谱路径回归：用于可解释表格学习的定向切比雪夫谐波
Spectral Path Regression: Directional Chebyshev Harmonics for Interpretable Tabular Learning
AI总结：
本文提出一种基于方向切比雪夫谐波的谱路径回归方法，通过方向化谐波模式实现多变量结构的可解释性，模型在保持精度的同时具备高效和可解释性。
摘要：
经典逼近基如切比雪夫多项式提供了原理性且可解释的表示，但其多变量张量积构造随维度增长呈指数级扩大，并强加轴对齐结构，这与现实表格数据不匹配。我们通过将张量化的振荡替换为方向谐波模式$\cos(\mathbf{m}^{\top}\arccos(\mathbf{x}))$，在角空间中通过方向组织多变量结构，而非通过坐标索引。这种表示方法产生了一种离散频谱回归模型，其复杂度通过选择少量结构化频率向量（频谱路径）来控制，训练仅需单次闭式岭解算，无需迭代优化。在标准连续特征表格回归基准上的实验表明，所得模型在准确率上与强非线性基线相当，同时保持紧凑、计算高效且通过解析表达式显式可解释。
英文摘要：
Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that is poorly matched to real tabular data. We address this by replacing tensorised oscillations with directional harmonic modes of the form $\cos(\mathbf{m}^{\top}\arccos(\mathbf{x}))$, which organise multivariate structure by direction in angular space rather than by coordinate index. This representation yields a discrete spectral regression model in which complexity is controlled by selecting a small number of structured frequency vectors (spectral paths), and training reduces to a single closed-form ridge solve with no iterative optimisation. Experiments on standard continuous-feature tabular regression benchmarks show that the resulting models achieve accuracy competitive with strong nonlinear baselines while remaining compact, computationally efficient, and explicitly interpretable through analytic expressions of learned feature interactions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
