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02/12/2019 ∙ by Debmalya Mandal, et al. ∙ 0 ∙ shareread it

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Causal Discovery from Subsampled Time Series Data by Constraint Optimization
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Nonlinear System Identification via Tensor Completion
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Boosted Sparse and LowRank Tensor Regression
We propose a sparse and lowrank tensor regression model to relate a uni...
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Learning Representations from Imperfect Time Series Data via Tensor Rank Regularization
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07/01/2019 ∙ by Paul Pu Liang, et al. ∙ 16 ∙ shareread it
Weighted Tensor Completion for TimeSeries Causal Information
Marginal Structural Models (MSM) Robins00 are the most popular models for causal inference from timeseries observational data. However, they have two main drawbacks: (a) they do not capture subject heterogeneity, and (b) they only consider fixed time intervals and do not scale gracefully with longer intervals. In this work, we propose a new family of MSMs to address these two concerns. We model the potential outcomes as a threedimensional tensor of low rank, where the three dimensions correspond to the agents, time periods and the set of possible histories. Unlike the traditional MSM, we allow the dimensions of the tensor to increase with the number of agents and time periods. We set up a weighted tensor completion problem as our estimation procedure, and show that the solution to this problem converges to the true model in an appropriate sense. Then we show how to solve the estimation problem, providing conditions under which we can approximately and efficiently solve the estimation problem. Finally we propose an algorithm based on projected gradient descent, which is easy to implement, and evaluate its performance on a simulated dataset.
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