Bayesian Networks are a very powerful tool for modelling and predicting complex relationships between variables. They provide a transparent way to map and understand variable relationships and how changes to networks might impact their accuracy. Their easily understandable network structure paired with flexible Bayesian Statistical methods lends itself well to investigating behaviors associated with small data sets for machine learning.
Greater understanding of how to adapt machine learning tools like BN to use with small datasets will ultimately help underserved areas like small volume manufacturing or military applications utilize the powerful predictive analytics of machine learning. The work in this dissertation took initial steps towards this goal by exploring the feasibility of using Kriging and Radial Basis Function models to generate data for four different Bayesian Networks. The goal of the network was to predict completion time for workers conducting assembly operations, predict the number of errors an assembly worker made, a buyer’s car choice, and the income level of an adult. Data for the project was collected from a human-subjects study that used augmented reality guided work instructions and from the UCI machine learning database.
Small amounts of data from each of these datasets were used to train the different BNs. Each of these training datasets were fitted with a Kriging and a Radial Basis Function model. Once models were created, they were randomly sampled to produce a larger dataset for training.
The four networks were then tested under multiple conditions including the use of PSO to tune network parameters. The first set of results looked at how varying the proportion of generated to original training data would impact network accuracy. Results showed that in some cases generated data could increase the accuracy of the trained networks. In addition,
it showed that the varying quantities of original to generated data could also impact the classification accuracy. From here, the authors generated larger amounts of data. Networks trained using ten thousand, one-hundred thousand, and a million data points were tested.
Results showed that depending on the data set, increasing amounts of data did help increase accuracy for more complex network structures.
Results from tuning network parameters using PSO showed that it can help to produce accurate networks that improve on baseline original data only performance. However, the PSO method in general increased the standard deviation of accuracy results and lowered the median accuracy. This result leads the authors to believe that an alternate PSO formulation taking into account more information about the parameters is necessary to see further accuracy enhancements.
In the end, the work demonstrated that when only small quantities of data are available it is possible to build an accurate BN. The answer to research question one appears to be a combination of data generation and optimization. The second research question asked how best to set priors when only small quantities of data are available. Results from the work presented above show that using data generated from meta-models can help compute accurate priors. Also, in some cases priors can be tuned using Particle Swarm Optimization. Although, results suggest this method is very sensitive to the objective function formulation. Research question three asked how to best set likelihood values for small datasets. Results show that data generation via meta-models, which in turn add more likelihood values to the dataset, can be a valid strategy for increasing BN accuracy.
Overall, the exploratory results presented in this paper demonstrate the feasibility of using meta-model generated data to increase the accuracy of small sample set trained BN.
Further developing this method will help underserved areas with access to only small datasets make use of the powerful predictive analytics of ML. Moving forward the authors will continue to refine the data generation methods and look at alternate prior optimization formulations.
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