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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Low-Rank Methods in Event Detection and Subsampled Point-...
Jakub Marecek, Stathis Maroulis, Vana Kalogeraki, Dimitrios Guno · 2018-02-11 · via cs.DS updates on arXiv.org

Monitoring of streamed data to detect abnormal behaviour (variously known as event detection, anomaly detection, change detection, or outlier detection) underlies many applications of the Internet of Things. There, one often collects data from a variety of sources, with asynchronous sampling, and missing data. In this setting, one can predict abnormal behavior using low-rank techniques. In particular, we assume that normal observations come from a low-rank subspace, prior to being corrupted by a uniformly distributed noise. Correspondingly, we aim to recover a representation of the subspace, and perform event detection by running point-to-subspace distance query for incoming data. In particular, we use a variant of low-rank factorisation, which considers interval uncertainty sets around "known entries", on a suitable flattening of the input data to obtain a low-rank model. On-line, we compute the distance of incoming data to the low-rank normal subspace and update the subspace to keep it consistent with the seasonal changes present. For the distance computation, we suggest to consider subsampling. We bound the one-sided error as a function of the number of coordinates employed using techniques from learning theory and computational geometry. In our experimental evaluation, we have tested the ability of the proposed algorithm to identify samples of abnormal behavior in induction-loop data from Dublin, Ireland.