Demo 1D

Here we introduce the application of the DGM library to some well-known probabilistic models. Particaulary, we show how to compose graphical models with the help of DirectGraphicalModels::CGraphPairwise class. We fill the model by hand with potentials and study inferece and decoding processes on them. First we demonstrate brute-force algorithms for exact decoding and inference on a small graph, and consider a possible use of marginal probabilities calculated by inference algorithm for approximate decoding. Next we show message-passing algorithms for approximate inference, and consider the difference between sum-product and max-sum approaches. Finally, we consider sum-product message-passing algorithms, which provide an efficient framework for exact inference in chain- and tree-structuresd graphs.

• Exact : An introduction to graphical models and the tasks of decoding and inference on a small graphical model where we can do everything by hand.
• Chain : An introduction to Markov independence properties on an example of a chain-structured graphical model, and to efficient dynamic programming algorithms for inference.
• Tree : This demo shows how to construct a tree-structured graphical model, for which also an exact message-passing inference algorithm exists.