I read on the literature that a replicator neural network is a particular feed-forward network which is trained by replicating input data points as desired outputs.
This network is claimed to be effective at detecting outliers, as less frequent patterns will result in higher regression error than most frequent ones.
However it seems to me that mapping each data point into itself can be trivially acieved by the identity function, with zero regression error for all data points.
What am I missing, then?
I thank you in advance.
The trick is that you must eliminate the errors of the first and second kind from the input patterns. Of course, there are other solutions to this problem without the use of RNN.
Dear All,
I wish to thank you for your kind replies. I would like to ask for some further clarification:
@Joachim:
I know that regression does not try to fit all data point, but to find the best tradeoff. However consider this simple 1D example:
I have an input dataset of 1004 data points, distributed as follows:
1000 data points drawn from a normal distribution mu = 0, sigma = 5;
4 data points drawn from another normal distribution, mu = 100, sigma = 0.5;
Obviously the 4 data points drawn from my distribution are the outliers I am trying to detect.
However, if I use the RNN method with a simple linear regression (which is the simplest possible neural network) I will get a 45 degree straight line that represents all point with zero error. Therefore, how do I detect the outliers?
@ Vasily: What do you exactly mean by "eliminate the errors of the first and second kind"?
Such errors include the absence of some necessary elements and the presence of false components in the input patterns.
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