Improved prediction accuracy for disease risk mapping using Gaussian process stacked generalization

Journal of the Royal Society Interface

Volumn 14, Issue 134, 2017, Pages

  Bhatt, Samir ^a   Cameron, Ewan ^b   Flaxman, Seth R ^d   Weiss, Daniel J ^b   Smith, David L ^c   Gething, Peter W ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c UNIVERSITY OF WASHINGTON   (United States)

^d UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Disease mapping; Gaussian process; Malaria; Stacked generalization

Indexed keywords

DISEASES; FUNCTIONS; GAUSSIAN NOISE (ELECTRONIC); MAPPING; UNCERTAINTY ANALYSIS;

DISEASE MAPPING; GAUSSIAN PROCESS REGRESSION; GAUSSIAN PROCESSES; MALARIA; MATHEMATICAL FRAMEWORKS; PLASMODIUM FALCIPARUM; SPATIAL INTERPOLATION; STACKED GENERALIZATION;

GAUSSIAN DISTRIBUTION;

AFRICA SOUTH OF THE SAHARA; ARTICLE; BAYES THEOREM; EXPERIMENTAL DESIGN; GAUSSIAN PROCESS REGRESSION; GEOSTATISTICAL ANALYSIS; HUMAN; INFECTION RISK; LINEAR REGRESSION ANALYSIS; MALARIA FALCIPARUM; MARKOV CHAIN; MATHEMATICAL PHENOMENA; NONHUMAN; NONLINEAR SYSTEM; PARASITE TRANSMISSION; PLASMODIUM FALCIPARUM; PREDICTION; PREVALENCE; PUBLIC HEALTH; RANDOM FOREST; STACKED GENERALIZATION; ANIMAL; BIOLOGICAL MODEL; TRANSMISSION;

AFRICA SOUTH OF THE SAHARA; ANIMALS; HUMANS; MALARIA, FALCIPARUM; MODELS, BIOLOGICAL; PLASMODIUM FALCIPARUM; PREVALENCE;

EID: 85031093066     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2017.0520     Document Type: Article

References (55)

1. Diggle P, Ribeiro PJ. 2007 Model-based geostatistics. New York, NY: Springer.
2. Hay SI. 2013 Global mapping of infectious disease. Phil. Trans. R. Soc. B 368, 20120250. (doi:10.1098/rstb.2012.0250)
3. Freifeld CC, Mandl KD, Reis BY, Brownstein JS. 2008 HealthMap: global infectious disease monitoring through automated classification and visualization of Internet media reports. J. Am. Med. Inform. Assoc. 15, 150-157. (doi:10.1197/jamia.M2544)
4. Bhatt S et al. 2015 The effect of malaria control on Plasmodium falciparum in Africa between 2000 and 2015. Nature 526, 207-211. (doi:10.1038/nature15535)
5. Rasmussen CE, Williams CKI. 2006 Gaussian processes for machine learning, vol. 14. Cambridge, MA: The MIT Press.
6. Bishop CM. 2006 Pattern recognition and machine learning, vol. 4. London, UK: Springer.
7. Gething PW, Patil AP, Smith DL, Guerra CA, Elyazar IRF, Johnston GL, Tatem AJ, Hay SI. 2011 A new world malaria map: Plasmodium falciparum endemicity in 2010. Malar. J. 10, 378. (doi:10.1186/1475-2875-10-378)
8. Hay SI et al.. 2009 A world malaria map: Plasmodium falciparum endemicity in 2007. PLoS Med. 6, 0286-0302. (doi:10.1371/annotation/a7ab5bb8-c3bb-4f01-aa34-65cc53af065d)
9. Gosoniu L, Msengwa A, Lengeler C, Vounatsou P. 2012 Spatially explicit burden estimates of malaria in Tanzania: Bayesian geostatistical modeling of the malaria indicator survey data. PLoS ONE 7, e23966. (doi:10.1371/journal.pone.0023966)
10. Adigun AB, Gajere EN, Oresanya O, Vounatsou P. 2015 Malaria risk in Nigeria: Bayesian geostatistical modelling of 2010 malaria indicator survey data. Malar. J. 14, 156. (doi:10.1186/s12936-015-0683-6)
11. Snoek J, Larochelle H, Adams RP. 2012 Practical Bayesian optimization of machine learning algorithms. Adv. Neural Inf. Process. Syst. 25, 2951-2959.
12. Hoffman MD, Gelman A. 2014 The no-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 15, 1593-1623.
13. Rue H, Martino S, Chopin N. 2009 Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 71, 319-392. (doi:10.1111/j.1467-9868.2008.00700.x)
14. Vanhatalo J, Pietiläinen V, Vehtari A. 2010 Approximate inference for disease mapping with sparse Gaussian processes. Stat. Med. 29, 1580-1607. (doi:10.1002/sim.3895)
15. Minka TP. 2001 Expectation propagation for approximate Bayesian inference. In Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence, pp. 362-369. Burlington, MA: Morgan Kaufmann Publishers.
16. Hensman J, Fusi N, Lawrence ND. 2013 Gaussian processes for big data. ArXiv 1309.6835. (http://arxiv.org/abs/1309.6835)
17. Opper M, Archambeau C. 2009 The variational Gaussian approximation revisited. Neural Comput. 21, 786-792. (doi:10.1162/neco.2008.08-07-592)
18. Dutta S, Mondal D. 2016 REML estimation with intrinsic Matérn dependence in the spatial linear mixed model. Electron. J. Stat. 10, 2856-2893. (doi:10.1214/16-EJS1125)
19. Rahimi A, Recht B. 2008 Random features for largescale kernel machines. Adv. Neural Inf. Process. Syst. 20, 1177-1184.
20. Quiñonero-Candela J, Rasmussen CE. 2005 A unifying view of sparse approximate Gaussian process regression. J. Mach. Learn. Res. 6, 1939-1959.
21. Lindgren F, Rue H, Lindström J. 2011 An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 73, 423-498. (doi:10.1111/j.1467-9868. 2011.00777.x)
22. Duvenaud D, Lloyd JR, Grosse R, Tenenbaum JB, Ghahramani Z. 2013 Structure discovery in nonparametric regression through compositional kernel search. ArXiv 1302.4922. (http://arxiv.org/abs/1302.4922)
23. Wilson AG, Adams RP. 2013 Gaussian process kernels for pattern discovery and extrapolation. ArXiv 1302.4245. (http://arxiv.org/abs/1302.4245)
24. Weiss DJJ, Mappin B, Dalrymple U, Bhatt S, Cameron E, Hay SII, Gething PWW. 2015 Reexamining environmental correlates of Plasmodium falciparum malaria endemicity: a data-intensive variable selection approach. Malar. J. 14, 68. (doi:10.1186/s12936-015-0574-x)
25. Fuglstad G-A, Simpson D, Lindgren F, Rue H. 2015 Does non-stationary spatial data always require non-stationary random fields? Spat. Stat. 14, 505-531. (doi:10.1016/j.spasta.2015.10.001)
26. Weiss DJJ, Bhatt S, Mappin B, VanBoeckel TPP, Smith DLL, Hay SII, Gething PWW. 2014 Air temperature suitability for Plasmodium falciparum malaria transmission in Africa 2000-2012: a highresolution spatiotemporal prediction. Malar. J. 13, 171. (doi:10.1186/1475-2875-13-171)
27. Hastie T, Tibshirani R, Friedman JH. 2009 The elements of statistical learning. Berlin, Germany: Springer.
28. Caruana R, Niculescu-Mizil A. 2006 An empirical comparison of supervised learning algorithms. In Proc. of the 23rd Int. Conf. on Machine Learning, pp. 161-168. New York, NY: ACM.
29. Friedman JH. 2001 Greedy function approximation: a gradient boosting machine. Ann. Stat. 29, 1189-1232. (doi:10.1214/aos/1013203451)
30. Breiman L. 2001 Random forests. Mach. Learn. 45, 5-32. (doi:10.1023/A:1010933404324)
31. Tibshirani R, Hastie T. 1986 Generalized additive models. Stat. Sci. 1, 297-310. (doi:10.1214/ss/1177013604)
32. Wood S. 2006 Generalized additive models: an introduction with R. Boca Raton, FL: CRC Press.
33. Friedman JH. 1991 Multivariate adaptive regression splines. Ann. Stat. 19, 1-67. (doi:10.1214/aos/1176347963)
34. Zou H, Hastie T. 2005 Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B (Stat. Methodol.). 67, 301-320. (doi:10.1111/j. 1467-9868.2005.00503.x)
35. Geman S, Bienenstock E, Doursat R. 1992 Neural networks and the bias/variance dilemma. Neural Comput. 4, 1-58. (doi:10.1162/neco.1992.4.1.1)
36. Wolpert DH. 1992 Stacked generalization. Neural Netw. 5, 241-259. (doi:10.1016/S0893-6080(05)80023-1)
37. Breiman L. 1996 Stacked regressions. Mach. Learn. 24, 49-64. (doi:10.1007/BF00117832)
38. Abu-Mostafa YS, Magdon-Ismail M, Lin HT. 2012 Learning from data. Pasadena, CA: AMLBook.
39. van der Laan MJ, Polley EC, Hubbard AE. 2007 Super learner. Stat. Appl. Genet. Mol. Biol. 6, 25. (doi:10.2202/1544-6115.1309)
40. Krogh A, Vedelsby J. 1995 Neural network ensembles, cross validation, and active learning. Adv. Neural Inf. Process. Syst. 7, 231-238.
41. Puurula A, Read J, Bifet A. 2014 Kaggle LSHTC4 winning solution. ArXiv 1405.0546. (https://arxiv. org/abs/1405.0546)
42. Domingos P. 2012 A few useful things to know about machine learning. Commun. ACM 55, 78-87. (doi:10.1145/2347736.2347755)
43. Clarke B, Bertrand@stat Ubc Ca. 2003 Comparing Bayes model averaging and stacking when model approximation error cannot be ignored. J. Mach. Learn. Res. 4, 683-712. (doi:10.1162/153244304773936090)
44. Weiss DJ, Atkinson PM, Bhatt S, Mappin B, Hay SI, Gething PW. 2014 An effective approach for gapfilling continental scale remotely sensed time-series. ISPRS J. Photogramm. Remote Sens. 98, 106-118. (doi:10.1016/j.isprsjprs.2014.10.001)
45. Friedman JH. 2002 Stochastic gradient boosting. Comput. Stat. Data Anal. 38, 367-378. (doi:10. 1016/S0167-9473(01)00065-2)
46. Elith J, Leathwick JR, Hastie T. 2008 A working guide to boosted regression trees. J. Anim. Ecol. 77, 802-813. (doi:10.1111/j.1365-2656.2008. 01390.x)
47. Sill J, Takacs G, Mackey L, Lin D. 2009 Featureweighted linear stacking. ArXiv 0911.0460. (https://arxiv.org/pdf/0911.0460.pdf )
48. Rasmussen C. 2004 Gaussian processes in machine learning. In Advanced lectures on machine learning (eds O Bousquet, U von Luxburg, G Rätsch), pp. 63-71. Berlin, Germany: Springer.
49. Smith DL, McKenzie FE. 2004 Statics and dynamics of malaria infection in Anopheles mosquitoes. Malar. J. 3, 13. (doi:10.1186/1475-2875-3-13)
50. Griffin JT, Ferguson NM, Ghani AC. 2014 Estimates of the changing age-burden of Plasmodium falciparum malaria disease in sub-Saharan Africa. Nat. Commun. 5, 3136. (doi:10. 1038/ncomms4136)
51. O'Hagan A. 1991 Bayes-Hermite quadrature. J. Stat. Plan. Inference 29, 245-260. (doi:10.1016/0378-3758(91)90002-V)
52. Hennig P, Osborne MA, Girolami M. 2015 Probabilistic numerics and uncertainty in computations. Proc. R. Soc. A 471, 20150142. (doi:10.1098/rspa.2015.0142)
53. Goldstein A, Kapelner A, Bleich J, Pitkin E. 2015 Peeking inside the black box: visualizing statistical learning with plots of individual conditional expectation. J. Comput. Graph. Stat. 24, 44-65. (doi:10.1080/10618600.2014. 907095)
54. Pigott DM et al. 2015 Prioritising infectious disease mapping. PLoS Negl. Trop. Dis. 9, e0003756. (doi:10. 1371/journal.pntd.0003756)
55. Bhatt S et al. 2013 The global distribution and burden of dengue. Nature 496, 504-507. (doi:10. 1038/nature12060)