A directed acyclic graph where the nodes represent random variables.
Not to be confused with Bayesian neural networks.
The chain rule for Bayesian networks¶
The joint distribution for all the variables in a network is equal to the product of the distributions for all the individual variables, conditional on their parents.
where denotes the parents of the node in the graph.
Restricted Boltzmann Machines (RBMs)¶
Trained with contrastive divergence.
Deep Belief Networks (DBNs)¶
Deep Belief Machines (DBMs)¶
A subset of a graph where the nodes are fully-connected, ie each node has an edge with every other node in the set.
Conditional Random Field (CRF)¶
Discriminative model that can be seen as a generalization of logistic regression.
Linear Chain CRFs¶
A simple sequential CRF.
A simple state transition model where the next state depends only on the current state. At any given time, if the current state is node i, there is a probability of transitioning to node j, where is the transition matrix.
A process is said to have the Markov property if the next state depends only on the current state, not any of the previous ones.
Markov Random Field (MRF)¶
A type of undirected graphical model which defines the joint probability distribution over a set of variables. Each variable is represented by one node in the graph.
One use for an MRF could be to model the distribution over the pixel values for a set of images. In order to keep the model tractable edges are only drawn between neighbouring pixels.
Naive Bayes Model¶
A simple classifier that models all of the features as independent, given the label.