Paper:
Local Causal Discovery of Direct Causes and Effects
We focus on the discovery and identification of direct causes and effects of a target variable in a causal network. State-of-the-art causal learning algorithms generally need to find the global causal structures in the form of complete partial directed acyclic graphs (CPDAG) in order to identify direct causes and effects of a target variable. While these algorithms are effective, it is often unnecessary and wasteful to find the global structures when we are only interested in the local structure of one target variable (such as class labels). We propose a new local causal discovery algorithm, called Causal Markov Blanket (CMB), to identify the direct causes and effects of a target variable based on Markov Blanket Discovery. CMB is designed to conduct causal discovery among multiple variables, but focuses only on finding causal relationships between a specific target variable and other variables. Under standard assumptions, we show both theoretically and experimentally that the proposed local causal discovery algorithm can obtain the comparable identification accuracy as global methods but significantly improve their efficiency, often by more than one order of magnitude.

Review:
The goal of the paper is to identify direct causes and effects of a given variable (target variable). The main contribution stands in that the authors achieve their goal without the need of first discovering the whole causal graph before restricting attention to the neighborhood of the target variable. Instead, they directly focus on discovering the local causal structure.Existing algorithms can discover the Markov blanket (MB) of a target variable and a subset of it that consists of the set of parents and children (PC) of the target variable. The goal of this paper is to identify which of the nodes in PC are parents and which children of the target.Significance & Originality:I consider the contribution of the paper significant. It improves on efficiency and scalability compared to previous methods which need to perform the intermediate step of global causal discovery to achieve the same goal.Clarity: I think that lack of clarity and flow in several parts is a drawback of the paper. I found some descriptions confusing. In general, I would suggest more explicit explanations, motivating examples and high level explanations before going into the technical parts.Specifically:- Last paragraph of Introduction: the authors refer to Local Causal Discovery. It took me some time to realize that they refer to existing work and not to theirs, since this term coincides with the title of the paper. I would suggest changing the title to something more specific like "local causal discovery of direct causes and effects". Moreover, I find the name of the proposed method "Causal Markov Blanket" also too general and maybe misleading. The authors could probably consider a common name for both title and method involving "direct causes and effects".- Section 3: Some high level explanations are necessary before going into the technical details. The authors could provide a short high level summary of all steps of the proposed method in the beginning of section 3.2.- I could be missing something in Algorithm 2: as far as I understand, ID_T should contain the causal identities of *just* the PC set of T. But in step 1 it is mentioned "..the causal identities of *all* nodes.." and in Algorithm 2 the size of ID_T is |V| where V is the entire variable space and no just the PC.- The output of Algorithm 2 is the ID_T. How is this converted to a CPDAG? For id_T 1 and 2 it is clear. For id_T =3 do you draw an indirect edge? Providing some visual examples of the output CPDAG of the Algorithm would be helpful.- Elaborating more on why failing to meet Lemma 3 leads to Markov equivalent structures, could be useful.- The authors could consider improving the flow in page 3.- Some parts are not very specific/explicit: e.g.: * Sec. 4, first par.: "causal identities for a target node": isn't it "causal identities of nodes in the target's PC set"? * I understand what is a CPDAG but it would be helpful to define what it is meant by the "CPDAG of a target variable". Is it a subset of the original CPDAG containing T and the parents and children of it? *In the proof of Theorem 3: "CMB will identify up to a graph's CPDAG": is this again the subset? * Footnote 3 is not clear * Sec. 3.1: what does it mean "some V-structure children and spouses" ? * Sec 3.1: "PC set of a MB" : isn't it "PC set of a target's MB"? * The terms "local causal discovery of the target" and "local causal nodes of the target" could be rephrasedQuality:I have not checked all the technical details but the paper seems to have a well-supported theoretical analysis followed by experimental results. The results show significant improvements in efficiency compared to global methods.   -Typos: * There are several typos in the references section. * Introduction: in term -> in terms *Sec. 3.1: "... no selection bias, every.." -> "...no selection bias, that every..." * Experiments: "along its standard deviation" -> "along with its...", "As shown in in Table"-> remove one "in"