Abstract
A fundamental goal of probabilistic classification is the ability to predict a probabilistic distribution over the output space given the input space. Rather than only predicting the most likely class that an input observation should belong to, a probabilistic classifier is able to provide reliable uncertainty information associated with the predictions. In many real-world applications with strict transparency and interpretability requirements, such as medical image classification, facial recognition and automated recruitment, understanding the uncertainties of the predictions is as important as improving the predictive performance. It is therefore no wonder that much attention has been devoted to learning probabilistic classifiers.
In this thesis, we approach the Multi-Dimensional Classification (MDC) problem, an extension of both the traditional Multi-Class Classification (MCC) problem and the well-known Multi-Label Classification (MLC) problem, in which an observation of input is characterized by multiple class variables. In probabilistic MDC, the main challenge is that one needs to predict multi-variate distributions instead of univariate distributions. Besides, there are common situations in which complex types of data coexist, such as numeric values, discrete signals, images, etc. Such type of data is also referred to as multi-modal data.
We propose Generalized Bayesian Network Classifier (GBNC), a generalized framework for solving probabilistic MDC problems with complex types of input. Unlike the existing Multi-dimensional Bayesian Network Classifier (MBNC) framework, GBNC imposes a new structural constraint to learn a discrete BN to model the class distribution by maximizing the Conditional Log-Likelihood (CLL). We present a theoretical analysis of the decomposability of the learning problem and leverage them to devise efficient learning algorithms. Experimental results on different types of benchmark data sets validate the superiority of GBNCs in comparison to existing probabilistic MDC baselines.
