Although the Random Forest classifier is not readily interpretable as is, for example, a linear model, the relative importance of each input variable to the overall prediction accuracy can be estimated.
Generally, a linear model represents each example E by a feature vector representation Φ(E) ∈ ℜ D and then estimates a linear function f(E) = w TΦ E) whose sign is used to predict whether the example E is classified into positive or negative.
Alternatively we can model the exposure-outcome association smoothly as a function of time, for example using a linear model, β(t) = β0 + β1 t.
This can be accomplished, for example, using a linear model with an effect size determined by the magnitude of the coefficients for the independent variables representing the selected genetic variants.
A simple linear example as an illustration is presented at the end.
In fact, in [37] the authors introduced a simple linear example without time-delay for which a common Lyapunov function does not exist.
A scalar linear example is included which adds insight into the key ideas of our approach and allows showing that, for linear systems, our Lyapunov-LS design with unfiltered regressor, presented in the note for unnormalized least-squares, can also be extended to normalized least-squares.
It forms a closed chain of linear reactions, and is intended as a more complicated, but still linear, example system.
These ions have a linear shape for example, [O=U=O]2+.
We apply our results to a linear quadratic example that makes contact with findings of T. Başar and P. Bernhard [H∞-Optimal Control and Related Minimax Design Problems, second ed., Birkhauser, Basel, 1995] and P. Whittle [Risk-sensitive Optimal Control, Wiley, New York, 1990].
