In structured prediction, decoding means predicting the output given the input. Decoding is also known as inference (see note below). The decoding algorithm is the algorithm used to make predictions (such as dynamic programming, beam search, integer linear programming, etc).

In NLP and graphical models, inference means making predictions (predicting the output $Y$ given the input $X$), and is another term for decoding. In statistics however, inference means learning (predicting the parameters).

• MAP inference in graphical models
• Dynamic Programming
• Weighted Logic Programming
• Integer Linear Programming

• Structured Prediction
• Integer Linear Programming
• Weighted Logic Programming