is defined by

$$W_{ij} = \frac{1 + \log\Big(\frac{N_{ij}}{\sum_{i=1}^{k}N_{ij}}\Big)}{d_j}.$$

$W$ is then normalized so each row lies on the unit sphere. $W$ can now be used for linear classification or regression with $\ell_2$ regularization on the parameters. This is commonly called Ridge Regression. For binary classification problems, labels are assigned values of $\{-1,1\}$ and a threshold determines predicted label. For categorical data with more than two labels, we train a classifier on each pair of labels. Predicted label is decided by majority vote of the $\frac{c(c-1)}{2}$ classifiers, where $c$ is the number of classes.

### Character-Level Convolutional Neural Network {#CNN}

For gender prediction, we also train a 49 layer character level convolutional neural network (char-CNN) described in [@conneau2017very]. Much like successful computer vision architectures [@krizhevsky2012imagenet], each character is embedded in continuous space and combined with neighbors by many layers of convolutional filters. Unlike BoW models, CNNs preserve the temporal dimension, allowing the use of syntactic information. While a great advantage, and theoretically more similar to human cognition, this requires different preprocessing. During training, all inputs must be the same length along the temporal axis despite the wide variation in total length of users’ statuses. We chose to split users’ concatenated statuses 