Bivariate Nonisotonic Statistical Regression by a Lookup Table Neural System

Linear data regression is a fundamental mathematical tool in engineering and applied sciences. However, for complex non-linear phenomena, the standard linear least-squares regression may prove ineffective, hence calling for more involved data modeling techniques. The current research work investigates, in particular, non-linear statistical regression of bivariate data that do not exhibit a monotonic dependency. The current contribution proposes a neural-network-based data processing method, termed data monotonization, followed by neural isotonic statistical regression. Such data monotonization processing is performed by means of an adaptive neural network that learns its non-linear transfer function from the training set. The artificial neural system that performs data monotonization is implemented through a look-up table (LUT), which entails few computationally-inexpensive algebraic operations to adapt and to compute the output from the input data-set. A number of learning rules to adapt such LUT-based neural system are introduced and compared, in order to elucidate their relative merits and drawbacks.