Structural Agnostic Modeling: Adversarial Learning of Causal Graphs

A new causal discovery method, Structural Agnostic Modeling (SAM), is presented in this paper. Leveraging both conditional independencies and distributional asymmetries in the data, SAM aims at recovering full causal models from continuous observational data along a multivariate non-parametric setting. The approach is based on a game between $d$ players estimating each variable distribution conditionally to the others as a neural net, and an adversary aimed at discriminating the overall joint conditional distribution, and that of the original data. An original learning criterion combining distribution estimation, sparsity and acyclicity constraints is used to enforce the end-to-end optimization of the graph structure and parameters through stochastic gradient descent. Besides the theoretical analysis of the approach in the large sample limit, SAM is extensively experimentally validated on synthetic and real data

Non-Parametric Causality Detection: An Application to Social Media and Financial Data

According to behavioral finance, stock market returns are influenced by emotional, social and psychological factors. Several recent works support this theory by providing evidence of correlation between stock market prices and collective sentiment indexes measured using social media data. However, a pure correlation analysis is not sufficient to prove that stock market returns are influenced by such emotional factors since both stock market prices and collective sentiment may be driven by a third unmeasured factor. Controlling for factors that could influence the study by applying multivariate regression models is challenging given the complexity of stock market data. False assumptions about the linearity or non-linearity of the model and inaccuracies on model specification may result in misleading conclusions. In this work, we propose a novel framework for causal inference that does not require any assumption about the statistical relationships among the variables of the study and can effectively control a large number of factors. We apply our method in order to estimate the causal impact that information posted in social media may have on stock market returns of four big companies. Our results indicate that social media data not only correlate with stock market returns but also influence them.Comment: Physica A: Statistical Mechanics and its Applications 201

Kernel-based Conditional Independence Test and Application in Causal Discovery

Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties