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Optimal 0−1 Loss Classification In Linear, Overlapping And Interpolation Settings
(University of Birmingham, 2022-09-07) Alanazi, Reem; Max, Little
Classification problems represent a major subject in machine learning, and addressing them requires solving underlying optimization problems. Optimis- ing the 0–1 loss function is the natural pathway to address the classification problem. Because of the properties of 0–1 loss, which are that it is non-convex and non-differentiable, 0–1 loss is mathematically intractable and classified as non-deterministic polynomial-time hard (NP-hard). Consequently, the 0– 1 loss function has been replaced by surrogate loss functions that can be optimized more efficiently, where their optimal solution is guaranteed with respect to these surrogate losses. At the same time, these functions may not provide the same optimal solution as the 0–1 loss function. Indeed, the loss function used during the empirical risk minimization (ERM) is not the same loss function used in the evaluation; the mismatch of the loss functions leads to an approximate solution that may not be an ideal solution for 0–1 loss. Thus, an additional source of error is produced because of this replacement.
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