This can be expressed as a logistic regression:

Algorithm 2 shows our adaptation of ADAGRAD with logistic regression for multi-class classification.

Note that when used with logistic regression , ADAGRAD takes a regular gradient instead of a subgradient method for updating weights.

4.2.2 Logistic Regression

We implemented Logistic Regression using L2-Normalization, finding this to outperform Ll-Normalized and non-normalized versions.

The strength of the normalization in the logistic regression required cross-validation, which we limited to 20 values logarithmically spaced between 10—4 and 104.

We trained a logistic regression model on a feature vector for every word that appears in the NPOV sentences from the training set, with the bias-inducing words as the positive class, and all the other words as the negative class.

The types of features used in the logistic regression model are listed in Table 3, together with their value space.

Logistic regression model that only uses the features based on Liu et al.’s (2005) lexicons of positive and negative words (i.e., features 26—29).

However, our logistic regression model reveals that epistemological and other features can usefully augment the traditional sentiment and subjectivity features for addressing the difficult task of identifying the bias-inducing word in a biased sentence.

Deduplication removes 8.5% of articles.5 For topic filtering, we apply a series of keyword filters to remove sports and finance news, and also apply a text classifier for diplomatic and military news, trained on several hundred manually labeled news articles (using El-regularized logistic regression with unigram and bigram features).

We also create a baseline El-regularized logistic regression that uses normalized dependency path counts as the features (10,457 features).

The verb-path logistic regression performs strongly at AUC 0.62; it outperforms all of the vanilla frame models.

Green line is the verb-path logistic regression baseline.

While past research has used logistic regression as a binary classifier (Newman et al., 2003), our experiments show that the best-performing classifiers allow for highly nonlinear class boundaries; SVM and RF models achieve between 62.5% and 91.7% accuracy across age groups — a significant improvement over the baselines of LR and NB, as well as over previous results.

These features were obtained with the Linguistic Inquiry and Word Count (LIWC) tool and used in a logistic regression classifier which achieved, on average, 61% accuracy on test data.

We evaluate five classifiers: logistic regression (LR), a multilayer perceptron (MLP), nai've Bayes (NB), a random forest (RF), and a support vector machine (SVM).

Here, na‘1've Bayes, which assumes conditional independence of the features, and logistic regression , which has a linear decision boundary, are baselines.

For multi-class classification, one possible extension is to use a multinomial logistic regression model for categorical variables Y by using topic representations Z as input features.

In fact, this is harder than the multinomial Bayesian logistic regression , which can be done via a coordinate strategy (Polson et al., 2012).

More specifically, we extend Polson’s method for Bayesian logistic regression (Polson et al., 2012) to the generalized logistic supervised topic models, which are much more challeng-

Moreover, the latent variables Z make the inference problem harder than that of Bayesian logistic regression models (Chen et al., 1999; Meyer and Laud, 2002; Polson et al., 2012).

Before describing extensions to the baseline logistic regression model, we define notation.

We define classifiers as functions f (:E —> y E Y); in practice, we use logistic regression via LibLINEAR (Fan et al., 2008).

We compare our methods against baselines including a majority baseline, a baseline logistic regression classifier with L2 regularized features, and two common ensemble methods, AdaBoost (Freund and Schapire, 1996) and bagging (Breiman, 1996) with logistic regression base c1assifiers5.