Bayes network is a type of probabilistic graphical model that can be used to build models to address business problems. Applications of this are quite wide. For example, it can be used in anomaly detection, predictive modeling, diagnostics, automated insights, and many other applications.

It is totally understandable that a few words used here would have been alien to you till now. For example, what do we mean by graphical here?

A graph forms out of a set of nodes and edges. Nodes are represented by N={N1,N2…..Nn}, where independent variables are sitting at every node. Edges are the connectors between nodes. Edges can be denoted by E={E1, E2…..En} and can be of two types:

• Directed, represented by 
• Undirected, represented by:

With the help of nodes and edges, a relationship between the variables is exhibited. It can be a conditional independence relationship or a conditional dependence relationship. BN is one a techniques that can introduce causality amongst variables. Although causality is not an essential part of it, having this (causality) in the network can make the structure quite compact.

Let's see it through an example. There are a number of variables, such as waking up late, an accident on the highway, a rainy day, a traffic jam, they will be late for work, and being late for a meeting. If an individual has got up late, it means being late for work. An accident on the highway can cause a traffic jam and, in turn, this will result in being late for work. On a rainy day, the roads can be more prone to accidents and, also, there can be slow-moving traffic that will cause a traffic jam and, in turn, this will result in being late for work. The following diagram explains the example:

This kind of network is called a directed acyclic graph. Acyclic means that there is no cycle in the network. We are talking about a relationship between variables here. For example, waking up late and being late for a meeting are typically not independent. But they are conditionally independent, given being late for work.

Also, it might seem that waking up late has no connection and relationship with an accident on the highway. That is, they may appear to be independent of each other. However, if you know the value of being late for work, then these two can be called conditionally independent.

So, BN allows conditional independence between nodes. At the same time, it is an efficient representation of joint probability distribution, which is enabled by a chain rule.

Let's say that X represents n independent variables or nodes. Arcs or a directed arrow represents the probabilistic dependence or independence amongst variables. An absence of an arc would mean probabilistic independence. The network is a directed acyclic graph wherein the local probability distribution is kept at each node, which is also called the conditional probability table (CPT).

If we talk about the previous network, then we need the probability distribution required to address the whole network. For the purpose of simplicity, we will keep all the nodes as Boolean.