Why a Nonlinear Solution for a Linear Problem?*

We emphasize a key point that when there is noise in the system, even if the system is linear, a nonlinear solution is more desirable. We derive a simple expression that shows that for a linear regression model, the logistic nonlinearity will be the natural match for modeling posterior class probabilities, and that the steepness of this logistic function is inversely proportional to the level of noise in the system. We note a problem that matches this data generation mechanism, equalization of an infinite impulse response channel, and show that for this example, the logistic type equalizer not only achieves lower bit error rate than its linear counterpart but is very efficient as well.