A Parametric Framework for the Comparison of Methods of Very Robust Regression

There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression data and the outliers. We introduce a parameter $\lambda$ that defines a parametric path in the space of models and enables us to study, in a systematic way, the properties of estimators as the groups of data move from being far apart to close together. We examine, as a function of $\lambda$, the variance and squared bias of five estimators and we also consider their power when used in the detection of outliers. This systematic approach provides tools for gaining knowledge and better understanding of the properties of robust estimators.Comment: Published in at http://dx.doi.org/10.1214/13-STS437 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A survey of outlier detection methodologies

Outlier detection has been used for centuries to detect and, where appropriate, remove anomalous observations from data. Outliers arise due to mechanical faults, changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. Their detection can identify system faults and fraud before they escalate with potentially catastrophic consequences. It can identify errors and remove their contaminating effect on the data set and as such to purify the data for processing. The original outlier detection methods were arbitrary but now, principled and systematic techniques are used, drawn from the full gamut of Computer Science and Statistics. In this paper, we introduce a survey of contemporary techniques for outlier detection. We identify their respective motivations and distinguish their advantages and disadvantages in a comparative review

Measuring the Influence of Observations in HMMs through the Kullback-Leibler Distance

We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting outliers in HMM data series

SubCMap: subject and condition specific effect maps

Current methods for statistical analysis of neuroimaging data identify condition related structural alterations in the human brain by detecting group differences. They construct detailed maps showing population-wide changes due to a condition of interest. Although extremely useful, methods do not provide information on the subject-specific structural alterations and they have limited diagnostic value because group assignments for each subject are required for the analysis. In this article, we propose SubCMap, a novel method to detect subject and condition specific structural alterations. SubCMap is designed to work without the group assignment information in order to provide diagnostic value. Unlike outlier detection methods, SubCMap detections are condition-specific and can be used to study the effects of various conditions or for diagnosing diseases. The method combines techniques from classification, generalization error estimation and image restoration to the identify the condition-related alterations. Experimental evaluation is performed on synthetically generated data as well as data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Results on synthetic data demonstrate the advantages of SubCMap compared to population-wide techniques and higher detection accuracy compared to outlier detection. Analysis with the ADNI dataset show that SubCMap detections on cortical thickness data well correlate with non-imaging markers of Alzheimer's Disease (AD), the Mini Mental State Examination Score and Cerebrospinal Fluid amyloid-β levels, suggesting the proposed method well captures the inter-subject variation of AD effects

Keyframe-based monocular SLAM: design, survey, and future directions

Extensive research in the field of monocular SLAM for the past fifteen years has yielded workable systems that found their way into various applications in robotics and augmented reality. Although filter-based monocular SLAM systems were common at some time, the more efficient keyframe-based solutions are becoming the de facto methodology for building a monocular SLAM system. The objective of this paper is threefold: first, the paper serves as a guideline for people seeking to design their own monocular SLAM according to specific environmental constraints. Second, it presents a survey that covers the various keyframe-based monocular SLAM systems in the literature, detailing the components of their implementation, and critically assessing the specific strategies made in each proposed solution. Third, the paper provides insight into the direction of future research in this field, to address the major limitations still facing monocular SLAM; namely, in the issues of illumination changes, initialization, highly dynamic motion, poorly textured scenes, repetitive textures, map maintenance, and failure recovery