Statistical hypothesis testing methods for
model-free functional dependency using asymptotic
chi-square or exact distributions. Functional
chi-squares 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-square tests, an exact functional
test, a comparative functional chi-square test, and also a
comparative chi-square test. The normalized non-constant
functional chi-square test was used by Best Performer
NMSUSongLab in HPN-DREAM (DREAM8) Breast Cancer Network
Inference Challenges. A function index derived from the
functional chi-square offers a new effect size measure for
the strength of function 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-square or Fisher's exact tests.

Model-Free Functional Chi-Squared and Exact Tests
c(person("Yang", "Zhang", role = "aut"),
person("Hua", "Zhong", role = "aut",
comment = c(ORCID = "0000-0003-1962-2603")),
person("Hien", "Nguyen", role = "aut"),
person("Ruby", "Sharma", role = "aut"),
person("Sajal", "Kumar", role = "aut"),
person("Joe", "Song", role = c("aut", "cre"),
email = "joemsong@cs.nmsu.edu",
comment = c(ORCID = "0000-0002-6883-6547")))
Yang Zhang [aut],
Hua Zhong [aut] (<https://orcid.org/0000-0003-1962-2603>),
Hien Nguyen [aut],
Ruby Sharma [aut],
Sajal Kumar [aut],
Joe Song [aut, cre] (<https://orcid.org/0000-0002-6883-6547>)
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) <arXiv:1311.2707> and an exact
functional test ('Zhong & Song' 2019)
<doi:10.1109/TCBB.2018.2809743>. 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' in press) ('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.