Robust risk aggregation with neural networks

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g. the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: Firstly, we derive a dual representation of the considered problem and prove that strong duality holds. Secondly, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real world instance.Comment: Revised version. Accepted for publication in "Mathematical Finance

A robust modulation classification method using convolutional neural networks

Automatic modulation classification (AMC) is a core technique in noncooperative communication systems. In particular, feature-based (FB) AMC algorithms have been widely studied. Current FB AMC methods are commonly designed for a limited set of modulation and lack of generalization ability; to tackle this challenge, a robust AMC method using convolutional neural networks (CNN) is proposed in this paper. In total, 15 different modulation types are considered. The proposed method can classify the received signal directly without feature extracion, and it can automatically learn features from the received signals. The features learned by the CNN are presented and analyzed. The robust features of the received signals in a specific SNR range are studied. The accuracy of classification using CNN is shown to be remarkable, particularly for low SNRs. The generalization ability of robust features is also proven to be excellent using the support vector machine (SVM). Finally, to help us better understand the process of feature learning, some outputs of intermediate layers of the CNN are visualized

Uncertainty assisted robust tuberculosis identification with Bayesian convolutional neural networks

Tuberculosis (TB) is an infectious disease that can lead towards death if left untreated. TB detection involves extraction of complex TB manifestation features such as lung cavity, air space consolidation, endobronchial spread, and pleural effusions from chest x-rays (CXRs). Deep learning based approach named convolutional neural network (CNN) has the ability to learn complex features from CXR images. The main problem is that CNN does not consider uncertainty to classify CXRs using softmax layer. It lacks in presenting the true probability of CXRs by differentiating confusing cases during TB detection. This paper presents the solution for TB identification by using Bayesian-based convolutional neural network (B-CNN). It deals with the uncertain cases that have low discernibility among the TB and non-TB manifested CXRs. The proposed TB identification methodology based on B-CNN is evaluated on two TB benchmark datasets, i.e., Montgomery and Shenzhen. For training and testing of proposed scheme we have utilized Google Colab platform which provides NVidia Tesla K80 with 12 GB of VRAM, single core of 2.3 GHz Xeon Processor, 12 GB RAM and 320 GB of disk. B-CNN achieves 96.42% and 86.46% accuracy on both dataset, respectively as compared to the state-of-the-art machine learning and CNN approaches. Moreover, B-CNN validates its results by filtering the CXRs as confusion cases where the variance of B-CNN predicted outputs is more than a certain threshold. Results prove the supremacy of B-CNN for the identification of TB and non-TB sample CXRs as compared to counterparts in terms of accuracy, variance in the predicted probabilities and model uncertainty