Randomized smoothing is currently the state-of-the-art method that provides certified robustness for deep neural networks. However, due to its excessively conservative nature, this method of incomplete verification often cannot achieve an adequate certified radius on real-world datasets. One way to obtain a larger certified radius is to use an input-specific algorithm instead of using a fixed Gaussian filter for all data points. Several methods based on this idea have been proposed, but they either suffer from high computational costs or gain marginal improvement in certified radius. In this work, we show that by exploiting the quasiconvex problem structure, we can find the optimal certified radii for most data points with slight computational overhead. This observation leads to an efficient and effective input-specific randomized smoothing algorithm. We conduct extensive experiments and empirical analysis on CIFAR-10 and ImageNet. The results show that the proposed method significantly enhances the certified radii with low computational overhead.

The new regulatory framework proposal on Artificial Intelligence (AI) published by the European Commission establishes a new risk-based legal approach. The proposal highlights the need to develop adequate risk assessments for the different uses of AI. This risk assessment should address, among others, the detection and mitigation of bias in AI. In this work we analyze statistical approaches to measure biases in automatic decision-making systems. We focus our experiments in face recognition technologies. We propose a novel way to measure the biases in machine learning models using a statistical approach based on the N-Sigma method. N-Sigma is a popular statistical approach used to validate hypotheses in general science such as physics and social areas and its application to machine learning is yet unexplored. In this work we study how to apply this methodology to develop new risk assessment frameworks based on bias analysis and we discuss the main advantages and drawbacks with respect to other popular statistical tests.