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Many real-world problems can be formulated as geometric optimization problems in high dimensions, especially in the fields of machine learning and data mining. Moreover, we often need to take into account of outliers when optimizing the…
In practice, network applications have to deal with failing nodes, malicious attacks, or, somehow, nodes facing highly corrupted data --- generally classified as outliers. This calls for robust, uncomplicated, and efficient methods. We…
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…
Now that Bayesian Networks (BNs) have become widely used, an appreciation is developing of just how critical an awareness of the sensitivity and robustness of certain target variables are to changes in the model. When time resources are…
In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…
Outlying observations can be challenging to handle and adversely affect subsequent analyses, especially in data with increasing dimensional complexity. Although outliers are not always undesired anomalies in the data and may possess…
The support vector machine (SVM) is one of the most successful learning methods for solving classification problems. Despite its popularity, SVM has a serious drawback, that is sensitivity to outliers in training samples. The penalty on…
We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions. We consider a standard stability condition from the recent robust…
Impulsed noise outliers are data points that differs significantly from other observations.They are generally removed from the data set through local regression or Kalman filter algorithm.However, these methods, or their generalizations,…
We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on $\gamma$-divergence. A novel feature of the…
In this paper, we address the problem of how to robustly train a ConvNet for regression, or deep robust regression. Traditionally, deep regression employs the L2 loss function, known to be sensitive to outliers, i.e. samples that either lie…
Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…
Model mis-specification (e.g. the presence of outliers) is commonly encountered in astronomical analyses, often requiring the use of ad hoc algorithms which are sensitive to arbitrary thresholds (e.g. sigma-clipping). For any given dataset,…
Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being…
In many machine learning tasks, a common approach for dealing with large-scale data is to build a small summary, {\em e.g.,} coreset, that can efficiently represent the original input. However, real-world datasets usually contain outliers…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
Outliers are ubiquitous in modern data sets. Distance-based techniques are a popular non-parametric approach to outlier detection as they require no prior assumptions on the data generating distribution and are simple to implement. Scaling…
We propose a general approach to handle data contaminations that might disrupt the performance of feature selection and estimation procedures for high-dimensional linear models. Specifically, we consider the co-occurrence of mean-shift and…
Coping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice. In this context, the present paper develops novel fixed-lag and…
We consider the robust filtering problem for a state-space model with outliers in correlated measurements. We propose a new robust filtering framework to further improve the robustness of conventional robust filters. Specifically, the…