Ranking Causal Influence of Financial Markets via Directed Information Graphs

A non-parametric method for ranking stock indices according to their mutual causal influences is presented. Under the assumption that indices reflect the underlying economy of a country, such a ranking indicates which countries exert the most economic influence in an examined subset of the global economy. The proposed method represents the indices as nodes in a directed graph, where the edges' weights are estimates of the pair-wise causal influences, quantified using the directed information functional. This method facilitates using a relatively small number of samples from each index. The indices are then ranked according to their net-flow in the estimated graph (sum of the incoming weights subtracted from the sum of outgoing weights). Daily and minute-by-minute data from nine indices (three from Asia, three from Europe and three from the US) were analyzed. The analysis of daily data indicates that the US indices are the most influential, which is consistent with intuition that the indices representing larger economies usually exert more influence. Yet, it is also shown that an index representing a small economy can strongly influence an index representing a large economy if the smaller economy is indicative of a larger phenomenon. Finally, it is shown that while inter-region interactions can be captured using daily data, intra-region interactions require more frequent samples.Comment: To be presented at Conference on Information Sciences and Systems (CISS) 201

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

Learning Loosely Connected Markov Random Fields

We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test based algorithm for learning the underlying graph structure. The novel maximization step in our algorithm ensures that the true edges are detected correctly even when there are short cycles in the graph. The number of samples required by our algorithm is C*log p, where p is the size of the graph and the constant C depends on the parameters of the model. We show that several previously studied models are examples of loosely connected Markov random fields, and our algorithm achieves the same or lower computational complexity than the previously designed algorithms for individual cases. We also get new results for more general graphical models, in particular, our algorithm learns general Ising models on the Erdos-Renyi random graph G(p, c/p) correctly with running time O(np^5).Comment: 45 pages, minor revisio