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arXiv · 2402.10474

One-Bit Quantization and Sparsification for Multiclass Linear Classification with Strong Regularization

Reza Ghane·Danil Akhtiamov·Babak Hassibi
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Abstract

We study the use of linear regression for multiclass classification in the over-parametrized regime where some of the training data is mislabeled. In such scenarios it is necessary to add an explicit regularization term, $\lambda f(w)$, for some convex function $f(\cdot)$, to avoid overfitting the mislabeled data. In our analysis, we assume that the data is sampled from a Gaussian Mixture Model with equal class sizes, and that a proportion $c$ of the training labels is corrupted for each class. Under these assumptions, we prove that the best classification performance is achieved when $f(\cdot) = \|\cdot\|^2_2$ and $\lambda \to \infty$. We then proceed to analyze the classification errors for $f(\cdot) = \|\cdot\|_1$ and $f(\cdot) = \|\cdot\|_\infty$ in the large $\lambda$ regime and notice that it is often possible to find sparse and one-bit solutions, respectively, that perform almost as well as the one corresponding to $f(\cdot) = \|\cdot\|_2^2$.

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Reza Ghane, Danil Akhtiamov, Babak Hassibi. 2024-02-16. One-Bit Quantization and Sparsification for Multiclass Linear Classification with Strong Regularization. https://arxiv.org/abs/2402.10474

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