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Robust PCA via Outlier Pursuit
TLDR
This work presents an efficient convex optimization-based algorithm that it calls outlier pursuit, which under some mild assumptions on the uncorrupted points recovers the exact optimal low-dimensional subspace and identifies the corrupted points.
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Online Robust PCA via Stochastic Optimization
TLDR
An Online Robust PCA (OR-PCA) is developed that processes one sample per time instance and hence its memory cost is independent of the number of samples, significantly enhancing the computation and storage efficiency.
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Robustness and generalization
We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is “similar” to a training sample, then the testing error is close to the…
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Robustness and Regularization of Support Vector Machines
TLDR
This work considers regularized support vector machines and shows that they are precisely equivalent to a new robust optimization formulation, thus establishing robustness as the reason regularized SVMs generalize well and gives a new proof of consistency of (kernelized) SVMs.
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Provable Subspace Clustering: When LRR Meets SSC
TLDR
A new algorithm is proposed, termed Low-rank sparse subspace clustering (LRSSC), by the combining SSC and LRR, and theoretical guarantees of the success of the algorithm are developed, revealing interesting insights into the strengths and the weaknesses of the methods.
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Robust Subspace Segmentation with Block-Diagonal Prior
TLDR
The subspace segmentation problem is addressed by effectively constructing an exactly block-diagonal sample affinity matrix by proposing a graph Laplacian constraint based formulation, and developing an efficient stochastic subgradient algorithm for optimization.
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Robust Regression and Lasso
TLDR
It is shown that robustness of the solution explains why the solution is sparse, and a theorem is proved which states that sparsity and algorithmic stability contradict each other, and hence Lasso is not stable.
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Online Low-Rank Subspace Clustering by Basis Dictionary Pursuit
TLDR
A novel online implementation of LRR that reduces the memory cost from O(n2) to O(pd), with p being the ambient dimension and d being some estimated rank, and the theoretical guarantee that the sequence of solutions produced by the algorithm converges to a stationary point of the expected loss function asymptotically is established.
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Distributionally Robust Markov Decision Processes
TLDR
It is shown that finding the optimal distributionally robust strategy can be reduced to the standard robust MDP where parameters are known to belong to a single uncertainty set; hence, it can be computed in polynomial time under mild technical conditions.
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Clustering Partially Observed Graphs via Convex Optimization
TLDR
This paper takes a novel yet natural approach to the problem of clustering a partially observed unweighted graph, by focusing on finding the clustering that minimizes the number of "disagreements" -i.e. the sum of the numbers of missing edges within clusters, and present edges across clusters.
View PDF on arXiv
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