Learning an L1-regularized Gaussian Bayesian Network in the Equivalence Class Space

Learning the structure of a graphical model from data is a common task in a wide range of practical applications. In this paper, we focus on Gaussian Bayesian networks, i.e., on continuous data and directed acyclic graphs with a joint probability density of all variables given by a Gaussian. We propose to work in an equivalence class search space, specifically using the k-greedy equivalence search algorithm. This, combined with regularization techniques to guide the structure search, can learn sparse networks close to the one that generated the data. We provide results on some synthetic networks and on modeling the gene network of the two biological pathways regulating the biosynthesis of isoprenoids for the Arabidopsis thaliana plan

Causality and aggregation in economics: the use of high dimensional panel data in micro-econometrics and macro-econometrics

This study proposes one plausible procedure to address two methodological issues, which are common in micro- and macro- econometric analyses, for the full realization of research potential brought by recently available high dimensional data. To address the issue of how to infer the causal structure from empirical regularities, graphical causal models are proposed to inductively infer causal structure from non-temporal and non-experimental data. However, the (probabilistic) stability condition for the graphical causal models can be violated for high dimensional data, given that close co-movements and thus near deterministic relations are oftentimes observed among variables in high dimensional data. Aggregation methods are proposed as one possible way to address this matter, allowing one to infer causal relationships among disaggregated variables based on aggregated variables. Aggregation methods also are helpful to address the issue of how to incorporate a large information set into an empirical model, given that econometric considerations, such as degrees-of-freedom and multicollinearity, require an economy of parameters in empirical models. However, actual aggregation requires legitimate classifications for interpretable and consistent aggregation. Based on the generalized condition for the consistent and interpretable aggregation derived from aggregation theory and statistical dimensional methods, we propose plausible methodological procedure to consistently address the two related issues of causal inference and actual aggregation procedures. Additional issues for empirical studies of micro-economics and macro-economics are also discussed. The proposed procedure provides an inductive guidance for the specification issues among the direct, inverse, and mixed demand systems and an inverse demand system, which is statistically supported, is identified for the consumer behavior of soft drink consumption. The proposed procedure also provides ways to incorporate large information set into an empirical model with allowing structural understanding of U.S. macro-economy, which was difficult to obtain based on the previously used factor augmented vector autoregressive (FAVAR) framework. The empirical results suggest the plausibility of the proposed method to incorporate large information sets into empirical studies by inductively addressing multicollinearity problem in high dimensional data