Causal Lifting and Link Prediction

Spearman's work started a revolution that gave us, among other things, matrix and tensor factorizations, Principal Component Analysis (PCA), and Independent Component Analysis (ICA). Simultaneously, The Abilities of Man also warned us about interpreting the factors of subject i as innate rather than acquired abilities. For instance, regarding Woolley and Fischer's observation that "boys are enormously superior [to girls] at [... ] spatial relations" (i.e., in how objects relate in space) [76], Spearman warns that "evidence of this difference being really innate [rather than acquired] is still dubious". Today, we can describe Spearman's warning as being about two competing causal hypotheses that describe link formation between young children and their abilities. A path-dependent hypothesis where past links influence future links [46] and an innate factors hypothesis where link formation is just a manifestation of latent innate factors [75]. In Woolley and Fischer's experiments, both hypotheses are able to describe the data: Either boys are innately better than girls at spatial reasoning (innate factors hypothesis), or boys in 1914 just happened to have had more playtime with spatial tasks than girls, with each task further improving Work partially done at Purdue University and Intel Labs.