For each sentence, this assigns probability to the join of a word at some position in a sentence and the dependency type label that connects the word token to the argument token in the dependency parse tree with the trigger types and argument types of the two tokens. Here, triggerType denotes the prediction from a pre-trained support vector machine for triggering some information extracted from the text. This way, high-dimensional, sophisticated features become available to the relational probabilistic model. Moreover, as with Google’s Knowledge Vault [Dong et al., 2014], the parameters of the relational probabilistic model or even (parts) of its structure can be learned from data.

      Example 1.4 Language modeling The aim of language modeling is to estimate a distribution over words that best represents the text of a corpus. This is central to speech recognition, machine translation, and text generation, among others, and the parameters of language models are commonly used as features or as initialization for other natural language processing approaches. Examples include the word distributions learned by probabilistic topic models, or the word embeddings learned through neural language models. In practice, however, the size of the vocabulary traditionally limited the distributions applicable for this task: specifically, one has to either resort to local optimization methods, such as those used in neural language models, or work with heavily constrained distributions. Jernite et al. [2015] overcame these limitations. They model the entire corpus as an undirected graphical model, whose structure is illustrated in Fig. 1.5. Because of parameter sharing in the model, each of the random variables is indistinguishable and by exploiting this symmetry, Jernite et al. derived an efficient approximation of the partition function using lifted variational inference with complexity independent of the length of the corpus.

      Figure 1.5: Instance of the cyclic language model [Jernite et al., 2015] with added start and end < S > tokens based on two sentences. Each word of a sentence is a random variable and probabilistically depends on the words being at most two steps away. The model exhibits symmetries that are exploitable during parameter estimation using lifted probabilistic inference.

      Figure 1.6: A Blocks World planning problem and a plan to solve the goal to have c clear.

      Example 1.5 Planning under uncertainty The Blocks World, see Fig. 1.6, consists of a number of blocks stacked into towers on a table large enough to hold them all. The positioning of the towers on the table is irrelevant. The planning problem is to turn an initial state of the blocks into a goal state, by moving one block at a time from the top of a tower onto another tower or to the table. However, the effects of moving a block may not be perfectly predictable. For example, the gripper of a robot may be slippery so moving a block may not succeed. This uncertainty compounds the already complex problem of planning a course of action to achieve the goal.

      The classical representation and algorithms for planing under uncertainty require the enumeration of the state space. Thus, although arguably a simple planning problem, we get already a rather large representation. For instance, if there are just 10 blocks, there are more than 50 million states. More importantly, we lose the structure implicit in the problem description. Decision-theoretic planning [Boutilier et al., 1999] generalized state-based planning under uncertainty to include features. But features are not enough to exploit all of the structure of the world. Each Blocks World planning instance is composed of these same basic individuals relations, but the instances differ in the arrangements of the blocks. We would like the agent to make use of this structure in terms of computing plans that apply across multiple scenarios. This can be achieved using relational models. For instance, the following parameterized plan, which says that we do nothing if block c is clear. If c is not clear than we move a clear block B that is above c to the floor, achieves the goal to have the block c clear