Multi-Output Dependence (MOD) learning is a generalization of standard classification problems that allows for multiple outputs that are dependent on each other. A primary issue that arises in the context of MOD learning is that for any given input pattern there can be multiple correct output patterns. This changes the learning task from function approximation to relation approximation. Previous algorithms do not consider this problem, and thus cannot be readily applied to MOD problems. To perform MOD learning, we introduce the Hierarchical Multi-Output Nearest Neighbor model (HMONN) that employs a basic learning model for each output and a modified nearest neighbor approach to refine the initial results.
@cite_9: Statistical Relational Learning (SRL) is a subarea of machine learning which combines elements from statistical and probabilistic modeling with languages which support structured data representations. In this survey, we will: 1) provide an introduction to SRL, 2) describe some of the distinguishing characteristics of SRL systems, including relational feature construction and collective classification, 3) describe three SRL systems in detail, 4) discuss applications of SRL techniques to important data management problems such as entity resolution, selectivity estimation, and information integration, and 5) discuss connections between SRL methods and existing database research such as probabilistic databases.
@cite_7: 
@cite_8: Data mining algorithms look for patterns in data. While most existing data mining approaches look for patterns in a single data table, multi-relational data mining (MRDM) approaches look for patterns that involve multiple tables (relations) from a relational database. In recent years, the most common types of patterns and approaches considered in data mining have been extended to the multi-relational case and MRDM now encompasses multi-relational (MR) association rule discovery, MR decision trees and MR distance-based methods, among others. MRDM approaches have been successfully applied to a number of problems in a variety of areas, most notably in the area of bioinformatics. This article provides a brief introduction to MRDM, while the remainder of this special issue treats in detail advanced research topics at the frontiers of MRDM.
While MOD learning is relation approximation, this should not be confused with relational learning. Statistical Relational Learning @cite_7 @cite_9 and Multi-Relational Learning @cite_8 both handle relational data, not relation approximation. These relational learning models learn a function from relational data and handle specially formatted and structured data.