Probabilistic Reasoning Under Uncertainty with Bayesian Networks
This webinar presents a workflow for encoding expert knowledge and subsequently performing omnidirectional probabilistic inference in the context of a real-world reasoning problem. It highlights the perhaps unexpected relevance of Bayesian networks for reasoning in everyday life. The example proves that “common-sense” reasoning can be rather tricky. On the other hand, encoding “common-sense knowledge” in a Bayesian network turns out to be uncomplicated. We want to demonstrate that reasoning with Bayesian networks can be as straightforward as doing arithmetic with a spreadsheet.
It is presumably fair to state that reasoning in complex environments creates cognitive challenges for humans. Adding uncertainty to our observations of the problem domain, or even considering uncertainty regarding the structure of the domain itself, makes matters worse. When uncertainty blurs so many premises, it can be particularly difficult to find a common reasoning framework for a group of stakeholders.
No Data, No Analytics.
If we had hard observations from our domain in the form of data, it would be quite natural to build a traditional analytic model for decision support. However, the real world often yields only fragmented data or no data at all. It is not uncommon that we merely have the opinions of individuals who are more or less familiar with the problem
To an Analyst With Excel, Every Problem Looks Like Arithmetic.
In the business world, it is typical to use spreadsheets to model the relationships between variables in a problem domain. Also, in the absence of hard observations, it is reasonable that experts provide assumptions instead of data. Any such expert knowledge is typically encoded in the form of single-point estimates and formulas. However, using of single values and formulas instantly oversimplifies the problem domain: firstly, the variables, and the relationships between them, become deterministic; secondly, the left-hand side versus right-hand side nature of formulas restricts inference to only one direction.
Taking No Chances!
Given that cells and formulas in spreadsheets are deterministic and only work with single-point values, they are well suited for encoding “hard” logic, but not at all for “soft” probabilistic knowledge that includes uncertainty. As a result, any uncertainty has to be addressed with workarounds, often in the form of trying out multiple scenarios or by working with simulation add-ons.
It Is a One-Way Street!
The lack of omnidirectional inference, however, may the bigger issue in spreadsheets. As soon as we create a formula linking two cells in a spreadsheet, e.g., B1=function(A1), we preclude any evaluation in the opposite direction, from B1 to A1. Assuming that A1 is the cause, and B1 is the effect, we can indeed use a spreadsheet for inference in the causal direction, i.e., perform a simulation. However, even if we were certain about the causal direction between them, unidirectionality would remain a concern. For instance, if we were only able to observe the effect B1, we could not infer the cause A1, i.e., we could not perform a diagnosis from effect to cause. The one-way nature of spreadsheet computations prevents this.
Bayesian Networks to the Rescue!
Bayesian networks are probabilistic by default and handle uncertainty “natively.” A Bayesian network model can work directly with probabilistic inputs, probabilistic relationships, and deliver correctly computed probabilistic outputs. Also, whereas traditional models and spreadsheets are of the form y=f(x), Bayesian networks do not have to distinguish between independent and dependent variables. Rather, a Bayesian network represents the entire joint probability distribution of the system under study. This representation facilitates omnidirectional inference, which is what we typically require for reasoning about a complex problem domain, such as the example in this webinar.
Example: Where is My Bag?
While most examples in previous webinars resemble proper research topics, we present a rather casual narrative to introduce probabilistic reasoning with Bayesian networks. It is a common situation taken straight from daily life, i.e., reasoning about a lost bag at an airport, for which a “common-sense interpretation” may appear more natural than our proposed formal approach. As we shall see, dealing formally with informal knowledge provides a robust basis for reasoning under uncertainty.