2010. 12. 14. 20:02
Computer Vision
Michael I. Jordan & Christopher M. Bishop, "Neural Networks", In Tucker, A. B. (Ed.) CRC Handbook of Computer Science, Boca Raton, FL: CRC Press, 1997.
download: http://www.cs.berkeley.edu/~jordan/papers/crc.ps
1. Introduction
Neural network methods have had their greatest impact in problems where statistical issues dominate and where data are easily obtained.
"conjunction of graphical algorithms and probability theory":
A neural network is first and foremost a graph with patterns represented in terms of numerical values attached to the nodes of the graph and transformations between patterns achieved via simple message-passing algorithms. Many neural network architectures, however, are also statistical processors, characterized by making particular probabilistic assumptions about data.
Based on a source of training data, the aim is to produce a statistical model of the process from which the data are generated so as to allow the best predictions to be made for new data.
statistical modeling - density estimation (unsupervised learning), classification & regression
density estimation ("unsupervised learning")
: to model the unconditional distribution of data described by some vector
- to train samples and a network model to build a representation of the probability density
- to label regions for a new input vector
classification & regression ("supervised learning")
: to distinguish between input variables and target variables
- to assign each input vector to one of classes and target variables to class labels
-> estimation of conditional densities from the joint input-target space
2. Representation
2.1 Density estimation
To form an explicit model of the input density
Gaussian mixture distribution
ref. An Introduction to Multivariate Statistical Analysis, 3rd Edition, T. W. Anderson, Wiley, 2003
2.2 Linear regression and linear discriminants
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Generic constraints on underspecified target trajectories.pdf