Monthly Archives: November 2017

A.Barra, G.Genovese, P.Sollich, D.Tantari (2017), Phase transitions in Restricted Boltzmann Machines with generic priors

We study generalized restricted Boltzmann machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as generalized Hopfield models. We underline the role of the retrieval phase for both inference and learning processes and we show that retrieval is robust for a large class of weight and unit priors, beyond the standard Hopfield scenario. Furthermore, we show how the paramagnetic phase boundary is directly related to the optimal size of the training set necessary for good generalization in a teacher-student scenario of unsupervised learning.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.042156

P.Barucca, P.Mazzarisi, F.Lillo, D.Tantari (2017), Disentangling group and link persistence in dynamic stochastic block models

We study the inference of a model of dynamic networks in which both communities and
links keep memory of previous network states. By considering maximum likelihood inference from
single snapshot observations of the network, we show that link persistence makes the inference of
communities harder, decreasing the detectability threshold, while community persistence tends to make
it easier. We analytically show that communities inferred from single network snapshot can share a
maximum overlap with the underlying communities of a specific previous instant in time. This leads
to time-lagged inference: the identification of past communities rather than present ones. Finally
we compute the time lag and propose a corrected algorithm, the Lagged Snapshot Dynamic (LSD)
algorithm, for community detection in dynamic networks. We analytically and numerically characterize
the detectability transitions of such algorithm as a function of the memory parameters of the model.

https://arxiv.org/pdf/1701.05804.pdf

Letizia E., Lillo F. (2017). Corporate payments networks and credit risk rating

This paper provides empirical evidences that corporate firms risk assessment could benefit from taking quantitatively into account the network of interactions among firms. Indeed, the structure of interactions between firms is critical to identify risk concentration and the possible pathways of propagation of financial distress. In this work, we consider the interactions by investigating a large proprietary dataset of payments between Italian firms. We first characterise the topological properties of the payment networks, and then we focus our attention on the relation between the networks and the risk of firms. Our main finding is to document the existence of an homophily of risk, i.e. the tendency of firms with similar risk profile to be statistically more connected among themselves. This effect is observed when considering both pairs of firms and communities or hierarchies identified in the network. We leverage this knowledge to demonstrate that network properties of a node can be used to predict the missing rating of a firm.

https://arxiv.org/pdf/1711.07677.pdf