according to certain categorical factors and their interactions  ...  For any questions regarding the paper and/or the R code, please contact the corresponding author: Xiao-Feng Wang (wangx6@ccf.org).  ... 
doi:10.5705/ss.202016.0055 fatcat:ttpeis6pdrel7fmpwl5qed7ytu

Interactive design of probability density functions for shape grammars

Minh Dang, Stefan Lienhard, Duygu Ceylan, Boris Neubert, Peter Wonka, Mark Pauly
2015 ACM Transactions on Graphics  
(Right) Our framework takes user specified preference scores as input and learns a new model probability density function (pdf) which samples models (with consistent style) proportionally to their predicted  ...  Fourth, we modify the original grammars to generate models with a pdf proportional to the user preference scores.  ...  Acknowledgement We thank the anonymous reviewers for their valuable comments. We also thank Cheryl Lau for assisting us in making the video.  ... 
doi:10.1145/2816795.2818069 fatcat:fpjjazjx35grtgraju6twei2oa

Learning to search: Functional gradient techniques for imitation learning

Nathan D. Ratliff, David Silver, J. Andrew Bagnell
2009 Autonomous Robots  
Such cost functions are usually manually designed and programmed. Recently, a set of techniques has been developed that explore learning these functions from expert human demonstration.  ...  ., 2006a) framework to admit learning of more powerful, non-linear cost functions.  ...  We are grateful for fruitful discussions with Siddhartha Srinivasa, Tony Stentz, David Bradley, Joel Chestnutt, John Langford, Yucheng Low, Brian Ziebart, Martin Zinkevich, Matt Zucker, and the UPI autonomy  ... 
doi:10.1007/s10514-009-9121-3 fatcat:sljcvigzcjaexpr6xo3b32yax4

Predictive discrete latent factor models for large scale dyadic data

Deepak Agarwal, Srujana Merugu
2007 Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '07  
We illustrate our method by working in a framework of generalized linear models, which include commonly used regression techniques like linear regression, logistic regression and Poisson regression as  ...  We also provide scalable generalized EM-based algorithms for model fitting using both "hard" and "soft" cluster assignments.  ...  PRELIMINARIES We begin with a brief review of (i) one parameter exponential families, generalized linear regression models, and (ii) co-clustering on dyadic data. Exponential Families.  ... 
doi:10.1145/1281192.1281199 dblp:conf/kdd/AgarwalM07 fatcat:vezgomg37vgxnfb5ayjzbytitq

Bayesian Nonparametric Inference for Random Distributions and Related Functions

Stephen G. Walker, Paul Damien, PuruShottam W. Laud, Adrian F. M. Smith
1999 Journal of The Royal Statistical Society Series B-statistical Methodology  
However, these advances have not received a full critical and comparative analysis of their scope, impact and limitations in statistical modelling; many aspects of the theory and methods remain a mystery  ...  In this paper, we discuss and illustrate the rich modelling and analytic possibilities that are available to the statistician within the Bayesian nonparametric and/or semiparametric framework.  ...  and ®nancial support from the Business School at the University of Michigan, Ann Arbor.  ... 
doi:10.1111/1467-9868.00190 fatcat:ji4zf5u57vapfkpcupeg6ph3bm

Bayesian Hierarchical Stacking: Some Models Are (Somewhere) Useful

Yuling Yao, Gregor Pirš, Aki Vehtari, Andrew Gelman
2021 Bayesian Analysis  
We generalize stacking to Bayesian hierarchical stacking. The model weights are varying as a function of data, partially-pooled, and inferred using Bayesian inference.  ...  We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can further improve the stacked mixture with a hierarchical model.  ...  Rather than to compete with a mixture-of-experts on combining weak learners, hierarchical stacking is more recommended to combine a mixture-of-experts with other sophisticated models.  ... 
doi:10.1214/21-ba1287 fatcat:czxrlqet5raerekg46fscqin3i

Twenty Years of Mixture of Experts

S. E. Yuksel, J. N. Wilson, P. D. Gader
2012 IEEE Transactions on Neural Networks and Learning Systems  
In this paper, we provide a comprehensive survey of the mixture of experts (ME).  ...  We follow the discussion with improvements to the ME model and focus particularly on the mixtures of Gaussian process experts.  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their valuable suggestions.  ... 
doi:10.1109/tnnls.2012.2200299 pmid:24807516 fatcat:xgo3v5yyw5dbtcex7zhf4j3mpy

Variational Inference: A Review for Statisticians [article]

David M. Blei, Alp Kucukelbir, Jon D. McAuliffe
2018 arXiv   pre-print
We review the ideas behind mean-field variational inference, discuss the special case of VI applied to exponential family models, present a full example with a Bayesian mixture of Gaussians, and derive  ...  The idea behind VI is to first posit a family of densities and then to find the member of that family which is close to the target. Closeness is measured by Kullback-Leibler divergence.  ...  This includes a number of widely used models, such as Bayesian mixtures of exponential families, factorial mixture models, matrix factorization models, certain hierarchical regression models (e.g., linear  ... 
arXiv:1601.00670v8 fatcat:opqknuo6t5cezfvluwhmu4cg7e

High dimensional structured additive regression models: Bayesian regularization, smoothing and predictive performance

Thomas Kneib, Susanne Konrath, Ludwig Fahrmeir
2011 Journal of the Royal Statistical Society, Series C: Applied Statistics  
The predictive ability of the resulting highdimensional structure additive regression models compared to expert models will be of particular relevance and will be evaluated on cross-validation test data  ...  Two applications demonstrate the usefulness of the proposed procedure: A geoadditive regression model for data from the Munich rental guide and an additive probit model for the prediction of consumer credit  ...  Acknowledgement: We thank Felix Heinzl for assistance in data analyses and gratefully acknowledge financial support from the German Science Foundation, grant FA 128/5-1.  ... 
doi:10.1111/j.1467-9876.2010.00723.x fatcat:5szj5n73p5c7pl7klm7uargui4

Limit laws for maxima of a stationary random sequence with random sample size

A. Freitas, J. Hüsler, M. G. Temido
2011 Test (Madrid)  
Mercadier [5], we give some approximations of this distribution in the case of stationary Gaussian field for very general parameter sets.  ...  Temido, Limit laws for maxima of a stationary random sequence with random sample size, Test (to appear), Abstract The Gnedenko theorem is a general result in extreme value theory establishing the asymptotic  ...  Abstract We develop a Bayesian hierarchical model for the prediction of monthly maximum 24 hour precipitation in Iceland.  ... 
doi:10.1007/s11749-011-0238-2 fatcat:3arppgyvnjarvjgsxfyewmqnam

Penalising model component complexity: A principled, practical approach to constructing priors [article]

Daniel P. Simpson, Håvard Rue, Thiago G. Martins, Andrea Riebler,, Sigrunn H. Sørbye
2015 arXiv   pre-print
Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both  ...  We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model.  ...  Robert and Malgorzata Roos for stimulating discussions and comments related to this work.  ... 
arXiv:1403.4630v4 fatcat:btq4shuktbe7hoa2osb3qnou24

A mixture of experts model for rank data with applications in election studies

Isobel Claire Gormley, Thomas Brendan Murphy
2008 Annals of Applied Statistics  
The Benter model for rank data is employed as the family of component densities within the mixture of experts model; generalized linear model theory is employed to model the influence of covariates on  ...  A mixture of experts model is a mixture model in which the model parameters are functions of covariates.  ...  Adrian Raftery, the members of the Center for Statistics and the Social Sciences and the members of the Working Group on Model-based Clustering at the University of Washington for numerous suggestions  ... 
doi:10.1214/08-aoas178 fatcat:dlvixib4qvg77fasbjk6urihta

Model-Based Reinforcement Learning for Stochastic Hybrid Systems [article]

Hany Abdulsamad, Jan Peters
2021 arXiv   pre-print
controllers derived from a locally polynomial approximation of a global value function.  ...  This paper adopts a hybrid-system view of nonlinear modeling and control that lends an explicit hierarchical structure to the problem and breaks down complex dynamics into simpler localized units.  ...  APPENDIX I EXPONENTIAL FAMILY The upcoming chapters mainly consider random variables with probability density functions belonging to the exponential family.  ... 
arXiv:2111.06211v1 fatcat:6vglrmtsw5bdjacz2sslolpo4y
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