基于代数结构的机器学习在小中数据集上表现媲美主流模型。
Algebraic Machine Learning for Small-to-Medium Datasets Is Competitive against Strong Standard Baselines
- 通过代数结构的子直积分解学习，不依赖数值优化。
- 50-2000样本下图像分类优于交叉验证的CNN，表格数据接近XGBoost。
- 无需调参和验证，通用代数先验适配多种任务。
符号方法通常被认为在真实监督任务上不如现代强模型。我们评估了代数机器学习（AML）框架，在不同规模训练集上与标准基线进行图像和表格分类对比。AML仅使用训练数据，不依赖验证或交叉验证，在50至2000个样本的小中型图像数据集上性能超过一系列经过交叉验证的基线方法，包括CNN。在相同规模的表格数据集上，XGBoost总体最优，但AML仍可与包含任务特异性偏置的方法（如LightGBM、随机森林）相媲美。AML在两种差异较大的数据类型上实现竞争力，使用的是通用代数归纳偏置，而非像CNN对图像或XGBoost对表格数据那样的模态特异性偏置，且因无任务相关超参数而无需交叉验证。
原文摘要 · Abstract (English)
Symbolic methods are generally not considered competitive with strong modern learners on realistic supervised tasks. We evaluate Algebraic Machine Learning (AML), a framework that learns through subdirect decomposition of algebraic structure rather than numerical optimization, against standard baselines on image and tabular classification across varying training-set sizes. We find that AML trained only on training data without using validation or cross-validation outperforms a family of cross-validated baseline methods including CNNs on small to medium image datasets (50--2000 training examples). On tabular datasets in the same size range, XGBoost is overall the best performing method, but AML is nonetheless comparable to methods incorporating task-specific biases such as LightGBM and random forests. AML achieves this competitive performance across two very different types of datasets using a generic algebraic inductive bias, rather than the modality-specific biases built into standard baselines like CNNs for images or XGBoost for tabular data, and requires no cross validation because it has no task-dependent hyperparameters to tune.
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