Laplace Variational Approximation for Semiparametric Regression in the Presence of Heteroscedastic Errors

Journal of Computational and Graphical Statistics

Volumn 25, Issue 1, 2016, Pages 225-245

  Bugbee, Bruce D ^a   Breidt, F Jay ^b   van der Woerd, Mark J ^b  

^a UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

^b Department of Environmental and Radiological Health Sciences   (United States)

Author keywords

Mean field variational Bayes; Penalized splines; Small angle X ray scattering

Indexed keywords

EID: 84961253364     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2014.983642     Document Type: Article

References (36)

1. H.Attias, (2000), “A Variational Bayesian Framework for Graphical Models,” Advances in Neural Information Processing Systems, 12, 209–215.
2. C.M.Bishop, (2006), Pattern Recognition and Machine Learning, Information Science and Statistics Series, New York: Springer.
3. D.M.Blei,, and J.D.Lafferty, (2007), “A Correlated Topic Model of Science,” The Annals of Applied Statistics, 1, 17–35.
4. F.J.Breidt,, A.Erciulescu,, and M.van der Woerd, (2012), “Autocovariance Structures for Radial Averages in Small-Angle X-Ray Scattering Experiments,” Journal of Time Series Analysis, 33, 704–717.
5. B.P.Carlin,, and N.G.Polson, (1991), “Inference for Nonconjugate Bayesian Models Using the Gibbs Sampler,” Canadian Journal of Statistics, 19, 399–405.
6. G.Casella,, and E.I.George, (1992), “Explaining the Gibbs Sampler,” The American Statistician, 46, 167–174.
7. D.Chan,, R.Kohn,, D.Nott,, and C.Kirby, (2006), “Locally Adaptive Semiparametric Estimation of the Mean and Variance Functions in Regression Models,” Journal of Computational and Graphical Statistics, 15, 915–936.
8. C.M.Crainiceanu,, D.Ruppert,, R.J.Carroll,, A.Joshi,, and B.Goodner, (2007), “Spatially Adaptive Bayesian Penalized Splines with Heteroscedastic Errors,” Journal of Computational and Graphical Statistics, 16, 265–288.
9. P.H.Eilers,, and B.D.Marx, (2010), “Splines, Knots, and Penalties,” Wiley Interdisciplinary Reviews: Computational Statistics, 2, 637–653.
10. P.H.Eilers, (1996), “Flexible Smoothing With B-Splines and Penalties,” Statistical Science, 11, 89–102.
11. C.Faes,, J.Ormerod,, and M.Wand, (2011), “Variational Bayesian Inference for Parametric and Nonparametric Regression With Missing Data,” Journal of the American Statistical Association, 106, 959–971.
12. H.Fischer,, M.Neto,, H.Napolitano,, I.Polikarpov,, and A.Craievich, (2009), “Determination of the Molecular Weight of Proteins in Solution From a Single Small-Angle X-Ray Scattering Measurement on a Relative Scale,” Journal of Applied Crystallography, 43, 101–109.
13. A.Guinier, (1939), “La Diffraction des Rayons X aux Très Petits Angles: Application a l’Étude de Phénoménes Ultramicrosopiques,” Annales de Physique, 12, 161–237.
14. H.Haario,, M.Laine,, A.Mira,, and E.Saksman, (2006), “DRAM: Efficient Adaptive MCMC,” Statistics and Computing, 16, 339–354.
15. I.Isenberg, (1979), “Histones,” Annual Review of Biochemistry, 48, 159–191.
16. T.Jaakkola,, and M.Jordan, (1997), “A Variational Approach to Bayesian Logistic Regression Models and Their Extensions,” in Sixth International Workshop on Artificial Intelligence and Statistics.
17. D.A.Knowles,, and T.Minka, (2011), “Nonconjugate Variational Message Passing for Multinomial and Binary Regression,” in Advances in Neural Information Processing Systems, pp. 1701–1709.
18. S.Kullback,, and R.A.Leibler, (1951), “On Information and Sufficiency,” The Annals of Mathematical Statistics, 22, 79–86.
19. M.Menictas,, and M.Wand, (2014), “Variational Inference for Heteroscedastic Semiparametric Regression,” The Selected Works of Matt Wand, available at http://works.bepress.com/matt_wand/12.
20. T.Minka,, J.Winn,, J.Guiver,, and D.Knowles, (2010), “Infer.NET 2.4. Microsoft Research Cambridge,” available at http://research.microsoft.com/infernet.
21. D.J.Nott,, M.-N.Tran,, A.Y.Kuk,, and R.Kohn, (2013), “Efficient Variational Inference for Generalized Linear Mixed Models With Large Datasets,” arXiv preprint arXiv:1307.7963.
22. D.J.Nott,, M.-N.Tran,, and C.Leng, (2012), “Variational Approximation for Heteroscedastic Linear Models and Matching Pursuit Algorithms,” Statistics and Computing, 22, 497–512.
23. J.Ormerod,, and M.Wand, (2010), “Explaining Variational Approximations,” The American Statistician, 64, 140–153.
24. T.H.Pham,, J.T.Ormerod,, and M.Wand, (2013), “Mean Field Variational Bayesian Inference for Nonparametric Regression With Measurement Error,” Computational Statistics & Data Analysis, 68, 375–387.
25. C.Putnam,, M.Hammel,, G.Hura,, and J.Tainer, (2007), “X-Ray Solution Scattering (SAXS) Combined With Crystallography and Computation: Defining Accurate Macromolecular Structures, Conformations and Assemblies in Solution,” Quarterly Reviews of Biophysics, 40, 191–285.
26. H.Rue,, S.Martino,, and N.Chopin, (2009), “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations,” Journal of the Royal Statistical Society, Series B, 71, 319–392.
27. D.Ruppert,, M.P.Wand,, and R.J.Carroll, (2003), Semiparametric Regression (vol. 12), Cambridge, UK: Cambridge University Press.
28. T.Salimans,, and D.A.Knowles, (2013), “Fixed-Form Variational Posterior Approximation Through Stochastic Linear Regression,” Bayesian Analysis, 8, 837–882.
29. L.S.Tan,, and D.J.Nott, (2013), “Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations,” Statistical Science, 28, 168–188.
30. D.Titterington, (2004), “Bayesian Methods for Neural Networks and Related Models,” Statistical Science, 19, 128–139.
31. M.J.Wainwright,, and M.I.Jordan, (2008), “Graphical Models, Exponential Families, and Variational Inference,” Foundations and Trends in Machine Learning, 1, 1–305.
32. M.Wand,, and J.Ormerod, (2008), “On Semiparametric Regression With O’Sullivan Penalized Splines,” Australian & New Zealand Journal of Statistics, 50, 179–198.
33. M.P.Wand,, J.T.Ormerod,, S.A.Padoan,, and R.Frührwirth, (2011), “Mean Field Variational Bayes for Elaborate Distributions,” Bayesian Analysis, 6, 1–48.
34. C.Wang,, and D.M.Blei, (2013), “Variational Inference in Nonconjugate Models,” The Journal of Machine Learning Research, 14, 1005–1031.
35. S.Wang,, and M.Wand, (2011), “Using Infer.NET for Statistical Analyses,” The American Statistician, 65, 115.
36. S.Wright,, and J.Nocedal, (1999), Numerical Optimization (vol. 2), New York: Springer.