Thumbs up? Sentiment Classification using Machine Learning Techniques

5.1 Naive Bayes

1. Give the Naive Bayes classifier used by Pang et al.
   \(P_{\text{NB}}(c \mid d) = \frac{P(c) \prod_{i=1}^{m} P(f_i \mid c)^{n_i(d)}}{P(d)}\), assuming features are conditionally independent given the class; \(P(c)\) and \(P(f_i \mid c)\) are relative frequencies with add-one smoothing, and \(P(d)\) is ignored when choosing \(\arg\max_c\).
   • Pang et al., 2002, Thumbs up? Sentiment Classification using Machine Learning Techniques (Proceedings of the 2002 Conference on Empirical Methods in Natural Language Processing (EMNLP 2002)), §5.1, p. 81
2. Why can Naive Bayes work well even though its independence assumption is false?
   Empirically it does well in text categorization, and Domingos and Pazzani (1997) showed it is optimal for some problem classes with highly dependent features; the classification can be right even when the probabilities are wrong.
   • Pang et al., 2002, Thumbs up? Sentiment Classification using Machine Learning Techniques (Proceedings of the 2002 Conference on Empirical Methods in Natural Language Processing (EMNLP 2002)), §5.1, p. 81