# Variational Learning for Multi-layer networks of Linear Threshold Units

Neil D. Lawrence, University of Sheffield

in Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics, pp 245-252

#### Abstract

Linear threshold units were originally proposed as models of biological neurons. They were widely studied in the context of the perceptron @Rosenblatt:book62. Due to the difficulties of finding a general algorithm for networks with hidden nodes, they never passed into general use. We derive an algorithm in the context of graphical models and show how it may be applied in multi-layer networks of linear threshold units. We demonstrate the algorithm through three well known datasets.

  @InProceedings{lawrence-ltu01, title = {Variational Learning for Multi-layer networks of Linear Threshold Units}, author = {Neil D. Lawrence}, booktitle = {Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics}, pages = {245}, year = {2001}, editor = {Tommi S. Jaakkola and Thomas S. Richardson}, address = {San Francisco, CA}, month = {00}, publisher = {Morgan Kauffman}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2001-01-01-lawrence-ltu01.md}, url = {http://inverseprobability.com/publications/lawrence-ltu01.html}, abstract = {Linear threshold units were originally proposed as models of biological neurons. They were widely studied in the context of the perceptron @Rosenblatt:book62. Due to the difficulties of finding a general algorithm for networks with hidden nodes, they never passed into general use. We derive an algorithm in the context of graphical models and show how it may be applied in multi-layer networks of linear threshold units. We demonstrate the algorithm through three well known datasets.}, crossref = {Jaakkola:aistats01}, key = {Lawrence:ltu01}, linkpdf = {http://www.thelawrences.net/neil/ltus.pdf}, linkpsgz = {http://www.thelawrences.net/neil/ltus.ps.gz}, OPTgroup = {} }
 %T Variational Learning for Multi-layer networks of Linear Threshold Units %A Neil D. Lawrence %B %C Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics %D %E Tommi S. Jaakkola and Thomas S. Richardson %F lawrence-ltu01 %I Morgan Kauffman %P 245--252 %R %U http://inverseprobability.com/publications/lawrence-ltu01.html %X Linear threshold units were originally proposed as models of biological neurons. They were widely studied in the context of the perceptron @Rosenblatt:book62. Due to the difficulties of finding a general algorithm for networks with hidden nodes, they never passed into general use. We derive an algorithm in the context of graphical models and show how it may be applied in multi-layer networks of linear threshold units. We demonstrate the algorithm through three well known datasets. 
 TY - CPAPER TI - Variational Learning for Multi-layer networks of Linear Threshold Units AU - Neil D. Lawrence BT - Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics PY - 2001/01/01 DA - 2001/01/01 ED - Tommi S. Jaakkola ED - Thomas S. Richardson ID - lawrence-ltu01 PB - Morgan Kauffman SP - 245 EP - 252 L1 - http://www.thelawrences.net/neil/ltus.pdf UR - http://inverseprobability.com/publications/lawrence-ltu01.html AB - Linear threshold units were originally proposed as models of biological neurons. They were widely studied in the context of the perceptron @Rosenblatt:book62. Due to the difficulties of finding a general algorithm for networks with hidden nodes, they never passed into general use. We derive an algorithm in the context of graphical models and show how it may be applied in multi-layer networks of linear threshold units. We demonstrate the algorithm through three well known datasets. ER - 
 Lawrence, N.D.. (2001). Variational Learning for Multi-layer networks of Linear Threshold Units. Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics :245-252