Multi-Entity Bayesian Networks for credit risk analysis


In simple terms, credit risk is the risk of a borrower not repaying a loan. Banks use credit scoring as a supportive measure for granting individual and business credit. In the banking system, the rules of gathering information are formalized, providing the basis for credit approval. This information is substantial for assessment of the level of risk of a credit.

There are typically 4 steps in the credit granting process:

  1. Initial acceptance of credit application
  2. Estimation of legality of enterprise
  3. Analysing creditability
  4. Deciding on the credit


Probabilistic graphical models represent a probability distribution by encoding conditional independence structure with graphs. This in turn enables graph techniques for inference and learning.

Bayesian Networks(BNs) are part of the family of probabilistic graphical models. They are directed acyclic graphs that can represent a domain and allow for inference and reasoning about that domain.

[1] [2] [3] Show the working application of BNs in the credit risk space. BNs are well known for working well under uncertainty; especially where there is a lot of information about that particular uncertain domain.

The case of uncertainty and a lot of information is pervasive in credit analysis, therefore BNs are good candidate solution for credit analysis.

The reasoning behind assigning the credit risk of an entity requires a methodically sound and computationally vigorous uncertainty calculus, and an underpinning inference engine that procedurally encodes the “statements of truth” of the calculus, the effectiveness to conflate information at several levels of abstraction, and the ability to assess complex and dynamic situations. The inference engine also needs to be capable of encapsulating expert knowledge and strong beliefs of the domain.

The vast diversified published applications of BNs consist of template models. A template model is appropriate for problem domains in which the relevant variables, their state spaces, and their probabilistic relationships do not vary from problem instance to problem instance [4]. This generic knowledge about the domain can be represented by a fixed BN over a fixed set of variables obtained by some combination of expert knowledge and learning from observation.

As BN technology is applied to more complex problems, the limitations of template models become more and more apparent; even when a domain can be represented by a template model, its size and complexity may make it necessary to represent it implicitly as a collection of modular sub-units. Figure 1 provides an example of a template model.

Figure 1 – A Bayesian Network (template model) for predicting creditability of an enterprise.

Laskey [5] [6] [7] developed Multi-Entity Bayesian Networks (MEBN), a first order version of Bayesian Networks, which rely on generalization of the typical BN representations rather than a logic-like language. MEBNs are a knowledge representation formalism that combines the expressive power of first-order logic with a sound logically consistent treatment of uncertainty [7].

MEBN’s power lies in the fact that it portrays the domain as comprised of entities and can therefore do its reasoning based on a specific situation at hand (Figure 2), whereas a BN will use a template model that may not be sufficient or use irrelevant information for certain problem instances. Laskey gives a practical example of this concept [7].

In essence, MEBNs allow for modelling a large and complex problem into smaller logical sub-units that can be replicated as required by the problem at hand.

Figure 2 – A Multi-Entity Bayesian Network that represents the same domain as in Figure 1.


Intelligent prediction systems rely highly on historical data and, with so much behavioural data readily available, prediction systems can be improved significantly. With that said, this aspect and many others such as the dynamic nature of a problem gives more complexity. Thus, a need for a more modular approach is of greatest importance.

The nature of credit risk scoring is complex and very dynamic and changes on a frequent basis. Many BN template models approaches have been used to solve this problem [2] [3]. But, an improvement may be made with a more expressive and modular approach using MEBNs as the growth in complexity requires.

I envisage a more flexible solution in MEBNs.


[1] Y. Zuo and E. Kita, “Up/Down Analysis of stock Index by using BNs,” Canadian Center of Science and Education, 2012.

[2] R. Pershad, “A Bayesian Belief Network for Corporate Credit Risk Assessment,” University of Toronto, Toronto, 2000.

[3] A. Witold, N. Marek and S. Joanna, “BNs as a decision support tool in credit scoring domain,” The Poznan University of Economics, 2003.

[4] K. Laskey, E. Wright, S. Mahoney, M. Takikawa and T. Levitt, “Multi-Entity Bayesian Networks for situation assessment,” Information Extraction & Transport, Arlington, 2002.

[5] C.Y. Park, K.B. Laskey, P.C.G. Costa and S. Matsumoto, “Multi-Entity Networks Learning Hybrid Variables, in Situation Awareness,” The sensor Fusion Lab I& center of Excellence in C41, 2001.

[6] C.Y. Park, K.B. Laskey, S. Matsumoto and P. Costa, “MEBN in predictive situation awareness,” 2001.

[7] N.C. Rommel, C.G.C. Paulo, B.L. Kathryn and C. KC, “PROGNOS,” The sensor Fusion Lab I& Center of Excellence in C41, 2004.


by Mthokozisi Myeza



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