Hypothesis Transfer Learning with Surrogate Classification Losses: Generalization Bounds through Algorithmic Stability

Hypothesis transfer learning (HTL) contrasts domain adaptation by allowing for a previous task leverage, named the source, into a new one, the target, without requiring access to the source data. Indeed, HTL relies only on a hypothesis learnt from such source data, relieving the hurdle of expansive data storage and providing great practical benefits. Hence, HTL is highly beneficial for real-world applications relying on big data. The analysis of such a method from a theoretical perspective faces multiple challenges, particularly in classification tasks. This paper deals with this problem by studying the learning theory of HTL through algorithmic stability, an attractive theoretical framework for machine learning algorithms analysis. In particular, we are interested in the statistical behaviour of the regularized empirical risk minimizers in the case of binary classification. Our stability analysis provides learning guarantees under mild assumptions. Consequently, we derive several complexity-free generalization bounds for essential statistical quantities like the training error, the excess risk and cross-validation estimates. These refined bounds allow understanding the benefits of transfer learning and comparing the behaviour of standard losses in different scenarios, leading to valuable insights for practitioners

Data-Dependent Stability of Stochastic Gradient Descent

We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for SGD which depend on the worst-case constants. By virtue of the data-dependent argument, our bounds provide new insights into learning with SGD on convex and non-convex problems. In the convex case, we show that the bound on the generalization error depends on the risk at the initialization point. In the non-convex case, we prove that the expected curvature of the objective function around the initialization point has crucial influence on the generalization error. In both cases, our results suggest a simple data-driven strategy to stabilize SGD by pre-screening its initialization. As a corollary, our results allow us to show optimistic generalization bounds that exhibit fast convergence rates for SGD subject to a vanishing empirical risk and low noise of stochastic gradient

Stable Feature Selection for Biomarker Discovery

Feature selection techniques have been used as the workhorse in biomarker discovery applications for a long time. Surprisingly, the stability of feature selection with respect to sampling variations has long been under-considered. It is only until recently that this issue has received more and more attention. In this article, we review existing stable feature selection methods for biomarker discovery using a generic hierarchal framework. We have two objectives: (1) providing an overview on this new yet fast growing topic for a convenient reference; (2) categorizing existing methods under an expandable framework for future research and development