Explain like I am a high school student: "Causal Discovery
Causal discovery can be defined as the search for the structure of causal relationships, by analyzing the statistical properties of observational evidence (Reference Spirtes, Glymour and ScheinesSpirtes et al. 2001). While observational evidence almost never suffices to fully characterize a causal graph, it often contains information helpful in reducing the number of possible structures of interdependence among variables. At the very least, the extra-statistical information assumed by the causal graph should be compatible with the observations. Over the past three decades, statisticians have developed numerous computational methods and algorithms for the discovery of causal relations, represented as directed acyclic graphs (see Reference Glymour, Zhang and SpirtesGlymour et al. 2019). These methods can be divided into the following classes: (a) constraint-based algorithms; (b) score-based algorithms; and (c) functional causal models (FCMs).

Constraint-based methods exploit conditional independence relationships in the data to recover the underlying causal structure. Two of the most widely used methods are the PC algorithm (named after its authors, Peter Spirtes and Clark Glymour), and the fast causal inference (FCI) algorithm (Reference Spirtes, Glymour and ScheinesSpirtes et al. 2000). The PC algorithm assumes that there are no latent (unobservable) confounders, and under this assumption the discovered causal information is asymptotically correct. The FCI algorithm gives asymptotically correct results even in the presence of latent confounders.

Score-based methods can be used in the absence of latent confounders. These algorithms attempt to find the causal structure by optimizing a defined score function. An example of a score-based method is the greedy equivalence search (GES) algorithm. This heuristic algorithm searches over the space of Markov equivalence classes, that is, the set of causal structures satisfying the same conditional independences, evaluating the fitness of each structure based on a score calculated from the data (Reference ChickeringChickering 2003). The GES algorithm is known to be consistent under certain assumptions, which means that as the sample size increases, the algorithm will converge to the true causal structure with probability approaching 1. However, this does not necessarily mean that the algorithm will converge to the true causal structure in finite time or with a reasonable sample size. GES is also known to be sensitive to the initial ordering of variables.

FCMs distinguish between different directed-acyclic graphs in the same equivalence class. This comes at the cost of making additional assumptions on the data distribution than conditional independence relations. A FCM models the effect variable  Y
  as  Y=f(X,ε)
  , where  f
  is a function of the direct causes  X
  and  ε
  is noise that is independent of  X
  . Subject to the aforementioned assumptions, the causal direction between  X
  and  Y
  is identifiable, because the independence condition between  ε
  and  X
  holds only for the true causal direction (Reference Shimizu, Hoyer, Hyvärinen and KerminenShimizu et al. 2006; Reference Hoyer, Janzing, Mooji, Peters and SchölkopfHoyer et al. 2009; and Reference Zhang and HyvärinenZhang and Hyvaerinen 2009).

Causal graphs can also be derived from nonnumerical data. For example, Reference Laudy, Denev and GinsbergLaudy et al. (2022) apply natural language processing techniques to news articles in which different authors express views of the form  X→Y
  . By aggregating those views, these researchers derive directed acyclic graphs that represent collective, forward-looking, point-in-time views of causal mechanisms.

Machine learning is a powerful tool for causal discovery. Various methods allow researchers to identify the important variables associated in a phenomenon, with minimal model specification assumptions. In doing so, these methods decouple the variable search from the specification search, in contrast with traditional statistical methods. Examples include mean-decrease accuracy, local surrogate models, and Shapley values (Reference López de PradoLópez de Prado 2020, pp. 3–4, Reference López de PradoLópez de Prado 2022a). Once the variables relevant to a phenomenon have been isolated, researchers can apply causal discovery methods to propose a causal structure (identify the links between variables, and the direction of the causal arrows)."