The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System's Configurations from a Given Temperature.

The restricted Boltzmann machine (RBM) is a generative neural network that can learn in an unsupervised way. This machine has been proven to help understand complex systems, using its ability to generate samples of the system with the same observed distribution. In this work, an Ising system is simulated, creating configurations via Monte Carlo sampling and then using them to train RBMs at different temperatures. Then, 1. the ability of the machine to reconstruct system configurations and 2. its ability to be used as a detector of configurations at specific temperatures are evaluated. The results indicate that the RBM reconstructs configurations following a distribution similar to the original one, but only when the system is in a disordered phase. In an ordered phase, the RBM faces levels of irreproducibility of the configurations in the presence of bimodality, even when the physical observables agree with the theoretical ones. On the other hand, independent of the phase of the system, the information embodied in the neural network weights is sufficient to discriminate whether the configurations come from a given temperature well. The learned representations of the RBM can discriminate system configurations at different temperatures, promising interesting applications in real systems that could help recognize crossover phenomena.

Equity Market Description under High and Low Volatility Regimes Using Maximum Entropy Pairwise Distribution.

The financial market is a complex system in which the assets influence each other, causing, among other factors, price interactions and co-movement of returns. Using the Maximum Entropy Principle approach, we analyze the interactions between a selected set of stock assets and equity indices under different high and low return volatility episodes at the 2008 Subprime Crisis and the 2020 COVID-19 outbreak. We carry out an inference process to identify the interactions, in which we implement the a pairwise Ising distribution model describing the first and second moments of the distribution of the discretized returns of each asset. Our results indicate that second-order interactions explain more than 80% of the entropy in the system during the Subprime Crisis and slightly higher than 50% during the COVID-19 outbreak independently of the period of high or low volatility analyzed. The evidence shows that during these periods, slight changes in the second-order interactions are enough to induce large changes in assets correlations but the proportion of positive and negative interactions remains virtually unchanged. Although some interactions change signs, the proportion of these changes are the same period to period, which keeps the system in a ferromagnetic state. These results are similar even when analyzing triadic structures in the signed network of couplings.

The predictive power of stock market's expectations volatility: A financial synchronization phenomenon.

We explore the use of implied volatility indices as a tool for estimate changes in the synchronization of stock markets. Specifically, we assess the implied stock market's volatility indices' predictive power on synchronizing global equity indices returns. We built the correlation network of 26 stock indices and implemented in-sample and out-of-sample tests to evaluate the predictive power of VIX, VSTOXX, and VXJ implied volatility indices. To measure markets' synchronization, we use the Minimum Spanning Tree length and the length of the Planar Maximally Filtered Graph. Our results indicate a high predictive power of all the volatility indices, both individually and together, though the VIX predominates over the evaluated options. We find that an increase in the markets' volatility expectations, captured by the implied volatility indices, is a good Granger predictor of an increase in the synchronization of returns in the following month. Estimating, monitoring, and predicting returns' synchronization is essential for investment decision-making, especially for diversification strategies and regulating financial systems.

Modeling Verdict Outcomes Using Social Network Measures: The Watergate and Caviar Network Cases.

Modelling criminal trial verdict outcomes using social network measures is an emerging research area in quantitative criminology. Few studies have yet analyzed which of these measures are the most important for verdict modelling or which data classification techniques perform best for this application. To compare the performance of different techniques in classifying members of a criminal network, this article applies three different machine learning classifiers-Logistic Regression, Naïve Bayes and Random Forest-with a range of social network measures and the necessary databases to model the verdicts in two real-world cases: the U.S. Watergate Conspiracy of the 1970's and the now-defunct Canada-based international drug trafficking ring known as the Caviar Network. In both cases it was found that the Random Forest classifier did better than either Logistic Regression or Naïve Bayes, and its superior performance was statistically significant. This being so, Random Forest was used not only for classification but also to assess the importance of the measures. For the Watergate case, the most important one proved to be betweenness centrality while for the Caviar Network, it was the effective size of the network. These results are significant because they show that an approach combining machine learning with social network analysis not only can generate accurate classification models but also helps quantify the importance social network variables in modelling verdict outcomes. We conclude our analysis with a discussion and some suggestions for future work in verdict modelling using social network measures.