A framework is developed for investigating complex multivariate relationshipsin a dataset. This is based on using the universal approximation abilities ofa multi-layer perceptron (MLP) neural network to predict a quantity ofinterest from a large set of parameters. A measure of redundancy is derived,and used in such a way that the average influence on the predicted quantityfrom any parameter can be estimated. Input parameters can be ordered in termsof increasing redundancy and therefore assist in finding the most importantparameters a phenomenon of interest depends upon. In spite of the problembeing multi-dimensional, the functional form of the one-to-one relationshipbetween a parameter and a quantity of interest can be visualized. Thisframework is then used together with sensitivity analysis to investigate thedependence of the total radiated power of JET plasmas on a large number ofparameters, leading to the identification of a much smaller set of parametersto be used in an effective MLP predictor of total radiated power.