Biwei Huang

Causal discovery from nonstationary/heterogeneous data : skeleton estimation and orientation determination

It is commonplace to encounter nonstationary or heterogeneous data, of which the underlying generating process changes over time or across data sets (the data sets may have different experimental conditions or data collection conditions). Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper we develop a principled framework for causal discovery from such data, called Constraint-based causal Discovery from Nonstationary/heterogeneous Data (CD-NOD), which addresses two important questions. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a way to determine causal orientations by making use of independence changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. Experimental results on various synthetic and real-world data sets are presented to demonstrate the efficacy of our methods.

Generalized Score Functions for Causal Discovery

Discovery of causal relationships from observational data is a fundamental problem. Roughly speaking, there are two types of methods for causal discovery, constraint-based ones and score-based ones. Score-based methods avoid the multiple testing problem and enjoy certain advantages compared to constraint-based ones. However, most of them need strong assumptions on the functional forms of causal mechanisms, as well as on data distributions, which limit their applicability. In practice the precise information of the underlying model class is usually unknown. If the above assumptions are violated, both spurious and missing edges may result. In this paper, we introduce generalized score functions for causal discovery based on the characterization of general (conditional) independence relationships between random variables, without assuming particular model classes. In particular, we exploit regression in RKHS to capture the dependence in a nonparametric way. The resulting causal discovery approach produces asymptotically correct results in rather general cases, which may have nonlinear causal mechanisms, a wide class of data distributions, mixed continuous and discrete data, and multidimensional variables. Experimental results on both synthetic and real-world data demonstrate the efficacy of our proposed approach.

Causal Discovery of Feedback Networks with Functional Magnetic Resonance Imaging

We test the adequacies of several proposed and two new statistical methods for recovering the causal structure of systems with feedback that generate noisy time series closely matching real BOLD time series. We compare: an adaptation for time series of the first correct method for recovering the structure of cyclic linear systems; multivariate Granger causal regression; the GIMME algorithm; the Ramsey et al. non-Gaussian methods; two non-Gaussian methods proposed by Hyv¨arinen and Smith; a method due to Patel, et al.; and the GlobalMIT algorithm. We introduce and also compare two new methods, the Fast Adjacency Skewness (FASK) and Two-Step, which exploit non-Gaussian features of the BOLD signal in different ways. We give theoretical justifications for the latter two algorithms. Our test models include feedback structures with and without direct feedback (2-cycles), excitatory and inhibitory feedback, models using experimentally determined structural connectivities of macaques, and empirical resting state and task data. We find that averaged over all of our simulations, including those with 2-cycles, several of these methods have a better than 80% orientation precision (i.e., the probability a directed edge is in the true generating structure given that a procedure estimates it to be so) and the two new methods also have better than 80% recall (probability of recovering an orientation in the data generating model). Recovering inhibitory direct feedback loops between two regions is especially challenging.

Estimating feedforward and feedback effective connections from fMRI time series: Assessments of statistical methods

We test the adequacies of several proposed and two new statistical methods for recovering the causal structure of systems with feedback from synthetic BOLD time series. We compare an adaptation of the first correct method for recovering cyclic linear systems; Granger causal regression; a multivariate autoregressive model with a permutation test; the Group Iterative Multiple Model Estimation (GIMME) algorithm; the Ramsey et al. non-Gaussian methods; two non-Gaussian methods by Hyvärinen and Smith; a method due to Patel et al.; and the GlobalMIT algorithm. We introduce and also compare two new methods, Fast Adjacency Skewness (FASK) and Two-Step, both of which exploit non-Gaussian features of the BOLD signal. We give theoretical justifications for the latter two algorithms. Our test models include feedback structures with and without direct feedback (2-cycles), excitatory and inhibitory feedback, models using experimentally determined structural connectivities of macaques, and empirical human resting-state and task data. We find that averaged over all of our simulations, including those with 2-cycles, several of these methods have a better than 80% orientation precision (i.e., the probability of a directed edge is in the true structure given that a procedure estimates it to be so) and the two new methods also have better than 80% recall (probability of recovering an orientation in the true structure).