منیره نوائی لواسانی

Bayesian networks are a powerful tool to model static and dynamic systems and are applied in various fields such as: diagnosis, decision making, classification. A Bayesian network is a probabilistic graphical model which demonstrates the causal relationship between variables. It consists of a directed acyclic graph and a set of conditional probabilities. Two important factors when modeling a dataset using a Bayesian network are structure learning and parameter learning. Structure learning is to find a structure which fits the data properly and can be learned by techniques such as constraint-based, score-based and hybrid. Parameter learning is to find the elements of conditional probability table for categorical variables and to calculate regression coefficients for continuous variables. In fact, the purpose of parameter learning is to estimate the probability of each node given its parents. Learning a Bayesian network is possible if the dataset is complete. However, if there are missing values in a dataset, the problem is not easy to solve. One method to handle missing data is deletion. Due to losing information and biasness, this method is not efficient. Imputation is another technique which can have more accurate results in comparision with deletion. Structural expectation maximization is one of the powerful methods to learn a Bayesian network in presence of missing data. This algorithm is an advanced statistical learning technique designed for modeling in presence of incomplete, missing or hidden data. Unlike EM algorithm, which focuses solely on optimizing model parameters within a fixed structure, SEM allows for the simultaneous learning of both the structure and parameters of probabilistic models. This makes SEM particularely effective for learning probabilistic graphical models, such as Bayesian networks, when the model structure is unknown. In each iteration of SEM algorithm, the E-step estimates the expected sufficient statistics of the complete data given the observed data and the current model structure. In the M-step, the algorithm first updates the model structure and then re-estimstes the model parameters to maximize the expected complete-data log-likelihood. This iterative process continues untill convergence. SEM has wide applications in fields such as datamining, machine learning, bioinformatics and artificial intelligence. It is especially useful in scenarios where data is partially observed, the underlying system is complx or the model search space is large. By offering a principled approach to jointly learning structure and parameters, SEM provides a powerful framework for statistical modeling under uncertainty