L1 vs Deep Learning in Genomic Prediction

The paper below by some of my MSU colleagues examines the performance of a number of ML algorithms, both linear and nonlinear, including deep neural nets, in genomic prediction across several different species.

When I give talks about prediction of disease risks and complex traits in humans, I am often asked why we are not using fancy (trendy?) methods such as Deep Learning (DL). Instead, we focus on L1 penalization methods ("sparse learning") because 1. the theoretical framework (including theorems providing performance guarantees) is well-developed, and (relatedly) 2. the L1 methods perform as well or better than other methods in our own testing.

The term theoretical framework may seem unusual in ML, which is at the moment largely an empirical subject. Experience in theoretical physics shows that when powerful mathematical results are available, they can be very useful to guide investigation. In the case of sparse learning we can make specific estimates for how much data is required to "solve" a trait -- i.e., capture most of the estimated heritability in the predictor. Five years ago we predicted a threshold of a few hundred thousand genomes for height, and this turned out to be correct. Currently, this kind of performance characterization is not possible for DL or other methods.

What is especially powerful about deep neural nets is that they yield a quasi-convex (or at least reasonably efficient) optimization procedure which can learn high dimensional functions. The class of models is both tractable from a learning/optimization perspective, but also highly expressive. As I wrote here in my ICML notes (see also Elad's work which relates DL to Sparse Learning):

It may turn out that the problems on which DL works well are precisely those in which the training data (and underlying generative processes) have a hierarchical structure which is sparse, level by level. Layered networks perform a kind of coarse graining (renormalization group flow): first layers filter by feature, subsequent layers by combinations of features, etc. But the whole thing can be understood as products of sparse filters, and the performance under training is described by sparse performance guarantees (ReLU = thresholded penalization?).

However, currently in genomic prediction one typically finds that nonlinear interactions are small, which means features more complicated than single SNPs are unnecessary. (In a recent post I discussed a new T1D predictor that makes use of nonlinear haplotype interaction effects, but even there the effects are not large.) Eventually I expect this situation to change -- when we have enough whole genomes to work with, a DL approach which can (automatically) identify important features (motifs?) may allow us to go beyond SNPs and simple linear models.

Note, though, that from an information theoretic perspective (see, e.g., any performance theorems in compressed sensing) it is obvious that we will need much more data than we currently have to advance this program. Also, note that Visscher et al.'s recent GCTA work suggests that additive SNP models using rare variants (i.e., extracted from whole genome data), can account for nearly all the expected heritability for height. This implies that the power of nonlinear methods like DL may not yield qualitatively better results than simpler L1 approaches, even in the limit of very large whole genome datasets.

Benchmarking algorithms for genomic prediction of complex traits

Christina B. Azodi, Andrew McCarren, Mark Roantree, Gustavo de los Campos, Shin-Han Shiu

The usefulness of Genomic Prediction (GP) in crop and livestock breeding programs has led to efforts to develop new and improved GP approaches including non-linear algorithm, such as artificial neural networks (ANN) (i.e. deep learning) and gradient tree boosting. However, the performance of these algorithms has not been compared in a systematic manner using a wide range of GP datasets and models. Using data of 18 traits across six plant species with different marker densities and training population sizes, we compared the performance of six linear and five non-linear algorithms, including ANNs. First, we found that hyperparameter selection was critical for all non-linear algorithms and that feature selection prior to model training was necessary for ANNs when the markers greatly outnumbered the number of training lines. Across all species and trait combinations, no one algorithm performed best, however predictions based on a combination of results from multiple GP algorithms (i.e. ensemble predictions) performed consistently well. While linear and non-linear algorithms performed best for a similar number of traits, the performance of non-linear algorithms vary more between traits than that of linear algorithms. Although ANNs did not perform best for any trait, we identified strategies (i.e. feature selection, seeded starting weights) that boosted their performance near the level of other algorithms. These results, together with the fact that even small improvements in GP performance could accumulate into large genetic gains over the course of a breeding program, highlights the importance of algorithm selection for the prediction of trait values.