Abstract
Throughout this book a phrase like “assume the data have been generated by the following probability model” has been abundantly used. Indeed, the standard parametric assumption is that observed data represent one realisation from some given probability model and the goal can be to infer the parameters of the model. Alternatively and from a classical frequentist setting, conditionally on estimated parameters, the goal may be to predict future observations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bernard E (2021) Introduction to machine learning. Wolfram Media, Champaign
Bishop CM (2006) Pattern recognition and machine learning. Springer, Berlin
Breiman L (1996) Bagging predictors. Mach Learn 24:123–140
Breiman L (2001) Random forests. Mach Learn 45:5–32
de los Campos G, Gianola D, Rosa GJM (2009) Reproducing kernel Hilbert spaces regression: a general framework for genetic evaluation. J Anim Sci 87:1883–1887
de los Campos G, Gianola D, Rosa GJM, Weigel KA, Crossa J (2010) Semi-parametric genomic-enabled prediction of genetic values using reproducing kernel Hilbert spaces methods. Genet Res 92:295–308
Duvenaud D, Lloyd JR, Grosse R, Tenenbaum JB, Ghahramani Z (2013) Structure discovery in nonparametric regression through compositional kernel search. ArXiv:1302.4922
Gianola D, de los Campos G (2008) Inferring genetic values for quantitative traits non-parametrically. Genet Res 90:525–540
Gianola D, Fernando R, Schön CC (2020) Inferring trait-specific similarity among individuals from molecular markers and phenotypes with Bayesian regression. Theor Popul Biol 132:47–59
Glorot X, Bengio Y (2010) Understanding the difficulty of training deep feedforward neural networks. J Mach Learn Res Proc Track 9:249–256
Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, Cambridge
Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning. Springer, New York, p 745
Henderson CR, Kempthorne O, Searle SR, Von Krosigk CN (1959) Estimation of environmental and genetic trends from records subject to culling. Biometrics 15:192–218
Hill WG, Goddard ME, Visscher PM (2008) Data and theory point to mainly additive genetic variance for complex traits. PLoS Genet 4:e1000008
Hu Z, Zhang J, Ge Y (2021) Handling vanishing gradient problem using artificial derivative. IEEE Access 9:22,371–22,377
James G, Witten D, Hastie T, Tibshirani R (2017) An introduction to statistical learning. Springer, Berlin
Kimeldorf G, Wahba G (1971) Some results on Tchebycheffian spline functions. J Math Anal Appl 33:82–95
LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521:436–444
López OAM, López AM, Crossa J (2022) Mulitivariate statistical machine learning methods for genomic prediction. Springer, Berlin
Mäki-Tanila A, Hill WG (2014) Influence of gene interaction on complex trait variation with multilocus models. Genetics 198:355–367
McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:115–133
Neal RM (1996) Bayesian learning for neural networks. Springer-Verlag, Berlin
Perez P, de los Campos G (2014) Genome-wide regression and prediction with the BGLR statistical package. Genetics 198:483–495
Perez-Elizalde S, Cuevas J, Perez-Rodriguez P, Crossa J (2015) Selection of the bandwidth parameter in a Bayesian regression model for genomic-enabled prediction. J Agric Biol Environ Stat 20:512–532
Rousseauw J, du Plessis J, Benade A, Jordaan P, Kotze J, Jooste P (1983) Coronary risk factor screening in three rural communities. S Afr Med J 64:430–436
Rumelhart D, Hinton G, Williams R (1986) Learning representations by back-propagation. Nature 323:533–536
Wahba G (1990) Spline models for observational data. SIAM, Philadelphia
Zhao T, Fernando R, Cheng H (2021) Interpretable artificial neural networks incorporating Bayesian alphabet models for genome-wide prediction and association studies. G3. https://doi.org/10.1093/g3journal/jkab228
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Sorensen, D. (2023). Nonparametric Methods: A Selected Overview. In: Statistical Learning in Genetics. Statistics for Biology and Health. Springer, Cham. https://doi.org/10.1007/978-3-031-35851-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-031-35851-7_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-35850-0
Online ISBN: 978-3-031-35851-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)