Nonlinearity, Feedback and Uniform Consistency in Causal Structural Learning

The goal of Causal Discovery is to find automated search methods for learning causal structures from observational data. In some cases all variables of the interested causal mechanism are measured, and the task is to predict the effects one measured variable has on another. In contrast, sometimes the variables of primary interest are not directly observable but instead inferred from their manifestations in the data. These are referred to as latent variables. One commonly known example is the psychological construct of intelligence, which cannot directly measured so researchers try to assess through various indicators such as IQ tests. In this case, casual discovery algorithms can uncover underlying patterns and structures to reveal the causal connections between the latent variables and between the latent and observed variables. This thesis focuses on two questions in causal discovery: providing an alternative definition of k-Triangle Faithfulness that (i) is weaker than strong faithfulness when applied to the Gaussian family of distributions, (ii) can be applied to non-Gaussian families of distributions, and (iii) under the assumption that the modified version of Strong Faithfulness holds, can be used to show the uniform consistency of a modified causal discovery algorithm; relaxing the sufficiency assumption to learn causal structures with latent variables. Given the importance of inferring cause-and-effect relationships for understanding and forecasting complex systems, the work in this thesis of relaxing various simplification assumptions is expected to extend the causal discovery method to be applicable in a wider range with diversified causal mechanism and statistical phenomena

Rollover risk, network structure and systemic financial crises

The breakdown of short-term funding markets was a key feature of the global financial crisis of 2007/8. Combining insights from the literature on global games and network growth, we develop a simple model that sheds light on how network topology interacts with the funding structure of financial institutions to determine system-wide crises. We show how the arrival of bad news about a financial institution leads others to lose confidence in it and how this, in turn, spreads across the entire interbank network. The rate of system-wide bank failure is rendered endogenous, depending crucially on both the rate at which bad news arrives and on the maturity of debt contracts. The conditions under which the financial system makes a sharp transition from a dense network of credit relations to a sparse network where credit freezes readily occur are characterized. Our results also emphasize the role of hysteresis – once broken, credit relations take a long time to re-establish as a result of common knowledge of the equilibrium. Our findings shed light on the nature of public policy responses both during and after the crisis.interbank networks, credit crisis, liquidity freeze