explores the relationship between personality and easily extractable features such as number of Friends or Likes, geographic location, or user-Like pairs. For example, user-Like pairs are shown to be better predictors of a personality than one’s spouse [@youyou2015computer]. In 2013, Schwartz et al introduced the open vocabulary approach (or bag of words) to personality, gender, and age prediction [@schwartz2013personality]. This significantly outperforms closed-vocabulary approaches such as LIWC that rely on domain knowledge to assign each word to one or more of 69 categories. For an excellent overview of related work, we direct readers to that paper’s introduction [@schwartz2013personality].

Language Models
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### Bag of Words

The majority of our experiments use bag of words (BoW) term frequency-inverse document frequency (tf-idf) preprocessing followed by $\ell_2$ regularized regression. First, the vocabulary is limited to the $k$ most common words in a given training set. Then a matrix of word counts, $N$, is constructed, where $N_{ij}$ refers to how often word $j$ is used by subject $i$. Each row is normalized to sum to one, moved to a log scale, and divided by $d$, the ratio of documents in which each word appears. In more formal notation, each element of the tf-idf matrix 