A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market

We propose a dynamic network model where two mechanisms control the probability of a link between two nodes: (i) the existence or absence of this link in the past, and (ii) node-specific latent variables (dynamic fitnesses) describing the propensity of each node to create links. Assuming a Markov dynamics for both mechanisms, we propose an Expectation-Maximization algorithm for model estimation and inference of the latent variables. The estimated parameters and fitnesses can be used to forecast the presence of a link in the future. We apply our methodology to the e-MID interbank network for which the two linkage mechanisms are associated with two different trading behaviors in the process of network formation, namely preferential trading and trading driven by node-specific characteristics. The empirical results allow to recognise preferential lending in the interbank market and indicate how a method that does not account for time-varying network topologies tends to overestimate preferential linkage.Comment: 19 pages, 6 figure

Online Joint Topology Identification and Signal Estimation with Inexact Proximal Online Gradient Descent

Identifying the topology that underlies a set of time series is useful for tasks such as prediction, denoising, and data completion. Vector autoregressive (VAR) model based topologies capture dependencies among time series, and are often inferred from observed spatio-temporal data. When the data are affected by noise and/or missing samples, the tasks of topology identification and signal recovery (reconstruction) have to be performed jointly. Additional challenges arise when i) the underlying topology is time-varying, ii) data become available sequentially, and iii) no delay is tolerated. To overcome these challenges, this paper proposes two online algorithms to estimate the VAR model-based topologies. The proposed algorithms have constant complexity per iteration, which makes them interesting for big data scenarios. They also enjoy complementary merits in terms of complexity and performance. A performance guarantee is derived for one of the algorithms in the form of a dynamic regret bound. Numerical tests are also presented, showcasing the ability of the proposed algorithms to track the time-varying topologies with missing data in an online fashion.Comment: 14 pages including supplementary material, 2 figures, submitted to IEEE Transactions on Signal Processin

Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations