Representation learning involves transforming data so that it is useful for solving a particular supervised learning problem. The aim is to learn a representation function which maps inputs to some representation space, and an hypothesis which maps the representation space to targets. It is possible to learn a representation function using unlabeled data or data from a probability distribution other than that of the main problem of interest, which is helpful if labeled data is scarce. This approach has been successfully applied in practice, for example through pre-trained neural networks in computer vision and word embeddings in natural language processing. This thesis explores when it is possible to learn representations that are provably useful.
We consider learning a representation function from unlabeled data, and propose an approach to identifying conditions where this technique will be useful for a subsequent supervised learning task. The approach requires shared structure in the labeled and unlabeled distributions, as well as a compatible representation function class and hypothesis class. We provide an example where representation learning can exploit cluster structure present in the data.
We also consider learning a representation function from a source task distribution and re-using it on a target task of interest, and again propose conditions where this approach will be successful. In this case the conditions depend on shared structure between source and target task distributions. We provide an example involving the transfer of weights in a two-layer feedforward neural network.
Representation learning can be applied to another topic of interest: fairness in machine learning. The issue of fairness arises when machine learning systems make or provide advice on decisions about people. A common approach to defining fairness is measuring differences in decisions made by an algorithm for one demographic group compared to another. One approach to preventing discrimination against particular groups is to learn a representation of the data from which it is not possible for an adversary to determine an individual's group membership, but which preserves other useful information. We quantify the costs and benefits of such an approach with respect to several possible fairness definitions. We also examine the relationships between different definitions of fairness and show cases where they cannot simultaneously be satisfied.
We explore the use of representation learning for fairness through two case studies: predicting domestic violence recidivism while avoiding discrimination on the basis of race, and predicting student outcomes at university while avoiding discrimination on the basis of gender. Our case studies reveal both the utility of fair representation learning and the trade-offs between accuracy and the definitions of fairness considered
