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Classification versus regression in overparameterized regimes: Does the loss function matter?

  • Vidya Muthukumar (Georgia Institute of Technology)
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Abstract

Recent years have seen substantial interest in a first-principles theoretical understanding of the behavior of overparameterized models that interpolate noisy training data, based on their surprising empirical success. In this talk, I compare classification and regression tasks in the overparameterized linear model. On the one hand, we show that with sufficient overparameterization, solutions obtained by training on the squared loss ( minimum-norm interpolation) typically used for regression, are identical to those produced by training on exponential and polynomially-tailed losses (e.g. the max-margin support-vector-machine), typically used for classification. On the other hand, we show that there exist regimes where these solutions are consistent when evaluated by the 0-1 test loss function, but inconsistent if evaluated by the mean-squared-error test loss function. Our results demonstrate that: a) different loss functions at the training (optimization) phase can yield similar solutions, and b) a significantly higher level of effective overparameterization admits good generalization in classification tasks as compared to regression tasks.

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seminar
05.12.24 19.12.24

Math Machine Learning seminar MPI MIS + UCLA

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