MLN combines first order logic with probability. The domain rules or domain knowledge is represented in an MLN using weighted first order logic rules. Stronger the belief about any rule, higher is its associated weight. Inference in such an MLN gives the most probable true groundings of certain (query) predicates, while ensuring maximum weighted satisfiability of the rules. 

University of Michigan - Ann Arbor

1. Integer Linear Programming 
2. Markov Logic Networks (MLN)
3. Joint Label
4. Beam Search
5. Parsing

Joint Inference Techniques

Techniques for Jointly Extracting Entities and Relations: A Survey

A global decision is taken by using Integer Linear Programming which is consistent with some domain constraints. First, learn independent local classifiers for entity and relation extraction. During inference, given a sentence, a global decision is produced such that the domain-specific or task-specific constraints are satisfied. Often these constraints capture mutual compatibility of entity and relation types. 

Integer Linear Programming for Joint Inference

Markov Logic Networks (MLN) for Joint Inference

This tagging scheme reduces the joint extraction task to a tagging problem. Intuitively, a single tag is assigned to a word that encodes entity as well as relation label information, automatically leading to joint inference. 

Joint Label for Joint Inference

It formulates the joint extraction task as a structured prediction problem to reveal the linguistic and logical properties of the hidden structures. Here, the output structure of each sentence was interpreted as a graph in which entity mentions are nodes and relations are directed arcs labeled with relation types. It designs several local as well as global features to characterize and score these structures. Hence, the joint extraction problem was reduced to predicting a structure with the highest score for any given sentence.

Beam Search for Joint Inference

It's based on a graph or tree format parsing output and attempts to find the most probable labelling of all of its nodes which corresponds the entity and relation types.

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