for $U$ when both traits are part of $T$.

In this paper, $X$ is the tf-idf word matrix, $T$ is defined by our labels, and the model weights are some estimate of $U$ we define as $\hat{U}$. Row dependencies in $\hat{U}$ are based on how words function. For example, ‘camp’ and ‘camping’ perform similar roles in a status. Likewise, the relationship between IQ and agreeableness will be embedded in the columns of $\hat{U}$. However, many of the tasks have little training data and the solution is ill-posed. Regularization encourages generalization, but does not provide any guarantees. Further, sometimes $\epsilon$ dominates the model when observations are not very explanatory or the relationship to a trait is not linear. Given these challenges, what confidence can be placed in the estimate $\hat{U}$?

These problems mirror those faced when clustering data. Clustering does not come with guarantees it will yield sensible answers in diverse scenarios [@kleinberg2003impossibility]. However, it is broadly useful when exploring large sets of data [@jain1999data; @shamir20021; @dixon2003classification]. Similarly, $\hat{U}$ can be viewed as a way of ranking features for exploration. A highly ranked observation is not proof it is important. But several highly ranked observations with functional coherence may suggest a 