Artificial Neural Network What-If Theory

General Theory

Using an auto-encoder ANN we will approximate the implicit function of any dataset during the learning phase and to assign a fuzzy output to any new input during the recall phase. A fuzzy output is a value in the range [0..1] in which zero means complete absence or non-membership in the output and a one means complete membership. Any other value indicates the degree of partial membership.

Recent research has improved the auto-encoder ANNs in order to optimize a deep learning process (Hinton, Osindero & Teh, 2006) or to select the fundamental hidden features of a large dataset (Le, et. al., 2012) or to reduce the dimensionality of data (Hinton & Salakhutdinov, 2006; Raina, Madhavan & Ng, 2009; Raiko, Valpola & LeCun, 2012). Other approaches have tried to use auto-encoders as unsupervised ANNs able to perform supervised tasks (Larochelle & Bengio, 2008; Bengio, 2009).

We have chosen to look at the auto-encoders from a different point of view: we define the testing phase of a trained auto-encoder as the interpretation of a dataset (traditionally referred to as the Testing Dataset) using the logic present in another dataset (the Training Dataset). We define this point of view a seminal approach for a new theory, named AWIT (Artificial Neural Networks What If Theory).

The algorithm to implement this new approach to data analysis follows:

• •

  Let DB1 and DB2 be two different datasets with the same types of variables but possessing different records;

• •

  The function f() is a non-linear function optimally interpolating DB1 by means of an auto-encoder ANN consisting of one hidden layer:x_DB1 = f(h, v*)(1)h = g(x_DB1, w*)(2)

  • v*, w* = parameters to be estimated by ANN,

  • x = input variables.

• •

  The dataset DB2 is rewritten using the ANN trained on the DB1dataset:

  
  (3)h = g(x_DB2, w)(4)

  • v, w = Trained parameters estimated b ANN using DB1

  • = output variables.