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• W2908999823 abstract "We consider the problem of learning a multivariate function from a set of scattered observations using a sparse low-rank separated representation (SSR) model. The model structure considered here is promising for high-dimensional learning problems; however, existing training algorithms based on alternating least-squares (ALS) are known to have convergence difficulties, particularly when the rank of the model is greater than 1. In the present work, we supplement the model structure with sparsity constraints to ensure the well posedness of the approximation problem. We propose two fast training algorithms to estimate the model parameters: (i) a cyclic coordinate descent algorithm and (ii) a block coordinate descent (BCD) algorithm. While the first algorithm is not provably convergent owing to the non-convexity of the optimization problem, the BCD algorithm guarantees convergence to a Nash equilibrium point. The computational cost of the proposed algorithms is shown to scale linearly with respect to all of the parameters in contrast to methods based on ALS. Numerical studies on synthetic and real-world regression datasets indicate that the proposed SSR model structure holds significant potential for machine learning problems." @default.
• W2908999823 created "2019-01-25" @default.
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• W2908999823 date "2019-01-01" @default.
• W2908999823 modified "2023-09-24" @default.
• W2908999823 title "Sparse low-rank separated representation models for learning from data" @default.
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• W2908999823 doi "https://doi.org/10.1098/rspa.2018.0490" @default.
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