We study the problem of robustly estimating the mean of a $d$-dimensional distribution given $N$ examples, where most coordinates of every example may be missing and $\varepsilon N$ examples may be arbitrarily corrupted. Assuming each coordinate appears in a constant factor more than $\varepsilon N$ examples, we show algorithms that estimate the mean of the distribution with information-theoretically optimal dimension-independent error guarantees in nearly-linear time $\widetilde O(Nd)$. Our results extend recent work on computationally-efficient robust estimation to a more widely applicable incomplete-data setting.
We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a weaker condition than most other properties considered so far in the literature, and yet enables robust estimation in a broader variety of settings. We provide new information-theoretic results on robust distribution learning, robust estimation of stochastic block models, and robust mean estimation under bounded $k$th moments. We also provide new algorithmic re…
A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic samples, referred to as outliers. Building upon recent random matrix advances in the area of robust statistics, we specifically show that the so-called Maronna M-estimator of scatter asymptotically behaves similar to well-known random matrices when the population and sample sizes grow together to infinity. The introduction of outliers leads the robust estimator …
University of Iowa（爱荷华大学）；University of Texas, Austin（德克萨斯大学奥斯汀分校）
This paper considers the problem of recovering signals from compressed measurements contaminated with sparse outliers, which has arisen in many applications. In this paper, we propose a generative model neural network approach for reconstructing the ground truth signals under sparse outliers. We propose an iterative alternating direction method of multipliers (ADMM) algorithm for solving the outlier detection problem via $\ell_1$ norm minimization, and a gradient descent algorithm for solving the outlier detection problem via squared $\ell_1$ norm minimization. We establish the recovery guaran…
Handling mild outliers and unobserved values in compositional datasets using finite mixtures of mean-parametrised Dirichlet models
University of Pretoria（比勒陀利亚大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（理论与计算科学国家研究所）；San José State University（圣何塞州立大学）；University of Catania（卡塔尼亚大学）
Model-Agnostic Influential Outlier Detection for Mixed Effects and Multi-Level Models
Institute for Data Science, Carleton University（卡尔顿大学数据科学研究所）；School of Computer Science, Carleton University（卡尔顿大学计算机科学学院）；Department of Psychology, Carleton University（卡尔顿大学心理系）
Support Vector Machines are a widely used classification technique. They are computationally efficient and provide excellent predictions even for high-dimensional data. Moreover, Support Vector Machines are very flexible due to the incorporation of kernel functions. The latter allow to model nonlinearity, but also to deal with nonnumerical data such as protein strings. However, Support Vector Machines can suffer a lot from unclean data containing, for example, outliers or mislabeled observations. Although several outlier detection schemes have been proposed in the literature, the selection of …
This paper addresses network anomography, that is, the problem of inferring network-level anomalies from indirect link measurements. This problem is cast as a low-rank subspace tracking problem for normal flows under incomplete observations, and an outlier detection problem for abnormal flows. Since traffic data is large-scale time-structured data accompanied with noise and outliers under partial observations, an efficient modeling method is essential. To this end, this paper proposes an online subspace tracking of a Hankelized time-structured traffic tensor for normal flows based on the Cande…
New York University（纽约大学）；Microsoft Research（微软研究院）；University of Florida（佛罗里达大学）
We consider the dynamic assortment optimization problem under the multinomial logit model (MNL) with unknown utility parameters. The main question investigated in this paper is model mis-specification under the $\varepsilon$-contamination model, which is a fundamental model in robust statistics and machine learning. In particular, throughout a selling horizon of length $T$, we assume that customers make purchases according to a well specified underlying multinomial logit choice model in a $(1-\varepsilon)$-fraction of the time periods, and make arbitrary purchasing decisions instead in the rem…
Tencent AI Lab（腾讯AI实验室）；Peng Cheng Laboratory（鹏城实验室）
Nowadays, how to effectively evaluate visual properties has become a popular topic for fine-grained visual comprehension. In this paper we study the problem of how to estimate such visual properties from a ranking perspective with the help of the annotators from online crowdsourcing platforms. The main challenges of our task are two-fold. On one hand, the annotations often contain contaminated information, where a small fraction of label flips might ruin the global ranking of the whole dataset. On the other hand, considering the large data capacity, the annotations are often far from being com…
Robust Mixture Learning when Outliers Overwhelm Small Groups
ETH Zurich（苏黎世联邦理工学院）；TU Munich（慕尼黑工业大学）；Lucerne School of Computer Science and Information Technology（卢塞恩计算机科学与信息技术学院）；University of Copenhagen（哥本哈根大学）
We give the first outlier-robust efficient algorithm for clustering a mixture of $k$ statistically separated d-dimensional Gaussians (k-GMMs). Concretely, our algorithm takes input an $ε$-corrupted sample from a $k$-GMM and whp in $d^{\text{poly}(k/η)}$ time, outputs an approximate clustering that misclassifies at most $k^{O(k)}(ε+η)$ fraction of the points whenever every pair of mixture components are separated by $1-\exp(-\text{poly}(k/η)^k)$ in total variation (TV) distance. Such a result was not previously known even for $k=2$. TV separation is the statistically weakest possible notion of …
The 1-center clustering with outliers problem asks about identifying a prototypical robust statistic that approximates the location of a cluster of points. Given some constant $0 < α< 1$ and $n$ points such that $αn$ of them are in some (unknown) ball of radius $r,$ the goal is to compute a ball of radius $O(r)$ that also contains $αn$ points. This problem can be formulated with the points in a normed vector space such as $\mathbb{R}^d$ or in a general metric space. The problem has a simple randomized solution: a randomly selected point is a correct solution with constant probability, and its …
