FunChisq

Statistical hypothesis testing methods for inferring model-free functional dependency using asymptotic chi-squared or exact distributions. Functional test statistics are asymmetric and functionally optimal, unique from other related statistics. Tests in this package reveal evidence for causality based on the causality-by- functionality principle. They include asymptotic functional chi-squared tests (Zhang & Song 2013) , an adapted functional chi-squared test (Kumar & Song 2022) doi:10.1093/bioinformatics/btac206, and an exact functional test (Zhong & Song 2019) doi:10.1109/TCBB.2018.2809743 (Nguyen et al. 2020) doi:10.24963/ijcai.2020/372. The normalized functional chi-squared test was used by Best Performer 'NMSUSongLab' in HPN-DREAM (DREAM8) Breast Cancer Network Inference Challenges (Hill et al. 2016) doi:10.1038/nmeth.3773. A function index (Zhong & Song 2019) doi:10.1186/s12920-019-0565-9 (Kumar et al. 2018) doi:10.1109/BIBM.2018.8621502 derived from the functional test statistic offers a new effect size measure for the strength of functional dependency, a better alternative to conditional entropy in many aspects. For continuous data, these tests offer an advantage over regression analysis when a parametric functional form cannot be assumed; for categorical data, they provide a novel means to assess directional dependency not possible with symmetrical Pearson's chi-squared or Fisher's exact tests.