Improving the explainability of autoencoder factors for commodities through forecast-based Shapley values.

Autoencoders are dimension reduction models in the field of machine learning which can be thought of as a neural network counterpart of principal components analysis (PCA). Due to their flexibility and good performance, autoencoders have been recently used for estimating nonlinear factor models in finance. The main weakness of autoencoders is that the results are less explainable than those obtained with the PCA. In this paper, we propose the adoption of the Shapley value to improve the explainability of autoencoders in the context of nonlinear factor models. In particular, we measure the relevance of nonlinear latent factors using a forecast-based Shapley value approach that measures each latent factor's contributions in determining the out-of-sample accuracy in factor-augmented models. Considering the interesting empirical instance of the commodity market, we identify the most relevant latent factors for each commodity based on their out-of-sample forecasting ability.

Clustering networked funded European research activities through rank-size laws.

This paper treats a well-established public evaluation problem, which is the analysis of the funded research projects. We specifically deal with the collection of the research actions funded by the European Union over the 7th Framework Programme for Research and Technological Development and Horizon 2020. The reference period is 2007-2020. The study is developed through three methodological steps. First, we consider the networked scientific institutions by stating a link between two organizations when they are partners in the same funded project. In doing so, we build yearly complex networks. We compute four nodal centrality measures with relevant, informative content for each of them. Second, we implement a rank-size procedure on each network and each centrality measure by testing four meaningful classes of parametric curves to fit the ranked data. At the end of such a step, we derive the best fit curve and the calibrated parameters. Third, we perform a clustering procedure based on the best-fit curves of the ranked data for identifying regularities and deviations among years of research and scientific institutions. The joint employment of the three methodological approaches allows a clear view of the research activity in Europe in recent years.

Financial interbanking networks resilience under shocks propagation.

The concept of resilience-i.e., the ability of a unified structure to absorb shocks-is of high relevance in the context of network modelling and analysis, mainly when referred to finance. This paper starts from this premise, and deals with the resilience of a financial interbanking system. At this aim, we firstly introduce a new measure of the resilience of a network, by taking into full consideration the influence of the topology of the network and the weights of its links in the shocks propagation; then, we build one financial network model related to the quarterly-based interbanking sector, whose weights are calibrated on high quality empirical data; lastly, we compute the resilience measure of the considered networks. A discussion of the results is provided, by considering both finance and network theory perspectives.

Network constraints on the mixing patterns of binary node metadata.

We consider the network constraints on the bounds of the assortativity coefficient, which aims to quantify the tendency of nodes with the same attribute values to be connected. The assortativity coefficient can be considered as the Pearson's correlation coefficient of node metadata values across network edges and lies in the interval [-1,1]. However, properties of the network, such as degree distribution and the distribution of node metadata values, place constraints upon the attainable values of the assortativity coefficient. This is important as a particular value of assortativity may say as much about the network topology as about how the metadata are distributed over the network-a fact often overlooked in literature where the interpretation tends to focus simply on the propensity of similar nodes to link to each other, without any regard on the constraints posed by the topology. In this paper we quantify the effect that the topology has on the assortativity coefficient in the case of binary node metadata. Specifically, we look at the effect that the degree distribution, or the full topology, and the proportion of each metadata value has on the extremal values of the assortativity coefficient. We provide the means for obtaining bounds on the extremal values of assortativity for different settings and demonstrate that under certain conditions the maximum and minimum values of assortativity are severely limited, which may present issues in interpretation when these bounds are not considered.

Evaluating relevance and redundancy to quantify how binary node metadata interplay with the network structure.

Networks are real systems modelled through mathematical objects made up of nodes and links arranged into peculiar and deliberate (or partially deliberate) topologies. Studying these real-world topologies allows for several properties of interest to be revealed. In real networks, nodes are also identified by a certain number of non-structural features or metadata. Given the current possibility of collecting massive quantity of such metadata, it becomes crucial to identify automatically which are the most relevant for the observed structure. We propose a new method that, independently from the network size, is able to not only report the relevance of binary node metadata, but also rank them. Such a method can be applied to networks from any domain, and we apply it in two heterogeneous cases: a temporal network of technology transfer and a protein-protein interaction network. Together with the relevance of node metadata, we investigate the redundancy of these metadata displaying by the results on a Redundancy-Relevance diagram, which is able to highlight the differences among vectors of metadata from both a structural and a non-structural point of view. The obtained results provide insights of a practical nature into the importance of the observed node metadata for the actual network structure.