Extreme Value Theory Filtering Techniques for Outlier Detection

We introduce asymptotic parameter-free hypothesis tests based on extreme value theory to detect outlying observations in finite samples. Our tests have nontrivial power for detecting outliers for general forms of the parent distribution and can be implemented when this is unknown and needs to be estimated. Using these techniques this article also develops an algorithm to uncover outliers masked by the presence of influential observations

Robust Regression with High Coverage

An important parameter for several high breakdown regression algorithm estimators is the number of cases given weight one, called the coverage of the estimator. Increasing the coverage is believed to result in a more stable estimator, but the price paid for this stability is greatly decreased resistance to outliers. A simple modification of the algorithm can greatly increase the coverage and hence its statistical performance while maintaining high outlier resistance

Learning Representations for Novelty and Anomaly Detection

The problem of novelty or anomaly detection refers to the ability to automatically identify data samples that differ from a notion of normality. Techniques that address this problem are necessary in many applications, like in medical diagnosis, autonomous driving, fraud detection, or cyber-attack detection, just to mention a few. The problem is inherently challenging because of the openness of the space of distributions that characterize novelty or outlier data points. This is often matched with the inability to adequately represent such distributions due to the lack of representative data. In this dissertation we address the challenge above by making several contributions. (a)We introduce an unsupervised framework for novelty detection, which is based on deep learning techniques, and which does not require labeled data representing the distribution of outliers. (b) The framework is general and based on first principles by detecting anomalies via computing their probabilities according to the distribution representing normality. (c) The framework can handle high-dimensional data such as images, by performing a non-linear dimensionality reduction of the input space into an isometric lower-dimensional space, leading to a computationally efficient method. (d) The framework is guarded from the potential inclusion of distributions of outliers into the distribution of normality by favoring that only inlier data can be well represented by the model. (e) The methods are evaluated extensively on multiple computer vision benchmark datasets, where it is shown that they compare favorably with the state of the art

PROBE-GK: Predictive Robust Estimation using Generalized Kernels

Many algorithms in computer vision and robotics make strong assumptions about uncertainty, and rely on the validity of these assumptions to produce accurate and consistent state estimates. In practice, dynamic environments may degrade sensor performance in predictable ways that cannot be captured with static uncertainty parameters. In this paper, we employ fast nonparametric Bayesian inference techniques to more accurately model sensor uncertainty. By setting a prior on observation uncertainty, we derive a predictive robust estimator, and show how our model can be learned from sample images, both with and without knowledge of the motion used to generate the data. We validate our approach through Monte Carlo simulations, and report significant improvements in localization accuracy relative to a fixed noise model in several settings, including on synthetic data, the KITTI dataset, and our own experimental platform.Comment: In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'16), Stockholm, Sweden, May 16-21, 201