Comprehensive review of Bayesian network applications in gastrointestinal cancers

Table 1 Six Bayesian network parameter learning algorithms

Algorithms	For incomplete datasets	Basic principle	Advantages & disadvantages	Ref.
Maximum likelihood estimate	No	Estimates parameters by maximizing the likelihood function based on observed data	Fast convergence; no prior knowledge used, leading to slow convergence	[18]
Bayesian method	No	Uses a prior distribution (often Dirichlet) and updates it with observed data to obtain a posterior distribution	Incorporates prior knowledge; computationally intensive	[19]
Expectation-maximization	Yes	Estimates parameters by iteratively applying expectation (E) and maximization (M) steps to handle missing data	Effective with missing data; can converge to local optima	[20]
Robust bayesian estimate	Yes	Estimates parameters using probability intervals to represent the ranges of conditional probabilities without assumptions	Does not require assumptions about missing data; interval width indicates reliability of estimation	[12]
Monte-Carlo method	Yes	Uses random sampling (e.g., Gibbs sampling) to estimate the expectation of the joint probability distribution	Flexible and can handle complex models; computationally expensive and convergence can be slow	[21]