This paper concerns, more specifically, the inconsistency of separating sets used to remove dispensable edges, iteratively, based on conditional independence tests.

The proof follows from Lemma 1. Lemma 2. Let G be a PAGn-representing a causal DAGD. We refer to the proof for the anytime FCI algorithm (Spirtes, 2001). Let the true underlying DAG beD(O,L,S), and G be the graph returned after an ICD iteration. The first ICD iterationr = 0 is trivial, where every pair of nodes is tested for marginalindependence (ICDisinitialized withacomplete graph). Let A B|[Z] S in D, such that|Z| = 1 (a single-node set).

Understanding the underlying mechanisms is crucial for tasks such asexplaining aphenomenon, predicting, anddecision making. Pearl(2009) providedamachinery for automating the process of answering interventional and (retrospective) counterfactual queries even when only observed data is available, and determining if a query cannot be answered given the available data type (identifiability). This requires knowledge about the true underlying causal structure; however,inmanyreal-world situations, thisstructure isunknown.

This paper concerns, more specifically, the inconsistency of separating sets used to remove dispensable edges, iteratively, based on conditional independence tests.

This paper describes the development of a counterfactual Root Cause Analysis diagnosis approach for an industrial multivariate time series environment. It drives the attention toward the Point of Incipient Failure, which is the moment in time when the anomalous behavior is first observed, and where the root cause is assumed to be found before the issue propagates. The paper presents the elementary but essential concepts of the solution and illustrates them experimentally on a simulated setting. Finally, it discusses avenues of improvement for the maturity of the causal technology to meet the robustness challenges of increasingly complex environments in the industry.

We present a sound and complete algorithm, called iterative causal discovery (ICD), for recovering causal graphs in the presence of latent confounders and selection bias. ICD relies on the causal Markov and faithfulness assumptions and recovers the equivalence class of the underlying causal graph. It starts with a complete graph, and consists of a single iterative stage that gradually refines this graph by identifying conditional independence (CI) between connected nodes. Independence and causal relations entailed after any iteration are correct, rendering ICD anytime. Essentially, we tie the size of the CI conditioning set to its distance on the graph from the tested nodes, and increase this value in the successive iteration. Thus, each iteration refines a graph that was recovered by previous iterations having smaller conditioning sets -- a higher statistical power -- which contributes to stability. We demonstrate empirically that ICD requires significantly fewer CI tests and learns more accurate causal graphs compared to FCI, FCI+, and RFCI algorithms.