论文标题
稀疏回归的有效张量核法
Efficient Tensor Kernel methods for sparse regression
论文作者
论文摘要
最近，通过引入合适的张量内核扩展了经典核方法，以促进基础回归问题解决方案的稀疏性。实际上，他们解决了LP-Norm正则化问题，其中P = M/（M-1）和M什至整数恰好接近套索问题。但是，该方法的主要缺点是存储张量子需要大量内存，最终限制其适用性。在这项工作中，我们通过提出两个进步来解决这个问题。首先，我们通过将新的，更有效的布局用于存储数据，直接减少了内存需求。其次，我们使用NyStrom型子采样方法，该方法允许具有较少数据点的训练阶段，因此可以降低计算成本。在合成数据集和读取数据集的实验中，实验显示了拟议改进的有效性。最后，我们采用在C ++中实施COSE的案例，以进一步加速计算。
Recently, classical kernel methods have been extended by the introduction of suitable tensor kernels so to promote sparsity in the solution of the underlying regression problem. Indeed, they solve an lp-norm regularization problem, with p=m/(m-1) and m even integer, which happens to be close to a lasso problem. However, a major drawback of the method is that storing tensors requires a considerable amount of memory, ultimately limiting its applicability. In this work we address this problem by proposing two advances. First, we directly reduce the memory requirement, by intriducing a new and more efficient layout for storing the data. Second, we use a Nystrom-type subsampling approach, which allows for a training phase with a smaller number of data points, so to reduce the computational cost. Experiments, both on synthetic and read datasets, show the effectiveness of the proposed improvements. Finally, we take case of implementing the cose in C++ so to further speed-up the computation.
