To;dr: fairly strong and reliable correlation between depression and posting images that are bluer, grayer and darker. This is predictive in that users can be identified as depressed before they are disgnosed. # of faces appearing in user pics was also indicative of depression. Fewer faces per picture correlated with depression. # of comments more weakly correlated with depression, and # of likes was negatively correlated. Mechanical Turk-tasked humans were also able to fairly accurately identify depressed users, but often identified different users than the machine.
Statistical methods: Bayesian feature extraction with uninformed priors. 100-tree random forest for classification.
Some points of caution: depression is a broad, fairly fuzzy term. The authors acknowledge that this complicates matters. Some self-selection bias possible, as users had to provide permission to access Instagram streams and many users opted not to.