Statistical Relational Learning

Abstract

Relational learning refers to learning from data that have a complex structure. This structure may be either internal (a data instance may itself have a complex structure) or external (relationships between this instance and other data elements). Statistical relational learning refers to the use of statistical learning methods in a relational learning context, and the challenges involved in that. In this chapter we give an overview of statistical relational learning. We start with some motivating problems, and continue with a general description of the task of (statistical) relational learning and some of its more concrete forms (learning from graphs, learning from logical interpretations, learning from relational databases). Next, we discuss a number of approaches to relational learning, starting with symbolic (non-probabilistic) approaches, and moving on to numerical and probabilistic methods. Methods discussed include inductive logic programming, relational neural networks, and probabilistic logical or relational models. If relationships are present among examples, then the examples may not be independent and identically distributed (i.i.d.). Many learning algorithm assume they are, and when this assumption is violated, this can be detrimental to learning performance, as Jensen and Neville [31] show. On the other hand, knowledge about the relationships among examples can be beneficially exploited by the learning algorithm. Collective classification techniques [32], for example, take the class labels of related examples into account when classifying a new instance, which can lead to better predictive results.Thus, to an attribute-value learner, relations between instances may hamper accurate learning, but to a relational learner, this relations are a source of information that can be put to good use.Learning from examples with a complex internal structure In this setting, each example may have a complex internal structure, but no relationships exist that relate different examples to one another. Learning algorithms typically use individual-centered representations in this setting, such as logical interpretations [9] or strongly typed terms [42], which store all the data available about a given instance. Special cases of this setting include applications where the examples can be represented as graphs, trees, or sequences.Example 3. Consider a database of candidate chemical compounds to be used in drugs. The molecular structure of each compound can be represented as a graph where the vertices are atoms and the edges are bonds. Each atom is labeled with its element type and the bonds can be single, double, triple, or aromatic bonds. Compounds are classified as active or inactive with regard to a given disease and the goal is to build models that are able to distinguish active from inactive compounds based on their molecular structure. Such models can, for instance, be used to gain insight in the common substructures, such as binding sites, that determine a compound's activity.

Learning, Probability and Logic: Toward a Unified Approach for Content-Based Music Information Retrieval

“…StarAI approaches have been successfully applied to a multitude of problems in various structured, uncertain domains. We refer the reader to Getoor and Taskar (2007), Raedt and Kersting (2008), Domingos and Lowd (2009), Blockeel (2013), Kimmig et al (2015), De Raedt et al (2016), and Besold and Lamb (2017) for surveys of StarAI.…”

Probabilistic Event Calculus for Event Recognition

“…This situation causes the standard gradient descent methods to converge very slowly, since there is no single appropriate learning rate for all soft-constrained clauses. An alternative approach to CLL function optimisation is max-margin training, which is better suited to problems where the goal is to maximise the classification accuracy [Huynh and Mooney 2009;2011]. Instead of optimising the CLL function, max-margin training aims to maximise the ratio between the probability of the correct truth assignment of CEs to hold and the closest competing incorrect truth assignment.…”

“…Beyond the advantages stemming from the fact that it is a logic-based formalism with clear semantics, one of the most interesting properties of the Event Calculus is that it handles the persistence of CEs with domain-independent axioms. On the other hand, MLNs are a generic statistical relational framework that combines the expressivity of firstorder logic with the formal probabilistic properties of undirected graphical modelssee de Salvo Braz et al [2008], Raedt and Kersting [2010] and Blockeel [2011] for surveys on logic-based relational probabilistic models. By combining the Event Calculus with MLNs, we present a principled and powerful probabilistic logic-based method for event recognition.…”

Parameter estimation from aggregate observations: a Wasserstein distance-based sequential Monte Carlo sampler

“…This discrepancy more reasonably characterizes the differences between these distributions and addresses the aforementioned issue with the TV distance. WD has been widely used in many applications in statistics and machine learning, such as [ 17 , 18 ], as it has many desired properties. Additionally, it has been shown to be effective in mitigating information loss caused by the utilization of summary statistics in basic ABC techniques [ 19 ].…”