Robust Regression via Model Based Methods

• URL: http://arxiv.org/abs/2106.10759v2
• Date: Tue, 22 Jun 2021 02:24:13 GMT
• Title: Robust Regression via Model Based Methods
• Authors: Armin Moharrer, Khashayar Kamran, Edmund Yeh, and Stratis Ioannidis
• Abstract summary: We propose an algorithm inspired by so-called model-based optimization (MBO) [35, 36], which replaces a non-objective with a convex model function. We apply this to robust regression, proposing SADM, a function of the Online Alternating Direction Method of Multipliers (OOADM) [50] to solve the inner optimization in MBO. Finally, we demonstrate experimentally (a) the robustness of l_p norms to outliers and (b) the efficiency of our proposed model-based algorithms in comparison with methods on autoencoders and multi-target regression.
• Score: 13.300549123177705
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The mean squared error loss is widely used in many applications, including auto-encoders, multi-target regression, and matrix factorization, to name a few. Despite computational advantages due to its differentiability, it is not robust to outliers. In contrast, l_p norms are known to be robust, but cannot be optimized via, e.g., stochastic gradient descent, as they are non-differentiable. We propose an algorithm inspired by so-called model-based optimization (MBO) [35, 36], which replaces a non-convex objective with a convex model function and alternates between optimizing the model function and updating the solution. We apply this to robust regression, proposing SADM, a stochastic variant of the Online Alternating Direction Method of Multipliers (OADM) [50] to solve the inner optimization in MBO. We show that SADM converges with the rate O(log T/T). Finally, we demonstrate experimentally (a) the robustness of l_p norms to outliers and (b) the efficiency of our proposed model-based algorithms in comparison with gradient methods on autoencoders and multi-target regression.

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