mathematics

Statistical relational learning

Statistical relational learning is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Statistical relational learning rather than just read about it. In short: Statistical relational learning (SRL) is a subdiscipline of artificial intelligence and machine learning that is concerned with domain models that exhibit both uncertainty (which can be dealt with using statistical methods) and complex, relational structure. Typically, the knowledge representation formalisms developed in SRL use (a subset of) first-order logic to describe relational properties of a domain in a gener…

Key takeaways

Statistical relational learning belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Statistical relational learning to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Statistical relational learning from memory before moving on to harder problems.

Reference excerpt

Statistical relational learning (SRL) is a subdiscipline of artificial intelligence and machine learning that is concerned with domain models that exhibit both uncertainty (which can be dealt with using statistical methods) and complex, relational structure. Typically, the knowledge representation formalisms developed in SRL use (a subset of) first-order logic to describe relational properties of a domain in a general manner (universal quantification) and draw upon probabilistic graphical models (such as Bayesian networks or Markov networks) to model the uncertainty; some also build upon the methods of inductive logic programming. Significant contributions to the field have been made since the late 1990s. As is evident from the characterization above, the field is not strictly limited to learning aspects; it is equally concerned with reasoning (specifically probabilistic inference) and knowledge representation. Therefore, alternative terms that reflect the main foci of the field include statistical relational learning and reasoning (emphasizing the importance of reasoning) and first-order probabilistic languages (emphasizing the key properties of the languages with which models are represented). Another term that is sometimes used in the literature is relational machine learning (RML).

Canonical tasks A number of canonical tasks are associated with statistical relational learning, the most common ones being.

collective classification, i.e. the (simultaneous) prediction of the class of several objects given objects' attributes and their relations link prediction, i.e. predicting whether or not two or more objects are related link-based clustering, i.e. the grouping of similar objects, where similarity is determined according to the links of an object, and the related task of collaborative filtering, i.e. the filtering for information that is relevant to an entity (where a piece of information is considered relevant to an entity if it is known to be relevant to a similar entity) social network modelling object identification/entity resolution/record linkage, i.e. the identification of equivalent entries in two or more separate databases/datasets

Representation formalisms

One of the fundamental design goals of the representation formalisms developed in SRL is to abstract away from concrete entities and to represent instead general principles that are intended to be universally applicable. Since there are countless ways in which such principles can be represented, many representation formalisms have been proposed in recent years. In the following, some of the more common ones are listed in alphabetical order:

Bayesian logic program BLOG model Markov logic networks Multi-entity Bayesian network Probabilistic logic programs Probabilistic relational model – a Probabilistic Relational Model (PRM) is the counterpart of a Bayesian network in statistical relational learning. Probabilistic soft logic Recursive random field Relational Bayesian network Relational dependency network Relational Markov network Relational Kalman filtering

See also Association rule learning Formal concept analysis Fuzzy logic Grammar induction Knowledge graph embedding

Resources Brian Milch, and Stuart J. Russell: First-Order Probabilistic Languages: Into the Unknown, Inductive Logic Programming, volume 4455 of Lecture Notes in Computer Science, page 10–24. Springer, 2006 Rodrigo de Salvo Braz, Eyal Amir, and Dan Roth: A Survey of First-Order Probabilistic Models, Innovations in Bayesian Networks, volume 156 of Studies in Computational Intelligence, Springer, 2008 Hassan Khosravi and Bahareh Bina: A Survey on Statistical Relational Learning, Advances in Artificial Intelligence, Lecture Notes in Computer Science, Volume 6085/2010, 256–268, Springer, 2010 Ryan A. Rossi, Luke K. McDowell, David W. Aha, and Jennifer Neville: Transforming Graph Data for Statistical Relational Learning, Journal of Artificial Intelligence Research (JAIR), Volume 45, page 363-441, 2012 Luc De Raedt, Kristian Kersting, Sriraam Natarajan and David Poole, "Statistical Relational Artificial Intelligence: Logic, Probability, and Computation", Synthesis Lectures on Artificial Intelligence and Machine Learning" March 2016 ISBN 9781627058414.

References

Worked examples

Example 1 — a first encounter with Statistical relational learning

Start with the simplest possible case. Write down what Statistical relational learning claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Statistical relational learning before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Statistical relational learning ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Statistical relational learning

In research: Statistical relational learning appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Statistical relational learning in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Statistical relational learning is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computational statistics, Machine learning, so understanding it makes those chapters shorter.
In everyday life: Look for Statistical relational learning outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Statistical relational learning in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Statistical relational learning means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Statistical relational learning out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Statistical relational learning in simple terms?

Why does Statistical relational learning matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Statistical relational learning?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Statistical relational learning.