Uncertainty Propagation Based MINLP Approach for Artificial Neural Network Structure Reduction

The performance of artificial neural networks (ANNs) is highly influenced by the selection input variables and architecture defined hyper parameters such as number neurons in hidden layer connections between network variables. Although there are some black-box trial error based studies literature to deal with these issues, it fair state that a rigorous systematic method providing global unique solution still missing. Accordingly, this study, mixed integer nonlinear programming (MINLP) formulation proposed detect best features among elements while propagating parameter output uncertainties for regression problems. objective minimize covariance estimated (i) detecting ideal neurons, (ii) synthesizing connection configuration those inputs outputs, (iii) selecting optimum multi variable data set design ensure identifiable ANN architectures. As result, suggested approach provides robust optimal tighter prediction bounds obtained from propagation uncertainty, higher accuracy compared traditional fully connected other benchmarks. Furthermore, after elimination approximately 85% 90% connections, two case respectively, addition significant reduction subset.