Bayesian Networks and Their Value - An Essay, Part 2

If you have not read Part 1, make sure to check it out before reading this post!

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Supervised learning refers to when algorithms have training data. Unsupervised learning occurs when there is no training data available. In other words, in supervised learning, we already know the results and the model learns to reach those results. In unsupervised learning, we do not have previous knowledge of the results. Therefore it is up to the algorithm to identify patterns on its own and reach a conclusion. Unsupervised learning is closer to artificial intelligence (Castle, 2017). Research in supervised learning has showed naive Bayes to be competitive with famous, complex, and respected classifiers such as C4.5 (Friedman et al., 1997). As mentioned above, the assumption when using naive Bayes is that all variables are conditionally independent and that they have a parent node to all variables. This condition is completely unrealistic. Consider a BN for assessing the risk in loan applications. Correlations will most likely exist among variables such as age, education level, and income. That is why the good performance of naive Bayes is somewhat surprising. In machine learning, classification is a common task for data analysis and pattern recognition. In order to classify, the creation of a classifier is need. A classifier is a function that assigns a category or label to an instance that is described by a set of attributes. Many classifiers have graph-like representations connecting nodes. Some of those representations include decision trees, decision lists, neural networks, decision graphs, and of course, BNs.

Once a BN has been constructed, it can answer any query about probabilities given a set of evidence and priors. In addition, given evidence, it can update its probabilities by using smart algorithms, called bayesian updating. This is especially important and useful since humans have been shown to be inefficient in this sort of updating (T. D. Pilditch, Hahn, & Lagnado, under review). Furthermore, as humans, we are skilled at qualitative inference, but not at quantitative inference. BNs can be regarded as tools for quantitative inference and therefore be of much use to us. Finally, BNs are machine learning compatible. Machine learning and artificial intelligence algorithms might be some of the strongest tools of our era. Thanks to the flexibility and the simple portrayal of complex situations of BNs, different algorithms from machine learning can be used for the learning portion of a specific BN. This characteristic of BNs makes them very appealing for complex data analysis.

As a BN grows, its complexity grows even faster. Take the naive Bayes classifier I mentioned above, for example. When two variables are perfectly correlated, than the removal of one of them will improve the performance of the classifier. Nevertheless, problems arise if these variables are only partially correlated. If one of those variables is removed, useful information can be lost, and if both stay, the calculations become more expensive. Furthermore, BNs help us portray uncertainty. However, the portrayal of uncertainty is very hard to achieve accurately. When uncertainty meets complexity, the problem becomes exponentially hard to solve adequately. This is a possible make-it-or-break-it point for BNs. Uncertainty needs to be monitored over carefully to make sure it is being portrayed as accurately as possible while the increment in complexity needs to be avoided when possible. When a variable is added, complexity increases. Therefore, a series of actions need to be taken. Uncertainty needs to be revisited to make sure it is being appropriately captured, and complex interactions, mixed types of evidence, and mixed types of relations need to be accounted for.

BNs can provide value to several very important real world scenarios. Since the 1990s, BNs have been studied in the context of medical decision making (P. Lucas, n.d.). BNs bring the statistical and causal knowledge that is very much required in doctors while also taking into account uncertainty that is very present in the medical field. Uncertainties are involved when dealing with diagnosis, treatment selection, planning, and prediction of prognosis (P. J. F. Lucas, Boot, & Taal, 1998). BNs have been tested and used for both diagnosis and treatment selection for patients. The unique structure of BNs allow questions like “What is likely to be the result for the patient if I prescribe X treatment?” to be answered. Nevertheless, developing a model of a realistic medical problem is not easy, and BNs are no exception.

A more concrete example of how BNs can be used in the medical field can be found in the diagnosis and treatment selection for ventilator-associated pneumonia (VAP). VAP is very common in hospitals, especially in the intensive care unit (ICU). Many patients that are admitted into the ICU need respiratory support by mechanical ventilation. Furthermore, many of the patients in the ICU are severely ill which in turn negatively affects their immune system. Both the respiratory support by mechanical ventilation and the negative impact on the immune system of a severe illness are promoters of the development of bacterial pneumonia (Bartlett, 1997). In hospitals, and particularly in the ICU, there is a widespread dissemination of multi-resistant bacteria. In turn, this dissemination will cause the colonization of more individuals after some time. Therefore, the effective treatment of VAP is imperative. In this context, the “right” treatment would be one where the selected antibiotics are effective without causing major side effects. Prescription of antibiotics can be reduced to one of three cases, prescribing none, one, or two drugs. Assume that d represents the total number of possible drugs. Then we would have (d-1 choose 2) + d possible prescriptions. BNs can be expanded to display all these possible combinations. When developing a BN revolving around VAP, its structure can be designed using causal knowledge, dependencies, influences, and correlations. These can be obtained from knowledge of domain experts, literature, or extracted using structure-learning algorithms. The BN can be created with a defined probability distribution but later refined by using existing data.