Renato M. Assunção

Flavio Figueiredo, José Geraldo Fernandes, Jackson Silva et al.

Copulas are powerful statistical tools for capturing dependencies across data dimensions. Applying Copulas involves estimating independent marginals, a straightforward task, followed by the much more challenging task of determining a single copulating function, $C$, that links these marginals. For bivariate data, a copula takes the form of a two-increasing function $C: (u,v)\in \mathbb{I}^2 \rightarrow \mathbb{I}$, where $\mathbb{I} = [0, 1]$. This paper proposes 2-Cats, a Neural Network (NN) model that learns two-dimensional Copulas without relying on specific Copula families (e.g., Archimedean). Furthermore, via both theoretical properties of the model and a Lagrangian training approach, we show that 2-Cats meets the desiderata of Copula properties. Moreover, inspired by the literature on Physics-Informed Neural Networks and Sobolev Training, we further extend our training strategy to learn not only the output of a Copula but also its derivatives. Our proposed method exhibits superior performance compared to the state-of-the-art across various datasets while respecting (provably for most and approximately for a single other) properties of C.

Paulo Rezeck, Renato M. Assunção, Luiz Chaimowicz

This paper presents a novel methodology that allows a swarm of robots to perform a cooperative transportation task. Our approach consists of modeling the swarm as a {\em Gibbs Random Field} (GRF), taking advantage of this framework's locality properties. By setting appropriate potential functions, robots can dynamically navigate, form groups, and perform cooperative transportation in a completely decentralized fashion. Moreover, these behaviors emerge from the local interactions without the need for explicit communication or coordination. To evaluate our methodology, we perform a series of simulations and proof-of-concept experiments in different scenarios. Our results show that the method is scalable, adaptable, and robust to failures and changes in the environment.

Flavio Figueiredo, Guilherme Borges, Pedro O. S. Vaz de Melo et al.

We here focus on the task of learning Granger causality matrices for multivariate point processes. In order to accomplish this task, our work is the first to explore the use of Wold processes. By doing so, we are able to develop asymptotically fast MCMC learning algorithms. With $N$ being the total number of events and $K$ the number of processes, our learning algorithm has a $O(N(\,\log(N)\,+\,\log(K)))$ cost per iteration. This is much faster than the $O(N^3\,K^2)$ or $O(K^3)$ for the state of the art. Our approach, called GrangerBusca, is validated on nine datasets. This is an advance in relation to most prior efforts which focus mostly on subsets of the Memetracker data. Regarding accuracy, GrangerBusca is three times more accurate (in Precision@10) than the state of the art for the commonly explored subsets Memetracker. Due to GrangerBusca's much lower training complexity, our approach is the only one able to train models for larger, full, sets of data.

Roberto C. S. N. P. Souza, Denise E. F de Brito, Renato M. Assunção et al.

Exploiting the large amount of available data for addressing relevant social problems has been one of the key challenges in data mining. Such efforts have been recently named "data science for social good" and attracted the attention of several researchers and institutions. We give a contribution in this objective in this paper considering a difficult public health problem, the timely monitoring of dengue epidemics in small geographical areas. We develop a generative simple yet effective model to connect the fluctuations of disease cases and disease-related Twitter posts. We considered a hidden Markov process driving both, the fluctuations in dengue reported cases and the tweets issued in each region. We add a stable but random source of tweets to represent the posts when no disease cases are recorded. The model is learned through a Markov chain Monte Carlo algorithm that produces the posterior distribution of the relevant parameters. Using data from a significant number of large Brazilian towns, we demonstrate empirically that our model is able to predict well the next weeks of the disease counts using the tweets and disease cases jointly.