Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations

Causal Transfer for Imitation Learning and Decision Making under Sensor-shift

Learning from demonstrations (LfD) is an efficient paradigm to train AI agents. But major issues arise when there are differences between (a) the demonstrator's own sensory input, (b) our sensors that observe the demonstrator and (c) the sensory input of the agent we train. In this paper, we propose a causal model-based framework for transfer learning under such "sensor-shifts", for two common LfD tasks: (1) inferring the effect of the demonstrator's actions and (2) imitation learning. First we rigorously analyze, on the population-level, to what extent the relevant underlying mechanisms (the action effects and the demonstrator policy) can be identified and transferred from the available observations together with prior knowledge of sensor characteristics. And we device an algorithm to infer these mechanisms. Then we introduce several proxy methods which are easier to calculate, estimate from finite data and interpret than the exact solutions, alongside theoretical bounds on their closeness to the exact ones. We validate our two main methods on simulated and semi-real world data.Comment: It appears in AAAI-202

Econometric modeling of systemic risk: going beyond pairwise comparison and allowing for nonlinearity

Financial instability and its destructive effects on the economy can lead to financial crises due to its contagion or spillover effects to other parts of the economy. Having an accurate measure of systemic risk gives central banks and policy makers the ability to take proper policies in order to stabilize financial markets. Much work is currently being undertaken on the feasibility of identifying and measuring systemic risk. In principle, there are two main schemes to measure interlinkages between financial institutions. One might wish to construct a mathematical model of financial market participant relations as a network/graph by using a combination of information extracted from financial statements like the market value of liabilities of counterparties, or an econometric model to estimate those relations based on financial series. In this paper, we develop a data-driven econometric framework that promotes an understanding of the relationship between financial institutions using a nonlinearly modified Granger-causality network. Unlike existing literature, it is not focused on a linear pairwise estimation. The method allows for nonlinearity and has predictive power over future economic activity through a time-varying network of relationships. Moreover, it can quantify the interlinkages between financial institutions. We also show how the model improve the measurement of systemic risk and explain the link between Granger-causality network and generalized variance decompositions network. We apply the method to the monthly returns of U.S. financial Institutions including banks, broker and insurance companies to identify the level of systemic risk in the financial sector and the contribution of each financial institution

Experimental Design for Causal Effect Identification

Pearl's do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the causal effect. In this work, we consider the problem of designing the collection of interventions with the minimum cost to identify the desired effect. First, we prove that this problem is NP-hard, and subsequently propose an algorithm that can either find the optimal solution or a logarithmic-factor approximation of it. This is done by establishing a connection between our problem and the minimum hitting set problem. Additionally, we propose several polynomial-time heuristic algorithms to tackle the computational complexity of the problem. Although these algorithms could potentially stumble on sub-optimal solutions, our simulations show that they achieve small regrets on random graphs.Comment: 53 pages, 13 figures, extending the findings of our ICML2022 pape

Sharp Analysis of Stochastic Optimization under Global Kurdyka-{\L}ojasiewicz Inequality

We study the complexity of finding the global solution to stochastic nonconvex optimization when the objective function satisfies global Kurdyka-Lojasiewicz (KL) inequality and the queries from stochastic gradient oracles satisfy mild expected smoothness assumption. We first introduce a general framework to analyze Stochastic Gradient Descent (SGD) and its associated nonlinear dynamics under the setting. As a byproduct of our analysis, we obtain a sample complexity of $\mathcal{O}(\epsilon^{-(4-\alpha)/\alpha})$ for SGD when the objective satisfies the so called $\alpha$-PL condition, where $\alpha$ is the degree of gradient domination. Furthermore, we show that a modified SGD with variance reduction and restarting (PAGER) achieves an improved sample complexity of $\mathcal{O}(\epsilon^{-2/\alpha})$ when the objective satisfies the average smoothness assumption. This leads to the first optimal algorithm for the important case of $\alpha=1$ which appears in applications such as policy optimization in reinforcement learning.Comment: The work was submitted for review in May, 2022 and was accepted to NeurIPS 2022 in Sep, 202