In this paper, we introduce a robust non-parametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness for a large class of anomalous data, potentially adversarial. In particular, while previous works only prove consistency results under very specific contamination models, this work provides finite-sample high-probability error-bounds without any prior knowledge on the outliers. To highlight the robustness of our method, we introduce an influence function adapted to the considered OUI framework. Finally, we show that MoM-KDE achieves competitive results when compared with other robust kernel estimators, while having significantly lower computational complexity.

Transfer learning has attracted growing attention from the machine learning community. It addresses real-world issues that were not considered in the classical methods, especially with model-based methods when source data is not available. Recent work on transfer learning for Decision Trees has been proposed in the form of two algorithms named SER and STRUT. These methods tackle with success potential changes between source and target data, however several classification tasks may face imbalance data, hence degrading the performance of such transfer methods. In this paper, we study the impact of class imbalance on these algorithms and propose an adaptation for each of them, named SER* and STRUT*. These variants have been tested on real and synthetic data, these latter revealing to be of great use to control at the same time various transformations between source and target along with imbalance conditions. Results on both types of data show the benefits of our approach and suggest several perspectives for further research.