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Penalized basis models for very large spatial datasets [article]

Mitchell Krock, William Kleiber, Stephen Becker
2019 arXiv   pre-print
Sparsity in the precision matrix is encouraged using a penalized likelihood framework.  ...  Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients.  ...  The optimal value is then used with the full sample covariance S in (11) to give a best guessQ for the simulated data.  ... 
arXiv:1902.06877v1 fatcat:bz6vvw7perdq7bptuu7lsgl2ey

Map approach to learning sparse Gaussian Markov networks

N. Bani Asadi, I. Rish, K. Scheinberg, D. Kanevsky, B. Ramabhadran
2009 2009 IEEE International Conference on Acoustics, Speech and Signal Processing  
Herein, we propose a maximum a posteriori probability (MAP) approach that investigates different priors on the regularization parameter and yields promising empirical results on both synthetic data and  ...  real-life application such as brain imaging data (fMRI).  ...  Missing edges in the above graphical model correspond to zero entries in the inverse covariance matrix C, and thus the problem of structure learning for the above probabilistic graphical model is equivalent  ... 
doi:10.1109/icassp.2009.4959935 dblp:conf/icassp/AsadiRSKR09 fatcat:ipaojny5vjfynlpfr22w7mcdqu

Sparse estimation of a covariance matrix

J. Bien, R. J. Tibshirani
2011 Biometrika  
In contrast to sparse inverse covariance estimation, our method's close relative, the sparsity attained here is in the covariance matrix itself rather than in the inverse matrix.  ...  We consider a method for estimating a covariance matrix on the basis of a sample of vectors drawn from a multivariate normal distribution.  ...  This method has been referred to in various literatures as the concave-convex procedure, the difference of convex functions algorithm, and multi-stage convex relaxations.  ... 
doi:10.1093/biomet/asr054 pmid:23049130 pmcid:PMC3413177 fatcat:arr36djunbgx3eilvj4ddi3e2u

Covariance Prediction via Convex Optimization [article]

Shane Barratt, Stephen Boyd
2021 arXiv   pre-print
The log-likelihood is a concave function of the predictor parameters, so fitting the predictor involves convex optimization.  ...  We describe a covariance predictor that has the form of a generalized linear model, i.e., an affine function of the features followed by an inverse link function that maps vectors to symmetric positive  ...  Acknowledgements The authors gratefully acknowledge conversations and discussions about some of the material in this paper with Misha van Beek, Linxi Chen, David Greenberg, Ron Kahn, Trevor Hastie, Rob  ... 
arXiv:2101.12416v1 fatcat:tv34sucl7fhqnkegqyxbtvrim4

Statistical analysis of big data on pharmacogenomics

Jianqing Fan, Han Liu
2013 Advanced Drug Delivery Reviews  
Their applications to gene network estimation and biomarker selection are used to illustrate the methodological power.  ...  Several new challenges of Big data analysis, including complex data distribution, missing data, measurement error, spurious correlation, endogeneity, and the need for robust statistical methods, are also  ...  Han Liu is supported by NSF Grant III-1116730 and a NIH sub-award from Johns Hopkins University.  ... 
doi:10.1016/j.addr.2013.04.008 pmid:23602905 pmcid:PMC3701723 fatcat:d2wof7vibvhipddta5xfalu4hu

DISCOMAX: A Proximity-Preserving Distance Correlation Maximization Algorithm [article]

Praneeth Vepakomma, Ahmed Elgammal
2017 arXiv   pre-print
The algorithm is iterative and is fomulated as a combination of the majorization-minimization and concave-convex optimization procedures.  ...  Our setting is different from subset-selection algorithms where the problem is to choose the best subset of features for regression.  ...  This leads to the loss being a sum of convex and concave functions which we utilize inorder to minimize it using the Concave Convex Procedure (CCCP) [15] .  ... 
arXiv:1306.2533v3 fatcat:p3fi2gcyyjezhbhtqu4qwxj36a

Generalized non-linear elastic inversion with constraints in model and data spaces

Philip M. Carrion
1989 Geophysical Journal International  
Non-linear inversion was developed in the frame work of an unconstrained optimization procedure.  ...  Such techniques as the Born inversion were recently applied to seismic data. Non-linear inversion is more complicated and involves extensive calculations.  ...  We can see from this equation that the magnitude of 'noise' will depend on the operator itself and on the value of the data associated with the background model.  ... 
doi:10.1111/j.1365-246x.1989.tb05257.x fatcat:6npot5fllnhgdbywfei2gvi4eq

A Generic Path Algorithm for Regularized Statistical Estimation [article]

Hua Zhou, Yichao Wu
2012 arXiv   pre-print
In this article we propose an exact path solver based on ordinary differential equations (EPSODE) that works for any convex loss function and can deal with generalized l_1 penalties as well as more complicated  ...  In practice, the EPSODE can be coupled with AIC, BIC, C_p or cross-validation to select an optimal tuning parameter.  ...  matrix, the inverse of the variance-covariance matrix.  ... 
arXiv:1201.3571v1 fatcat:q6axr4sqc5h4hetsowzmv5nqhq

On the Convergence of Bound Optimization Algorithms [article]

Ruslan R Salakhutdinov, Sam T Roweis, Zoubin Ghahramani
2012 arXiv   pre-print
Many practitioners who use the EM algorithm complain that it is sometimes slow. When does this happen, and what can be done about it?  ...  We report empirical results supporting our analysis and showing that simple data preprocessing can result in dramatically improved performance of bound optimizers in practice.  ...  Acknowledgments Funded in part by the IRIS project, Precam Canada.  ... 
arXiv:1212.2490v1 fatcat:sq5iprry35e5biytseenc4n3k4

Transposable regularized covariance models with an application to missing data imputation

Genevera I. Allen, Robert Tibshirani
2010 Annals of Applied Statistics  
Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix.  ...  By placing additive penalties on the inverse covariance matrices of the rows and columns, these so-called transposable regularized covariance models allow for maximum likelihood estimation of the mean  ...  Acknowledgments Thanks to Steven Boyd for a discussion about the minimization of biconvex functions.  ... 
doi:10.1214/09-aoas314 pmid:26877823 pmcid:PMC4751046 fatcat:m4c2ffayzfb4zmv4jl7dxonb6u

Semiparametric models: a generalized self-consistency approach

A. Tsodikov
2003 Journal of The Royal Statistical Society Series B-statistical Methodology  
The procedure for semiparametric models is used to demonstrate three methods to construct a surrogate objective function: using the difference of two concave functions, the EM way and the new quasi-EM  ...  The new approach is compared with other possible approaches by using simulations and analysis of real data. The proportional odds model is used as an example throughout the paper.  ...  Acknowledgments The author thanks Dr Ken Boucher, Dr Marvin Zelen, the referees and the Joint Editor for many helpful comments.  ... 
doi:10.1111/1467-9868.00414 pmid:21127741 pmcid:PMC2994590 fatcat:dcvonbztsbau3d7fumcs77l4qy

An EM algorithm for wavelet-based image restoration

M.A.T. Figueiredo, R.D. Nowak
2003 IEEE Transactions on Image Processing  
The EM algorithm herein proposed combines the efficient image representation offered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator obtained in the Fourier  ...  Moreover, our new approach performs competitively with, in some cases better than, the best existing methods in benchmark tests.  ...  ACKNOWLEDGMENT The authors would like to thank J. Fessler and A. Jalobeanu for helpful discussions and insightful comments that helped to improve this paper.  ... 
doi:10.1109/tip.2003.814255 pmid:18237964 fatcat:wqqh53mbf5awjjlpwhopd4rjfa

EM algorithms without missing data

Mark P Becker, Ilsoon Yang, Kenneth Lange
1997 Statistical Methods in Medical Research  
The EM algorithm is one of the most effective algorithms for maximization because it iteratively transfers maximization from a complex function to a simple, surrogate function.  ...  Beginning with the EM algorithm, we review in this paper several optimization transfer algorithms of substantial utility in medical statistics.  ...  Acknowledgements The authors gratefully acknowledge support from the National Institutes of Health (Grants CA53787 and GM53275) and the Statistics Center at Cornell University.  ... 
doi:10.1177/096228029700600104 pmid:9185289 fatcat:44slrt4g3batlf547j5wsvd57e

A Generic Path Algorithm for Regularized Statistical Estimation

Hua Zhou, Yichao Wu
2014 Journal of the American Statistical Association  
In this article we follow a recent idea by Wu and propose an exact path solver based on ordinary differential equations (EPSODE) that works for any convex loss function and can deal with generalized ℓ  ...  Nonasymptotic error bounds for the equality regularized estimates are derived.  ...  The case with inequality regularization is outside the scope of this article and will be pursued elsewhere. Suppose the data are generated from β * ∈ R p .  ... 
doi:10.1080/01621459.2013.864166 pmid:25242834 pmcid:PMC4167778 fatcat:iydhabcxprderbb3tczkky6p4i

Gaussian Graphical Models: An Algebraic and Geometric Perspective [article]

Caroline Uhler
2017 arXiv   pre-print
existence of the maximum likelihood estimator (MLE) and algorithms for computing the MLE.  ...  Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph.  ...  As described in Section 3, determining the MLE in a Gaussian model with linear constraints on the inverse covariance matrix is a convex optimization problem.  ... 
arXiv:1707.04345v1 fatcat:i7i5ps6gfbebzfsecutpg2lmhi
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