Variational inference of cluster-weighted models for local and global sensitivity analysis

Variational inference is employed to infer cluster-weighted models from input-output data. Variational relations are derived for hyperparameters of the joint probability density of the model's parameters and latent variables. The result is an alternative to inferring the parameters through expectation maximisation. Surrogate models derived from the resulting predictive distributions have high data fidelity, good regularity between the data, and are quickly evaluated. These traits make them well-suited to sampling-based global sensitivity analyses through variance decomposition. Moreover, analytical local derivatives of the regression functions are readily computed to support sampling of the derivatives throughout the factor space. Results are presented for local and global sensitivities of two examples based on cluster-weighted surrogate models inferred from limited samples. The first example is analytical; the second builds on previous work by the authors in global, full-field sensitivity analysis of computational models of near-ground sound propagation.