A guide for kernel generalized regression methods for genomic-enabled prediction

Abstract

The primary objective of this paper is to provide a guide on implementing Bayesian generalized kernel regression methods for genomic prediction in the statistical software R. Such methods are quite efficient for capturing complex non-linear patterns that conventional linear regression models cannot. Furthermore, these methods are also powerful for leveraging environmental covariates, such as genotype × environment (G×E) prediction, among others. In this study we provide the building process of seven kernel methods: linear, polynomial, sigmoid, Gaussian, Exponential, Arc-cosine 1 and Arc-cosine L. Additionally, we highlight illustrative examples for implementing exact kernel methods for genomic prediction under a single-environment, a multi-environment and multi-trait framework, as well as for the implementation of sparse kernel methods under a multi-environment framework. These examples are followed by a discussion on the strengths and limitations of kernel methods and, subsequently by conclusions about the main contributions of this paper.

Bayesian multitrait kernel methods improve multienvironment genome-based prediction

“…Another advantage of the Bayesian multitrait kernel methods is that they can significantly reduce the computational resources needed in comparison with Ridge regression multitrait models, since instead of directly using the inputs (independent variables), a transformed input is used that usually has less dimension than the dimension of the number of inputs. However, as with all kernel methods, due to this transformation of the input, the estimates of the beta coefficients are not interpretable as in conventional regression methods, and for this reason, these methods do not help to further understand the complex relationship between input and output, and as such, it is important to avoid false expectations about these methods ( Montesinos-López et al 2021 ) in terms of interpretability. Finally, as one reviewer pointed out, the successful implementation of the multitrait kernel method proposed here is straightforward when the dataset is balanced in the response variable (no missing data) and in the environments, but more complicated when the data are not balanced, but still the method works by only taking care of the imbalance situation.…”

“…However, the adoption of the Bayesian paradigm in plant breeding continues to grow due to the great computational advancements and new methodological applications and elucidations. Bayesian MT models offer some of the following advantages mentioned by Montesinos-López et al (2019b ): (1) they allow prior information to be incorporated; (2) they do not need good starting values to estimate parameters of interest such as the restricted maximum likelihood; (3) they increase the precision of parameter estimates (smaller standard errors); (4) conclusions can be drawn about the correlations between the dependent variables, notably, the extent to which the correlations depend on the individual and on the group level; (5) testing whether the effect of an explanatory variable on dependent variable Y1 is larger than its effect on Y2, when Y1 and Y2 data were observed (totally or partially) in the same individuals, is possible only by means of a multivariate analysis; (6) when attempting to carry out a single test of the joint effect of an explanatory variable on several dependent variables, a multivariate analysis is also required; such a single test can be useful, e.g. , to avoid the danger of chance capitalization, which is inherent to carry out a separate test for each dependent variable; and (7) it does not have strong identifiability problems.…”

Optimizing Plant Breeding Programs For Genomic Selection

“…The prediction accuracy of the approximate kernels depends on the number of subset lines and the decrease in eigenvalue decomposition of the GRM. Further, Montesinos-López et al [87] outlined the implementation of sparse matrices from Cuevas et al [76]. They integrated them with the Bayesian methods from Cuevas et al [85] to create linear, polynomial, sigmoid, Gaussian, and Arccosines with one or more hidden layers and exponential kernels in both a multi-environment and multi-trait framework.…”

A General-Purpose Machine Learning R Library for Sparse Kernels Methods With an Application for Genome-Based Prediction

“…Kernels have proven to be useful in helping the conventional machine learning algorithms capture non-linear patterns in data (Montesinos-López et al, 2021b;Montesinos-López et al, 2022a). In addition to capturing complex non-linear patterns, the sparse kernel version of kernel methods can also save significant computational resources without a relevant loss in prediction accuracy (Montesinos-López et al, 2021b;Montesinos-López, et al, 2022a).…”

“…Kernels have proven to be useful in helping the conventional machine learning algorithms capture non-linear patterns in data (Montesinos-López et al, 2021b;Montesinos-López et al, 2022a). In addition to capturing complex non-linear patterns, the sparse kernel version of kernel methods can also save significant computational resources without a relevant loss in prediction accuracy (Montesinos-López et al, 2021b;Montesinos-López, et al, 2022a). In this paper by sparse kernels we define those kernels that are built with only a fraction of the total amount of inputs by assuming that the input matrix is a sparse matrix, that is, a matrix that contain many information with zeros.…”