Markov Networks

Markov Networks, also known as Markov Random Fields, are probabilistic graphical models used to represent complex joint probability distributions over a set of random variables. They are defined by an undirected graph where each node represents a random variable and each edge represents a conditional dependence between the connected variables. Markov Networks are used in various applications such as image segmentation, natural language processing, and gene expression analysis. They are particularly useful in situations where the relationships between variables are complex and cannot be easily represented by a directed graph. In Markov Networks, the probability distribution is factorized into a product of potential functions, which are non-negative functions defined over subsets of the variables. The joint probability distribution is proportional to the product of these potential functions. The goal of inference in Markov Networks is to compute the marginal probabilities of the variables given evidence or to find the most probable configuration of the variables given the evidence.
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