Bayesian network is widely used to build causal relationships among its nodes. Each node of the networks has an arc to another representing a causal relationship with uncertainty and can be measured with a probabilistic value. In order to identify the causal relationships between genes that cause certain disease, it is helpful to infer Bayesian networks by using obtained gene data. In most cases, manipulations of genes are required to gain promising causal relationships. Complete manipulation, however, is hard to be done in real world because of the matter of cost, time, and space. Instead of doing the experiments to manipulate genes, promising causal relationships among genes can be discovered with only observed data by adding some latent variables in corresponding Bayesian network. Bayesian network has been applied to discover the one-way causal relationship of each pair of its node, not feedback relationship which can take place in real world.

• Bayesian Network is used to discover the probablistic values of an unobserved node via observed nodes that are connected to it.
• When some nodes are manipulated, we can assign a probability value of 1 to these nodes.
• Also, Bayesian network can be classfied into 6 categories of models with observational nodes and latent variables.
• To determine which model is more likely to occur, it is strongly recommended to manipulate one of the nodes consisting a certain model.
• When we measure the probability of each model, we have used ILVS (Implicit Latent Variable Scoring) scoring method.
• In this project, I added two new models that give a feedback relationship between nodes
• My main role was to implement new alogirhtm that scores these newly added models in C++ with UNIX machine.

• I have extended ILVS methods to examine feedback relationships and named it as ILVSf.
• I also implemented ILVSf (Implicit Latent Variable Scoring for Feedback relationships) based on the equation that produces probabilty of a node given its parents
• In the result, E7 and E8 did not clearly show the best promising feedback relationships.
• This is because feedback relationships seems to appear that there is no relationship when two nodes cause each other over time (Data sets are obtained at different time).
• In conclusion, if ILVSf method times, it will allow us to detect promising trends
• For example, if node X causes Y at certain moment and Y causes X after certain time, we can say that there is a feedback relationship.
• So, modeling time in ILVSf will be the future work of this project.