Variational Bayesian Inference for Robust Streaming Tensor Factorization and Completion

Zhang, Zheng; Hawkins, Cole

doi:10.1109/icdm.2018.00200

Cited by 25 publications

(37 citation statements)

References 18 publications

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“…Robust factorization approaches for incomplete and contaminated tensor streams have also been studied. Zhang et al [14] proposed BRST, which aims to distinguish sparsely corrupted outliers from low-rank tensor streams via variational Bayesian inference. Najafi et al [15] proposed OR-MSTC, an outlier-robust completion algorithm for multiaspect incomplete tensor streams.…”

Section: Related Workmentioning

confidence: 99%

“…At the same time, real-world tensors are easily corrupted by outliers due to unpredicted events during data collection, such as sensor malfunctions and malicious tampering. Recovering incomplete and at the same time contaminated tensors is a challenging and unwieldy task since tensor factorization, which most tensor completion techniques are based on, is vulnerable CP-WOPT [9] OnlineSGD [11] OLSTEC [12] MAST [13] BRST [14] OR-MSTC [15] SMF [16] CPHW [17] Others [18], [ to outliers. To find latent structure behind such a noisy tensor accurately, many efforts have been made to design a 'outlierrobust' tensor factorization algorithm [5], [20], [21].…”

Section: Introductionmentioning

confidence: 99%

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Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outliers

Shin

2021

2021 IEEE 37th International Conference on Data Engineering (ICDE)

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Consider multiple seasonal time series being collected in real-time, in the form of a tensor stream. Real-world tensor streams often include missing entries (e.g., due to network disconnection) and at the same time unexpected outliers (e.g., due to system errors). Given such a real-world tensor stream, how can we estimate missing entries and predict future evolution accurately in real-time?In this work, we answer this question by introducing SOFIA, a robust factorization method for real-world tensor streams. In a nutshell, SOFIA smoothly and tightly integrates tensor factorization, outlier removal, and temporal-pattern detection, which naturally reinforce each other. Moreover, SOFIA integrates them in linear time, in an online manner, despite the presence of missing entries. We experimentally show that SOFIA is (a) robust and accurate: yielding up to 76% lower imputation error and 71% lower forecasting error; (b) fast: up to 935× faster than the second-most accurate competitor; and (c) scalable: scaling linearly with the number of new entries per time step.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outliers

Shin

2021

2021 IEEE 37th International Conference on Data Engineering (ICDE)

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“…Bayesian Methods. Probabilistic Stream Tensors (POST) [5] and Variational Bayesian Inference (VBI) [28] are two papers that propose priors for the tensor model. POST considers models for both continuous and binary data.…”

Section: Other Workmentioning

confidence: 99%

Streaming Generalized Canonical Polyadic Tensor Decompositions

Phipps¹,

Johnson²,

Kolda³

2021

Preprint

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In this paper, we develop a method which we call OnlineGCP for computing the Generalized Canonical Polyadic (GCP) tensor decomposition of streaming data. GCP differs from traditional canonical polyadic (CP) tensor decompositions as it allows for arbitrary objective functions which the CP model attempts to minimize. This approach can provide better fits and more interpretable models when the observed tensor data is strongly non-Gaussian. In the streaming case, tensor data is gradually observed over time and the algorithm must incrementally update a GCP factorization with limited access to prior data. In this work, we extend the GCP formalism to the streaming context by deriving a GCP optimization problem to be solved as new tensor data is observed, formulate a tunable history term to balance reconstruction of recently observed data with data observed in the past, develop a scalable solution strategy based on segregated solves using stochastic gradient descent methods, describe a software implementation that provides performance and portability to contemporary CPU and GPU architectures and integrates with Matlab for enhanced useability, and demonstrate the utility and performance of the approach and software on several synthetic and real tensor data sets.

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“…As new tuples in the multi-aspect data stream arrive, a new (M − 1)-mode tensor is added to X once per period T . Additionally, in many previous studies on window-based tensor analysis [22]- [24], [26], the oldest (M − 1)-mode tensor is removed from X once per period T to fix the number of indices in the time mode to W . That is, at…”

Section: Multi-aspect Data Stream and Examplesmentioning

confidence: 99%

“…Xu et al [24] also suggested a Tucker decomposition algorithm for sliding window tensors and used it to detect anomalies in road networks. Zhang et al [26] used the sliding window model with exponential weighting for robust Bayesian probabilistic CP factorization and completion. Note that all these studies assume a time window moves 'discretely', while in our continuous tensor model, a time window moves 'continuously', as explained in Section IV.…”

Section: B Window-based Tensor Analysismentioning

confidence: 99%

SliceNStitch: Continuous CP Decomposition of Sparse Tensor Streams

Kwon

Park

Shin³

2021

Preprint

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Consider traffic data (i.e., triplets in the form of source-destination-timestamp) that grow over time. Tensors (i.e., multi-dimensional arrays) with a time mode are widely used for modeling and analyzing such multi-aspect data streams. In such tensors, however, new entries are added only once per period, which is often an hour, a day, or even a year. This discreteness of tensors has limited their usage for real-time applications, where new data should be analyzed instantly as it arrives.How can we analyze time-evolving multi-aspect sparse data 'continuously' using tensors where time is 'discrete'? We propose SLICENSTITCH for continuous CANDECOMP/PARAFAC (CP) decomposition, which has numerous time-critical applications, including anomaly detection, recommender systems, and stock market prediction. SLICENSTITCH changes the starting point of each period adaptively, based on the current time, and updates factor matrices (i.e., outputs of CP decomposition) instantly as new data arrives. We show, theoretically and experimentally, that SLICENSTITCH is (1) 'Any time': updating factor matrices immediately without having to wait until the current time period ends, (2) Fast: with constant-time updates up to 464× faster than online methods, and (3) Accurate: with fitness comparable (specifically, 72 − 100%) to offline methods.• Degradation of Fitness (Fig. 1c) An extremely fine-grained

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Variational Bayesian Inference for Robust Streaming Tensor Factorization and Completion

Cited by 25 publications

References 18 publications

Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outliers

Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outliers

Streaming Generalized Canonical Polyadic Tensor Decompositions

SliceNStitch: Continuous CP Decomposition of Sparse Tensor Streams

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