NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Monotonic Optimization: Problems and Solution Approaches
SIAM Journal on Optimization
Partially Monotone Networks Applied to Breast Cancer Detection on Mammograms
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
Monotonic multi-layer perceptron networks as universal approximators
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
Monotone and partially monotone neural networks
IEEE Transactions on Neural Networks
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Neural networks applied in control loops and safety-critical domains have to meet more requirements than just the overall best function approximation. On the one hand, a small approximation error is required; on the other hand, the smoothness and the monotonicity of selected input-output relations have to be guaranteed. Otherwise, the stability of most of the control laws is lost. In this article we compare two neural network-based approaches incorporating partial monotonicity by structure, namely the Monotonic Multi-Layer Perceptron (MONMLP) network and the Monotonic MIN-MAX (MONMM) network. We show the universal approximation capabilities of both types of network for partially monotone functions. On a number of datasets, we investigate the advantages and disadvantages of these approaches related to approximation performance, training of the model and convergence.