Identifying genes linked to the appearance of certain types of cancers and their phenotypes is a well-known and challenging problem in bioinformatics. Discovering marker genes which, upon genetic mutation, drive the proliferation of different types and subtypes of cancer is critical for the development of advanced tests and therapies that will specifically identify, target, and treat certain cancers. Therefore, it is crucial to find methods that are successful in recovering "cancer-critical genes" from the (usually much larger) set of all genes in the human genome. We approach this problem in the statistical context as a feature (or variable) selection problem for clustering, in the case where the number of important features is typically small (or rare) and the signal of each important feature is typically minimal (or weak). Genetic datasets typically consist of hundreds of samples (n) each with tens of thousands gene-level measurements (p), resulting in the well-known statistical "large p small n" problem. The class or cluster identification is based on the clinical information associated with the type or subtype of the cancer (either known or unknown) for each individual. We discuss and develop novel feature ranking methods, which complement and build upon current methods in the field. These ranking methods are used to select features which contain the most significant information for clustering. Retaining only a small set of useful features based on this ranking aids in both a reduction in data dimensionality, as well as the identification of a set of genes that are crucial in understanding cancer subtypes. In this paper, we present an outline of cutting-edge feature selection methods, and provide a detailed explanation of our own contributions to the field. We explain both the practical properties and theoretical advantages of the new tools that we have developed. Additionally, we explore a well-developed case study applying these new feature selection methods to different levels of genetic data to explore their practical implementation within the field of bioinformatics.

<div>By Machine Learning in the Open World, we are trying to build models that can be used in a more realistic setting where there could always be something "unknown" happening. Beyond the traditional machine learning tasks such as classification and segmentation where all classes are predefined, we are dealing with the challenges from newly emerged classes, irrelevant classes, outliers, and class imbalance.</div><div>At the beginning, we focus on the Non-Exhaustive Learning (NEL) problem from a statistical aspect. By NEL, we assume that our training classes are non-exhaustive, where the testing data could contain unknown classes. And we aim to build models that could simultaneously perform classification and class discovery. We proposed a non-parametric Bayesian model that learns some hyper-parameters from both training and discovered classes (which is empty at the beginning), then infer the label partitioning under the guidance of the learned hyper-parameters, and repeat the above procedure until convergence.</div><div>After obtaining good results on applications with plain and low dimensional data such flow-cytometry and some benchmark datasets, we move forward to Non-Exhaustive Feature Learning (NEFL). For NEFL, we extend our work with deep learning techniques to learn representations on datasets with complex structural and spatial correlations. We proposed a metric learning approach to learn a feature space with good discrimination on both training classes and generalize well on unknown classes. Then we developed some variants of this metric learning algorithm to deal with outliers and irrelevant classes. We applied our final model to applications such as open world image classification, image segmentation, and SRS hyperspectral image segmentation and obtained promising results.</div><div>Finally, we did some explorations with Out of Distribution detection (OOD) to detect irrelevant sample and outliers to complete the story.</div>

This thesis addresses the crucial problem of knowledge transfer and retention in deep neural networks. The ability to transfer knowledge from previously learned tasks and retain it for future use is essential for machine learning models to continually adapt to new tasks and improve their overall performance. In principle, knowledge can be transferred between any type of task, but we believe it to be particularly challenging in the field of computer vision, where the size and diversity of visual data often result in high compute requirements and the need for large, complex models. Hence, we analyze transfer and retention learning between unsupervised and supervised visual tasks, which form the main focus of this thesis. We categorize our efforts into several knowledge transfer and retention paradigms, and we tackle them with several contributions for the scientific community. The thesis proposes settings and methods based on knowledge distillation and self-supervised learning techniques. In particular, we devise two novel continual learning settings and seven new methods for knowledge transfer and retention, setting new state-of-the-art in a wide range of tasks. In conclusion, this thesis provides a valuable contribution to the field of computer vision and machine learning and sets a foundation for future work in this area.