Supervisor: Matthias Troffaes
Research area: machine learning, probability

Description

Classification is one of the most universal decision problems around us, and living creatures are remarkably good at performing this task. Some fish perform spatial pattern recognition and abstraction by exclusive use of active electrolocation. Humans classify characters, words, and the meanings they have in a particular context. With the advent of technology, many classifying tasks have been successfully delegated to machines. For instance, when we open our inboxes, email clients classify potential spam with remarkable accuracy.

Crucial to classification is learning. However, during the initial learning phase, traditional machine algorithms, such as the naive Bayes classifier, typically misclassify as they always need to produce a single classification outcome, whereas humans can simply produce a set of options to convey their lack of information, without discriminating further between the elements of that set. The subject of credal classification is exactly to model classification under circumstances where not much information is present, by allowing the classifier to produce sets of outcomes rather than single outcomes.

Group project

You will learn the basics of the naive Bayes classifier and its extension, the naive credal classifier. Essentially, in case the available information is insufficient to identify all probabilities that affect the classification problem, credal classification starts out with a set of probabilities, and naturally produces sets of classification outcomes, which become smaller (and eventually become singletons) as more information becomes available.

Specifically, you will study the idea of bounding probabilities, leading to robust Bayesian analysis when combined with data. This allows the filter to produce an "unsure" result in situations where there is limited training data.

By the end of the group project you will have learned:

• The naive assumption.
• How to construct a likelihood suitable to solve classification.
• How to construct a conjugate prior for this likelihood.
• How to robustify the model through sets of priors.
• How this translates to a robust decision model for classification.

By the end of the group project you will be able to:

• How to theoretically perform credal classification.
• Understand the benefits and downsides of credal classification compared to standard methods.

Individual project

The individual project will build on the knowledge we have gained in the group project and will explore additional advanced topics. The individual project caters for both theoretical and applied directions of research. A few examples of topics you will be able to investigate are:

• Study possible applications of the credal classifier on a real dataset that you identify, including (but not limited to) spam filtering, or medical diagnosis problems such as disease classification.
• How credal classifiers can be obtained from real data.
• Research the credal classifier model itself, e.g. relaxing the naive assumption, allowing continuous attributes, ...
• Explore how to evaluate credal classifiers and how to compare them against standard classifiers.
• Explore more general robust decision models beyond credal classification.
• Explore other applications of classification and decision making under severe uncertainty.

Mode of operation and evidence of learning

Both the group and individual project will revolve around learning through reading with focus on the underlying theory, mathematical rigour, and the development of deep conceptual understanding. Students will demonstrate their understanding by solving relevant problems, exploring examples and theoretical applications of the material, and clearly communicating it in both written and oral formats.

For the individual project (but not the group project), depending on the topic, students can additionally demonstrate understanding by comparing theory to simulation results, writing R code to implement core methodology, and analysing simulated and real data sets.

Prerequisites

Probability II or Statistical Inference II

Resources

• R. O. Duda and P. E. Hart. Pattern Classification and Scene Analysis. Wiley-Interscience, 1973.
• Zaffalon, M. (1999). A credal approach to naive classification. In de Cooman, G., Cozman, F. G., Moral, S., Walley, P. (Eds), ISIPTA '99: Proceedings of the First International Symposium on Imprecise Probabilities and Their Applications. The Imprecise Probabilities Project, Universiteit Gent, Belgium, pp. 405-414.
• Zaffalon, M. (2001). Statistical inference of the naive credal classifier. In de Cooman, G., Fine, T., Seidenfeld, T. (Eds), ISIPTA '01: Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications. Shaker Publishing, The Netherlands, pp. 384-393.
• Statistical classification on Wikipedia.
• Jonathan Zdziarski. Ending Spam: Bayesian Content Filtering and the Art of Statistical Language Classification. No Starch Press, 2005.
• Marco Zaffalon. The naive credal classifier. Journal of Statistical Planning and Inference 105:5-21, 2002.
• Zaffalon, M., Wesnes, K., Petrini, O. (2003). Reliable diagnoses of dementia by the naive credal classifier inferred from incomplete cognitive data. Artificial Intelligence in Medicine 29(1-2), 61-79.