Distributed Corruption Detection in Networks

We consider the problem of distributed corruption detection in networks. In this model, each vertex of a directed graph is either truthful or corrupt. Each vertex reports the type (truthful or corrupt) of each of its outneighbors. If it is truthful, it reports the truth, whereas if it is corrupt, it reports adversarially. This model, first considered by Preparata, Metze, and Chien in 1967, motivated by the desire to identify the faulty components of a digital system by having the other components checking them, became known as the PMC model. The main known results for this model characterize networks in which \emph{all} corrupt (that is, faulty) vertices can be identified, when there is a known upper bound on their number. We are interested in networks in which the identity of a \emph{large fraction} of the vertices can be identified. It is known that in the PMC model, in order to identify all corrupt vertices when their number is $t$, all indegrees have to be at least $t$. In contrast, we show that in $d$ regular-graphs with strong expansion properties, a $1-O(1/d)$ fraction of the corrupt vertices, and a $1-O(1/d)$ fraction of the truthful vertices can be identified, whenever there is a majority of truthful vertices. We also observe that if the graph is very far from being a good expander, namely, if the deletion of a small set of vertices splits the graph into small components, then no corruption detection is possible even if most of the vertices are truthful. Finally, we discuss the algorithmic aspects and the computational hardness of the problem

Data Imputation through the Identification of Local Anomalies

We introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources, e.g., an occluder in the case of a visual recording. Within this framework, we propose i) a novel algorithm to efficiently separate, i.e., detect and localize, possible corruptions from a given suspicious data instance and ii) a Maximum A Posteriori (MAP) estimator to impute the corrupted data. As a generalization to Euclidean distance, we also propose a novel distance measure, which is based on the ranked deviations among the data attributes and empirically shown to be superior in separating the corruptions. Our algorithm first splits the suspicious instance into parts through a binary partitioning tree in the space of data attributes and iteratively tests those parts to detect local anomalies using the nominal statistics extracted from an uncorrupted (clean) reference data set. Once each part is labeled as anomalous vs normal, the corresponding binary patterns over this tree that characterize corruptions are identified and the affected attributes are imputed. Under a certain conditional independency structure assumed for the binary patterns, we analytically show that the false alarm rate of the introduced algorithm in detecting the corruptions is independent of the data and can be directly set without any parameter tuning. The proposed framework is tested over several well-known machine learning data sets with synthetically generated corruptions; and experimentally shown to produce remarkable improvements in terms of classification purposes with strong corruption separation capabilities. Our experiments also indicate that the proposed algorithms outperform the typical approaches and are robust to varying training phase conditions

Deep Learning using K-space Based Data Augmentation for Automated Cardiac MR Motion Artefact Detection

Quality assessment of medical images is essential for complete automation of image processing pipelines. For large population studies such as the UK Biobank, artefacts such as those caused by heart motion are problematic and manual identification is tedious and time-consuming. Therefore, there is an urgent need for automatic image quality assessment techniques. In this paper, we propose a method to automatically detect the presence of motion-related artefacts in cardiac magnetic resonance (CMR) images. As this is a highly imbalanced classification problem (due to the high number of good quality images compared to the low number of images with motion artefacts), we propose a novel k-space based training data augmentation approach in order to address this problem. Our method is based on 3D spatio-temporal Convolutional Neural Networks, and is able to detect 2D+time short axis images with motion artefacts in less than 1ms. We test our algorithm on a subset of the UK Biobank dataset consisting of 3465 CMR images and achieve not only high accuracy in detection of motion artefacts, but also high precision and recall. We compare our approach to a range of state-of-the-art quality assessment methods.Comment: Accepted for MICCAI2018 Conferenc