Robust Estimators in High-Dimensions Without the Computational Intractability

Diakonikolas, Ilias; Kamath, Gautam; Kane, Daniel M.; Li, Jerry; Moitra, Ankur; Stewart, Alistair

doi:10.1137/17m1126680

Cited by 171 publications

(259 citation statements)

References 42 publications

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“…Outlier-robust estimation has received long-time attention in statistics and control [21], [62]. It has a fundamental applications, such as prediction and learning [63], linear decoding [64], and secure state estimation for control [65].…”

Section: B Outlier-robust Estimation In Statistics and Controlmentioning

confidence: 99%

Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees

Tzoumas

Antonante

Carlone

2019

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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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 perception is jeopardized by the presence of incorrect data association, and in general, outliers. Although techniques to handle outliers do exist, they can fail in unpredictable manners (e.g., RANSAC, robust estimators), or can have exponential runtime (e.g., branch-and-bound). In this paper, we advance the state of the art in outlier rejection by making three contributions. First, we show that even a simple linear instance of outlier rejection is inapproximable: in the worst-case one cannot design a quasi-polynomial time algorithm that computes an approximate solution efficiently. Our second contribution is to provide the first per-instance sub-optimality bounds to assess the approximation quality of a given outlier rejection outcome. Our third contribution is to propose a simple general-purpose algorithm, named adaptive trimming, to remove outliers. Our algorithm leverages recently-proposed global solvers that are able to solve outlier-free problems, and iteratively removes measurements with large errors. We demonstrate the proposed algorithm on three spatial perception problems: 3D registration, two-view geometry, and SLAM. The results show that our algorithm outperforms several state-of-the-art methods across applications while being a general-purpose method. * The authors contributed equally to this work.V. Tzoumas, P. Antonante, L. Carlone are with the

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Section: B Outlier-robust Estimation In Statistics and Controlmentioning

confidence: 99%

Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees

Tzoumas

Antonante

Carlone

2019

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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“…functions, a fundamentally different setting from the current paper. Our work is also related to the literature on robust statistics [11,12], and particularly, with the recently rekindled research efforts on high dimensional robust statistics [13][14][15]. These works will be the working horse for our attack resilient algorithm.…”

Section: Introductionmentioning

confidence: 89%

“…In this section, we describe two estimators for approximating θ (k) H [cf. (14)] from the received messages (9) without knowing the identity of links in H. To simplify notations, we define α ≥ |A|/N as a known upper bound to the fraction of compromised channels and assume α < 1/2 where less than half of the channels are compromised.…”

Section: Robust Distributed Resource Allocationmentioning

confidence: 99%

Resilient Distributed Optimization Algorithms for Resource Allocation

Uribe

Wai

Alizadeh

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Distributed algorithms provide flexibility over centralized algorithms for resource allocation problems, e.g., cyber-physical systems. However, the distributed nature of these algorithms often makes the systems susceptible to man-in-the-middle attacks, especially when messages are transmitted between price-taking agents and a central coordinator. We propose a resilient strategy for distributed algorithms under the framework of primal-dual distributed optimization. We formulate a robust optimization model that accounts for Byzantine attacks on the communication channels between agents and coordinator. We propose a resilient primal-dual algorithm using state-of-the-art robust statistics methods. The proposed algorithm is shown to converge to a neighborhood of the robust optimization model, where the neighborhood's radius is proportional to the fraction of attacked channels. * CAU and HTW have contributed equally. CAU is with LIDS, MIT, Cambridge, MA, USA. HTW is with

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“…Additionally, while we cannot visualize the distributions in multidimensional space, we can plot their projections onto a onedimensional space. To choose the vector on which we project the distributions, we use an idea from robust statistics [11,28]. We form a matrix consisting of the embedding vector of each example from both the source and target datasets.…”

Section: Motivationmentioning

confidence: 99%

Domain Adaptation for Enterprise Email Search

Tran

Karimzadehgan

Pasumarthi

et al. 2019

Proceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval

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In the enterprise email search setting, the same search engine often powers multiple enterprises from various industries: technology, education, manufacturing, etc. However, using the same global ranking model across different enterprises may result in suboptimal search quality, due to the corpora differences and distinct information needs. On the other hand, training an individual ranking model for each enterprise may be infeasible, especially for smaller institutions with limited data. To address this data challenge, in this paper we propose a domain adaptation approach that fine-tunes the global model to each individual enterprise. In particular, we propose a novel application of the Maximum Mean Discrepancy (MMD) approach to information retrieval, which attempts to bridge the gap between the global data distribution and the data distribution for a given individual enterprise. We conduct a comprehensive set of experiments on a large-scale email search engine, and demonstrate that the MMD approach consistently improves the search quality for multiple individual domains, both in comparison to the global ranking model, as well as several competitive domain adaptation baselines including adversarial learning methods.

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Robust Estimators in High-Dimensions Without the Computational Intractability

Cited by 171 publications

References 42 publications

Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees

Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees

Resilient Distributed Optimization Algorithms for Resource Allocation

Domain Adaptation for Enterprise Email Search

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