1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.
Beside the minimizationof the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability . Driven by these principles, we propose continuous-domain formulations for one-dimensional regression problems. In our first approach, we use the Lipschitz constant as a regularizer, which results in an implicit tuning of the overall robustness of the learned mapping. In our second approach, we control the Lipschitz constant explicitly using a user-defined upper-bound and make use of a sparsity-promoting regularizer to favor simpler (and, hence, more interpretable) solutions. The theoretical study of the latter formulation is motivated in part by its equivalence, which we prove, with the training of a Lipschitz-constrained two-layer univariate neural network with rectified linear unit (ReLU) activations and weight decay. By proving representer theorems, we show that both problems admit global minimizers that are continuous and piecewise-linear (CPWL) functions. Moreover, we propose efficient algorithms that find the sparsest solution of each problem: the CPWL mapping with the least number of linear regions. Finally, we illustrate numerically the outcome of our formulations.
© Copyright 2022 IEEE – All rights reserved. Use of this website signifies your agreement to the IEEE Terms and Conditions.
A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity.