A Bayesian network, Bayes network, belief network or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG).
Bayesian Network is Probabilistic Graphical Model that represents a set of random variables and their conditional probabilities dependencies via an Directed Acyclic Graphs (DAG) whose nodes are the random variables: they may be observable quantities, latent variables, unknown parameters or hypotheses and are represented by a Conditional Probability Table (CPT). Edges represent the conditional dependencies, where nodes which are not connected represent variables which are conditionally independent of each other. Each node is associated with a probability function that takes as input a particular set of values for the node's parent variables and gives the probability of the variable represented by the node. For example, if the parents are m boolean variables then the probability function could be represented by a table of 2m entries, one entry for each of the 2m possible combinations of its parents being true or false.
Bayesian Networks can be defined by an expert in cases where there is prior information, or be learned from training data. There are two learning phase: the structure learning and the parameters learning. In the structure learning the algorithms try to find the best DAG that describes the data, and in the parameters learning which ensure fitting CPTs to the data and the chosen structure.
Bayesian Networks can be used in a variety of applications, for example it could be used to represent the probabilistic relationships between diseases and symptoms. Given the symptoms, the network can be used to compute the probabilities of the presence of various diseases. Another common application of this model is to represent Gene Regulatory Networks (GRNs), where each node is a gene and the edges represents the probability of each gene regulating other.
