Exploring the Potential of Bilevel Optimization for Calibrating Neural Networks

Handling uncertainty is critical for ensuring reliable decision-making in intelligent systems. Modern neural networks are known to be poorly calibrated, resulting in predicted confidence scores that are difficult to use. This article explores improving confidence estimation and calibration through the application of bilevel optimization, a framework designed to solve hierarchical problems with interdependent optimization levels. A self-calibrating bilevel neural-network training approach is introduced to improve a model's predicted confidence scores. The effectiveness of the proposed framework is analyzed using toy datasets, such as Blobs and Spirals, as well as more practical simulated datasets, such as Blood Alcohol Concentration (BAC). It is compared with a well-known and widely used calibration strategy, isotonic regression. The reported experimental results reveal that the proposed bilevel optimization approach reduces the calibration error while preserving accuracy.

Cartoon-texture evolution for two-region image segmentation

Two-region image segmentation is the process of dividing an image into two regions of interest, i.e., the foreground and the background. To this aim, Chan et al. [Chan, Esedo\=glu, Nikolova, SIAM Journal on Applied Mathematics 66(5), 1632-1648, 2006] designed a model well suited for smooth images. One drawback of this model is that it may produce a bad segmentation when the image contains oscillatory components. Based on a cartoon-texture decomposition of the image to be segmented, we propose a new model that is able to produce an accurate segmentation of images also containing noise or oscillatory information like texture. The novel model leads to a non-smooth constrained optimization problem which we solve by means of the ADMM method. The convergence of the numerical scheme is also proved. Several experiments on smooth, noisy, and textural images show the effectiveness of the proposed model.