MLN 讨论 —— inference

We consider two types of inference:

• finding the most likely state of the world consistent with some evidence
• computing arbitrary conditional probabilities.

We then discuss two approaches to making inference more tractable on large , relational problems:

• lazy inference , in which only the groundings that deviate from a "default" value need to be instantiated;
• lifted inference , in which we group indistinguishable atoms together and treat them as a single unit during inference;

3.1 inference the most probable explanation

A basic inference task is finding the most probable state of the world y given some evidence x, where x is a set of literals;

For Markov logic , this is formally defined as follows:  $$ \begin{align} arg \; \max_y P(y|x) & = arg \; \max_y \frac{1}{Z_x} exp \left( \sum_i w_in_i(x, \; y) \right) \tag \\  & = arg \; \max_y \sum_i w_in_i(x, \; y) \tag{3.1} \end{align}  $$