An Analysis of Active Learning With Uniform Feature Noise

In active learning, the user sequentially chooses values for feature $X$ and an oracle returns the corresponding label $Y$. In this paper, we consider the effect of feature noise in active learning, which could arise either because $X$ itself is being measured, or it is corrupted in transmission to the oracle, or the oracle returns the label of a noisy version of the query point. In statistics, feature noise is known as "errors in variables" and has been studied extensively in non-active settings. However, the effect of feature noise in active learning has not been studied before. We consider the well-known Berkson errors-in-variables model with additive uniform noise of width $\sigma$. Our simple but revealing setting is that of one-dimensional binary classification setting where the goal is to learn a threshold (point where the probability of a $+$ label crosses half). We deal with regression functions that are antisymmetric in a region of size $\sigma$ around the threshold and also satisfy Tsybakov's margin condition around the threshold. We prove minimax lower and upper bounds which demonstrate that when $\sigma$ is smaller than the minimiax active/passive noiseless error derived in \cite{CN07}, then noise has no effect on the rates and one achieves the same noiseless rates. For larger $\sigma$, the \textit{unflattening} of the regression function on convolution with uniform noise, along with its local antisymmetry around the threshold, together yield a behaviour where noise \textit{appears} to be beneficial. Our key result is that active learning can buy significant improvement over a passive strategy even in the presence of feature noise.Comment: 24 pages, 2 figures, published in the proceedings of the 17th International Conference on Artificial Intelligence and Statistics (AISTATS), 201

Noise simulation in classification with the noisemodel R package: Applications analyzing the impact of errors with chemical data

Classification datasets created from chemical processes can be affected by errors, which impair the accuracy of the models built. This fact highlights the importance of analyzing the robustness of classifiers against different types and levels of noise to know their behavior against potential errors. In this con- text, noise models have been proposed to study noise-related phenomenology in a controlled environment, allowing errors to be introduced into the data in a supervised manner. This paper introduces the noisemodel R package, which contains the first extensive implementation of noise models for classification datasets, proposing it as support tool to analyze the impact of errors related to chemical data. It provides 72 noise models found in the specialized literature that allow errors to be introduced in different ways in classes and attributes. Each of them is properly documented and referenced, unifying their results through a specific S3 class, which benefits from customized print, summary and plot methods. The usage of the package is illustrated through four applica- tion examples considering real-world chemical datasets, where errors are prone to occur. The software presented will help to deepen the understanding of the problem of noisy chemical data, as well as to develop new robust algo- rithms and noise preprocessing methods properly adapted to different types of errors in this scenario.University of Granada/CBU

Noise Models in Classification: Unified Nomenclature, Extended Taxonomy and Pragmatic Categorization

This paper presents the first review of noise models in classification covering both label and attribute noise. Their study reveals the lack of a unified nomenclature in this field. In order to address this problem, a tripartite nomenclature based on the structural analysis of existing noise models is proposed. Additionally, a revision of their current taxonomies is carried out, which are combined and updated to better reflect the nature of any model. Finally, a categorization of noise models is proposed from a practical point of view depending on the characteristics of noise and the study purpose. These contributions provide a variety of models to introduce noise, their characteristics according to the proposed taxonomy and a unified way of naming them, which will facilitate their identification and study, as well as the reproducibility of future research