Probabilistic Language Models (Corpus-Based Approaches)

Statistical NLP methods model language as probability distributions derived from corpus analysis, allowing systems to make predictions based on observed patterns in text data rather than explicit rules.

Hidden Markov Models (HMMs) use probabilistic state transitions to model sequence data, becoming fundamental for tasks like part-of-speech tagging and early speech recognition. These models capture the likelihood of transitions between language states that aren't directly observable.

Naive Bayes classifiers apply Bayes' theorem with strong independence assumptions between features, providing surprisingly effective text classification despite their simplicity. Their probabilistic foundation made them particularly valuable for applications like spam filtering and sentiment analysis.

Term Frequency-Inverse Document Frequency (TF-IDF) transforms text into numerical vectors by weighting terms based on their frequency in a document relative to their rarity across a corpus. This technique forms the foundation of many information retrieval systems and remains widely used for document representation in modern applications.