用可学习张量分解优化特征，提速3-5倍且效果不降。
Tensor Network Based Feature Learning Model
- 将张量积特征表示为可学习的CP分解，替代传统交叉验证选超参数。
- 在真实多维数据集上训练速度提升3-5倍，预测性能相当。
- 适合需高效调参的大规模核方法应用，如高维特征学习。
为克服核方法的立方复杂度，已有研究采用张量积结构的多项式与傅里叶特征映射数据至高维空间，并通过张量网络重参数化缓解维度灾难。然而，特征超参数的最优选择仍未解决，通常依赖标准交叉验证。本文提出特征学习（FL）模型，将张量积特征表示为可学习的典型多线性分解（CPD），并利用交替最小二乘法（ALS）联合优化特征超参数与模型参数。在多种维度和规模的真实数据集上的实验表明，该模型可稳定实现3-5倍的训练加速，同时保持与标准交叉验证模型相当的预测性能。
原文摘要 · Abstract (English)
Many approximations were suggested to circumvent the cubic complexity of kernel-based algorithms, allowing their application to large-scale datasets. One strategy is to consider the primal formulation of the learning problem by mapping the data to a higher-dimensional space using tensor-product structured polynomial and Fourier features. The curse of dimensionality due to these tensor-product features was effectively solved by a tensor network reparameterization of the model parameters. However, another important aspect of model training - identifying optimal feature hyperparameters - has not been addressed and is typically handled using the standard cross-validation approach. In this paper, we introduce the Feature Learning (FL) model, which addresses this issue by representing tensor-product features as a learnable Canonical Polyadic Decomposition (CPD). By leveraging this CPD structure, we efficiently learn the hyperparameters associated with different features alongside the model parameters using an Alternating Least Squares (ALS) optimization method. We prove the effectiveness of the FL model through experiments on real data of various dimensionality and scale. The results show that the FL model can be consistently trained 3-5 times faster than and have the prediction quality on par with a standard cross-validated model.
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