Generalized Score Functions for Causal Discovery

By Biwei Huang, Kun Zhang, Yizhu Lin, Bernhard Schölkopf, Clark Glymour. 2018

204 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research, Probabilistic & Bayesian Methods

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Citations in the corpus

Gradient-Based Neural DAG Learning (2019, methodology): “GSF (Huang et al., 2018), is based on the same search algorithm as GES, but uses a generalized score function which can model nonlinear relationships.”
Causal Discovery from Heterogeneous/Nonstationary Data (2019, background): “, 2006), and the generalized score functions (Huang et al., 2018).”
Causal Discovery with Reinforcement Learning (2019, background): “Unfortunately, several effective score functions, e.g., the generalized score function proposed in [13] for possibly non-linear causal relationships, cannot be easily represented in closed-form loss functions and thus can not be used with this approach.”
Meaningful Explanations of Black Box AI Decision Systems (2019, background): “First, it is interesting to explore how the techniques for data-driven causal discovery, aimed at re-constructing plausible graphs of causal dependencies in observational data (see, e.g., (Huang et al. 2018)), may be used to achieve more informative and robust explanations.”
Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models (2019, methodology): “Score-based methods define a score function that measures how well an equivalence class fits the observed data and search through possible equivalence classes to find the best scored one (Heckerman et al., 1995; Chickering, 2003; Huang et al., 2018).”
Specific and Shared Causal Relation Modeling and Mechanism-Based Clustering (2019, background): “State-of-the-art approaches to causal discovery usually assume a ﬁxed causal model [33, 2, 13, 31, 14, 39, 16]; that is, causal mechanisms are invariant across instances in the data set.”
Masked Gradient-Based Causal Structure Learning (2019, methodology): “…several base-lines, including PC [31], PC-KCI (with kernel-based conditional independence tests) [40], GES [5], GES-GS (with generalized score) [10], CAM [3], NOTEARS [43], DAG-GNN [37], SAM [12], NOTEARS-MLP [44], and For synthetic data, experiments are conducted on data models varying along…”
Review of Causal Discovery Methods Based on Graphical Models (2019, background): “Readers who are interested in causal discovery from discrete variables or mixed discrete and continuous variables may refer to Peters et al. (2010); Cai et al. (2018); Huang et al. (2018).”
Learning Sparse Nonparametric DAGs (2019, methodology): “(Due to the large number of samples, we could not run GSGES on this dataset.)”
D’ya Like DAGs? A Survey on Structure Learning and Causal Discovery (2021, methodology): “[139]) user specified adds edges with probability p = 2e d 2−d Linear, GP Add, GP Mix, Sigmoid Add and Sigmoid Mix – mixed graph data CausalWorld [1] – comprehensive robotics dataset MPI3D [70] – visual disentanglement dataset Pendulum-light-shadow [267] – image data Phase coupled oscillator [5] – p”