J. A. Ramos

José A. Ramos, Guillaume Mercère

Recently \cite{Ramos2017a} presented a subspace system identification algorithm for 2-D purely stochastic state space models in the general Roesser form. However, since the exact problem requires an oblique projection of $Y_f^h$ projected onto $W_p^h$ along $\widehat{X}_f^{vh}$, where $W_p^h= \begin{bmatrix}\widehat{X}_p^{vh} \\ Y_p^h \end{bmatrix}$, this presents a problem since $\{\widehat{X}_p^{vh},\widehat{X}_f^{vh}\}$ are unknown. In the above mentioned paper, the authors found that by doing an orthogonal projection $Y_f^h/Y_p^h$, one can identify the future horizontal state matrix $\widehat{X}_f^{h}$ with a small bias due to the initial conditions that depend on $\{\widehat{X}_p^{vh},\widehat{X}_f^{vh}\}$. Nevertheless, the results on modeling 2-D images were very good despite lack of knowledge of $\{\widehat{X}_p^{vh},\widehat{X}_f^{vh}\}$. In this note we delve into the bias term and prove that it is insignificant, provided $i$ is chosen large enough and the vertical and horizontal states are uncorrelated. That is, the cross covariance of the state estimates $x_{r,s}^{h}$ and $x_{r,s}^{v}$ is zero, or $P_{hv}=0_{n_x\times n_x}$ and $P_{vh}=0_{n_x\times n_x}$. Our simulations use $i=30$. We also present a second iteration to improve the state estimates by including the vertical states computed from a vertical data processing step, i.e., by doing an orthogonal projection $Y_f^v/Y_p^v$. In this revised algorithm we include a step to compute the initial states. This new portion, in addition to the algorithm presented in \cite{Ramos2017a}, forms a complete 2-D stochastic subspace system identification algorithm.

Jaime D. Acevedo-Viloria, Luisa Roa, Soji Adeshina et al.

Large digital platforms create environments where different types of user interactions are captured, these relationships offer a novel source of information for fraud detection problems. In this paper we propose a framework of relational graph convolutional networks methods for fraudulent behaviour prevention in the financial services of a Super-App. To this end, we apply the framework on different heterogeneous graphs of users, devices, and credit cards; and finally use an interpretability algorithm for graph neural networks to determine the most important relations to the classification task of the users. Our results show that there is an added value when considering models that take advantage of the alternative data of the Super-App and the interactions found in their high connectivity, further proofing how they can leverage that into better decisions and fraud detection strategies.