Natural language is rich, ambiguous, and context-dependent. A single sentence can have multiple parses, a word can have multiple meanings, and the intent behind an utterance may be unclear. Bayesian methods address this pervasive ambiguity by maintaining probability distributions over linguistic hypotheses — word senses, topic assignments, syntactic parses, semantic interpretations — rather than committing to a single analysis. This probabilistic perspective has shaped NLP from its earliest days and remains influential despite the deep learning revolution.
Topic Models
Latent Dirichlet Allocation (LDA), introduced by David Blei, Andrew Ng, and Michael Jordan in 2003, is the paradigmatic Bayesian model for text analysis. LDA posits that each document is a mixture of topics, each topic is a distribution over words, and the topic proportions are drawn from a Dirichlet prior. Bayesian inference — via collapsed Gibbs sampling or variational methods — discovers the latent topic structure from the observed word counts.
z_{d,n} ~ Categorical(θ_d) (topic assignment for word n in document d)
w_{d,n} ~ Categorical(φ_{z_{d,n}}) (word drawn from assigned topic)
φ_k ~ Dirichlet(β) (word distribution for topic k)
Extensions of LDA — hierarchical Dirichlet processes for determining the number of topics, correlated topic models, dynamic topic models for tracking topic evolution over time, and supervised topic models for combining topic discovery with prediction — showcase the flexibility of the Bayesian generative modeling approach.
Bayesian Language Models
Before the neural era, Bayesian methods improved n-gram language models through hierarchical smoothing. The Pitman-Yor process prior on word distributions produces power-law frequency distributions that match the empirical statistics of natural language (Zipf's law). Hierarchical Pitman-Yor language models outperformed interpolated Kneser-Ney smoothing, the previous state of the art. While neural language models now dominate, Bayesian principles — particularly the treatment of uncertainty and the integration of prior knowledge — continue to influence their design and evaluation.
Even as transformer-based large language models (LLMs) have transformed NLP, Bayesian ideas remain relevant. Calibration — ensuring that model confidence aligns with actual accuracy — is a Bayesian concern. Bayesian methods are used for uncertainty estimation in LLM outputs, for active learning to select the most informative fine-tuning examples, and for prompt optimization via Bayesian optimization. The question of how to quantify and communicate the uncertainty in LLM-generated text is fundamentally Bayesian.
Text Classification and Sentiment Analysis
The naive Bayes classifier, despite its strong independence assumptions, remains a competitive baseline for text classification tasks including sentiment analysis, spam detection, and document categorization. Its Bayesian structure allows incorporation of prior knowledge about class frequencies and word distributions, and its computational simplicity enables real-time classification at scale. Bayesian approaches to sentiment analysis extend beyond bag-of-words to model aspect-level sentiment, temporal evolution of opinions, and the influence of social network structure on opinion formation.
Information Extraction and Structured Prediction
Bayesian methods for named entity recognition, relation extraction, and coreference resolution use probabilistic graphical models — hidden Markov models, conditional random fields with Bayesian parameter estimation, and Bayesian nonparametric models for entity linking. These models naturally handle the uncertainty inherent in mapping noisy, ambiguous text to structured knowledge.
"LDA showed that a simple Bayesian generative model could discover meaningful structure in text without any labeled data. It was a proof of concept for the power of Bayesian unsupervised learning." — David Blei, co-creator of Latent Dirichlet Allocation
Current Frontiers
Bayesian approaches to few-shot learning enable NLP systems to learn new tasks from handful of examples by leveraging prior knowledge. Bayesian methods for multilingual NLP share information across languages through hierarchical priors. And the integration of Bayesian reasoning with neural text generation — producing not just likely text but text with calibrated uncertainty — remains an open challenge with implications for trust, safety, and factuality in AI-generated content.