New Sequential Minimal Optimization Algorithm for Support Vector Regression with MAPE Loss
Researchers have developed a Sequential Minimal Optimization (SMO) algorithm specifically designed for support vector regression using Mean Absolute Percentage Error (MAPE) loss, addressing sample-dependent constraints not previously handled in published literature. The algorithm incorporates four efficiency improvements and resolves a convergence problem for odd-symmetry kernels through adaptive spectral regularization. This work is significant because it enables more efficient and practical forecasting applications where relative accuracy matters, as demonstrated by superior performance on real-world benchmarks compared to existing solvers.
The paper presents a theoretically-grounded SMO algorithm for support vector regression with MAPE loss, which is well-suited for forecasting tasks evaluated in relative rather than absolute terms. The key innovation is handling sample-dependent dual box constraints that arise from the MAPE formulation—a problem not previously addressed in the SMO literature. The authors prove a structural-invariance result showing that MAPE modifications affect only two SMO components (working-set selection and analytic-update clipping) while leaving gradient bookkeeping and curvature computation unchanged from classical epsilon-SVR. The algorithm incorporates four efficiency improvements: asymmetric freeze-counters, warm-starting, block working-set updates of size four, and per-pair tolerance scaling. Numerical validation across eleven synthetic configurations confirms solution agreement with reference solvers (OSQP, MOSEK, Clarabel), and wall-time benchmarks demonstrate the lowest median runtime on all tested configurations. Critically, on the California Housing benchmark at production scale, the new algorithm converges while a patched LIBSVM reference implementation fails to satisfy optimality conditions, demonstrating practical necessity of the theoretical improvements.
What's missing
The paper does not discuss computational memory requirements or scalability limits for very high-dimensional problems. Additionally, while MAPE loss is motivated for relative-error forecasting, the paper does not provide empirical comparison on real-world forecasting datasets (only synthetic configurations and one housing benchmark), limiting evidence of practical advantage in actual forecasting applications.
What different sources said
- arXiv stat.MLCenter
Sequential Minimal Optimization for $\varepsilon$-SVR with MAPE Loss and Sample-Dependent Box Constraints
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