Probabilistic modelling lies at the heart of machine learning.

The chain structure is also convenient to handle streaming data as we will explain later. We first give a brief introduction to the EP and CEP framework. Step 2. We construct a tilted distribution to combine the true likelihood, Step 3. We project the tilted distribution back to the exponential family, q KL( null p nullq) where q belongs to the exponential family. Step 4. We update the approximation term by's in parallel, and uses damping to avoid divergence. The above computation are very conveniently to implement.

In fact, in a particular limit, the optimal path is arithmetic.

's weights define an exponential family.

However, in many scenarios, nodes also have attributes that are correlated with the clustering structure. Thus, network information (edges) and node information (attributes) can be jointly leveraged to design high-performance clustering algorithms. Under a general model for the network and node attributes, this work establishes an information-theoretic criterion for the exact recovery of community labels and characterizes a phase transition determined by the Chernoff-Hellinger divergence of the model.