A Probabilistic Model for LCS

Contents

Having conceptually defined the LCS model, it will now be embedded into a formal setting. The formal model is initially designed for a fixed model structure $\mathcal{M}$; that is, the number of classifiers and where they are localised in the input space is constant during training of the model. Even though the LCS model could be characterised purely by its functional form [78], a probabilistic model will be developed instead. Its advantage is that rather than getting a point estimate $\hat{f}({\bf x})$ for the output y given some input x, the probabilistic model provides the probability distribution p(y|x, θ) that for some input x and model parameters θ describes the probability density of the output being the vector y. From this distribution its is possible to form a point estimate from its mean or its mode, and additionally to get information about the certainty of the prediction by the spread of the distribution.