This tutorial introduces conditional random fields (CRFs), a popular probabilistic method for structured prediction. CRFs combine the strengths of graphical models and classification methods, allowing for the modeling of complex dependencies among output variables while leveraging a large number of input features. The tutorial covers the modeling, inference, and parameter estimation of CRFs, including practical issues for implementing large-scale CRFs. It is designed to be accessible to practitioners from various fields, without requiring prior knowledge of graphical modeling. The tutorial begins by explaining the need for structured prediction methods, where multiple variables depend on each other and other observed variables. It then introduces graphical models, including generative and discriminative models, and discusses the advantages and limitations of each approach. The tutorial focuses on CRFs, which are discriminative models that directly model the conditional distribution \( p(\mathbf{y}|\mathbf{x}) \). Key topics include: - **Modeling**: Definitions of linear-chain and general CRFs, and their applications in various domains such as natural language processing, computer vision, and bioinformatics. - **Inference**: Algorithms for inference in CRFs, including forward-backward algorithms for linear-chain CRFs. - **Parameter Estimation**: Methods for estimating parameters in CRFs, including maximum likelihood and stochastic gradient methods. - **Implementation Details**: Practical considerations such as feature engineering, numerical stability, and scalability. The tutorial also highlights the relationship between CRFs and other models, such as logistic regression, hidden Markov models, and neural networks. It concludes with a discussion of future directions and related work.This tutorial introduces conditional random fields (CRFs), a popular probabilistic method for structured prediction. CRFs combine the strengths of graphical models and classification methods, allowing for the modeling of complex dependencies among output variables while leveraging a large number of input features. The tutorial covers the modeling, inference, and parameter estimation of CRFs, including practical issues for implementing large-scale CRFs. It is designed to be accessible to practitioners from various fields, without requiring prior knowledge of graphical modeling. The tutorial begins by explaining the need for structured prediction methods, where multiple variables depend on each other and other observed variables. It then introduces graphical models, including generative and discriminative models, and discusses the advantages and limitations of each approach. The tutorial focuses on CRFs, which are discriminative models that directly model the conditional distribution \( p(\mathbf{y}|\mathbf{x}) \). Key topics include: - **Modeling**: Definitions of linear-chain and general CRFs, and their applications in various domains such as natural language processing, computer vision, and bioinformatics. - **Inference**: Algorithms for inference in CRFs, including forward-backward algorithms for linear-chain CRFs. - **Parameter Estimation**: Methods for estimating parameters in CRFs, including maximum likelihood and stochastic gradient methods. - **Implementation Details**: Practical considerations such as feature engineering, numerical stability, and scalability. The tutorial also highlights the relationship between CRFs and other models, such as logistic regression, hidden Markov models, and neural networks. It concludes with a discussion of future directions and related work.