Graphical models are a powerful tool for reasoning under uncertainty. They are used to represent and reason about probability distributions over a set of random variables. A Bayesian network is a graphical model that encodes the probability of a set of random variables. It consists of a directed acyclic graph (DAG) with nodes representing random variables and arrows representing statistical relationships between the variables. Bayesian networks can be used to generate predictions from data, infer the probabilistic relationships between variables, and learn the structure and conditional probability tables (CPTs) from data. Naive Bayes is a classification algorithm based on Bayesian networks. It assumes that the features of a given data point are conditionally independent of each other, given the class label. This simplifies the model and makes it easier to learn from data. However, if there are dependencies between features, the accuracy of naive Bayes can be improved by taking these into account. This lab will explore graphical models, Bayesian networks, and naive Bayes classification. It will learn the structure and CPTs from data, understand the graphical models for inference under uncertainty, and build Bayesian networks in R. The results of this project can be used to improve the accuracy of naive Bayes classification when there are dependencies between features.
- understand the graphical models for inference under uncertainty
- build Bayesian Network in R
- Learn the structure and CPTs from Data
- naive Bayes classification with dependency between features
Graphical models have become an increasingly popular tool for dealing with uncertainty in various fields. These models are particularly useful when dealing with complex systems where the relationships between variables are not well understood or when the relationships are uncertain. Among the graphical models, Bayesian networks are particularly powerful and widely used. A Bayesian network is a graphical model that encodes the probability of a set of random variables. The model consists of a directed acyclic graph (DAG), where each node represents a random variable, and arrows represent the statistical relationships between variables. Bayesian networks can be used to generate predictions from data, infer the probabilistic relationships between variables, and learn the structure and conditional probability tables (CPTs) from data. One of the most popular applications of Bayesian networks is in classification tasks, where the goal is to assign a given data point to a pre-defined class. Naive Bayes is a classification algorithm based on Bayesian networks that assumes conditional independence between the features of a given data point, given the class label. While this simplifies the model and makes it easier to learn from data, it can limit its accuracy when dependencies between features exist. This lab explores the concepts of graphical models, Bayesian networks, and naive Bayes classification. It will cover the process of learning the structure and CPTs from data, as well as understanding the graphical models for inference under uncertainty. We will also learn how to build Bayesian networks in R and use them for classification tasks.
A Bayesian network is built to learn the dependencies between courses using the Hill-Climbing algorithm and K2 score metric. The Conditional Probability Tables (CPTs) for each course node are learned using the Bayesian network and the available data. In conclusion, by building a Bayesian network and analyzing the CPTs, we can learn the dependencies between courses and understand how grades in one course affect the grades in other courses. This information can be used to design better educational policies and programs to improve students’ academic performance.