Written by: Stephen Hsu
Primary Source: Information Processing
This paper is based on talks I’ve given in the last few years. See here and here for video. Although there isn’t much that hasn’t already appeared in the talks or on this blog (other than some Compressed Sensing results for the nonlinear case) it’s nice to have it in one place. The references are meant to be useful to people seriously interested in this subject, although I imagine they are nowhere near comprehensive. Apologies to anyone whose work I missed.
If you don’t like the word “intelligence” just substitute “height” and everything will be OK. We live in strange times.
On the genetic architecture of intelligence and other quantitative traits (arXiv:1408.3421)
Comments: 30 pages, 13 figures
How do genes affect cognitive ability or other human quantitative traits such as height or disease risk? Progress on this challenging question is likely to be significant in the near future. I begin with a brief review of psychometric measurements of intelligence, introducing the idea of a “general factor” or g score. The main results concern the stability, validity (predictive power), and heritability of adult g. The largest component of genetic variance for both height and intelligence is additive (linear), leading to important simplifications in predictive modeling and statistical estimation. Due mainly to the rapidly decreasing cost of genotyping, it is possible that within the coming decade researchers will identify loci which account for a significant fraction of total g variation. In the case of height analogous efforts are well under way. I describe some unpublished results concerning the genetic architecture of height and cognitive ability, which suggest that roughly 10k moderately rare causal variants of mostly negative effect are responsible for normal population variation. Using results from Compressed Sensing (L1-penalized regression), I estimate the statistical power required to characterize both linear and nonlinear models for quantitative traits. The main unknown parameter s (sparsity) is the number of loci which account for the bulk of the genetic variation. The required sample size is of order 100s, or roughly a million in the case of cognitive ability.