A Non-convex One-Pass Framework for Generalized Factorization Machine and Rank-One Matrix Sensing
A Non-convex One-Pass Framework for Generalized Factorization Machine and Rank-One Matrix Sensing
复制标题
一种用于广义因式分解机和一阶矩阵传感的非凸一次性框架
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Jieping Ye
中科院分区：
文献类型：
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作者：
Ming Lin;Jieping Ye
我们开发了一个高效的交互框架，用于学习广义因子化机器(GFM)在具有可证明保证的数据流上的学习。当样本取自$d$维随机高斯向量，且GFM中的目标二阶系数矩阵的秩为$k$时，该算法线性收敛，在检索$O(k^{3}dlog(1/epsilon))$训练实例后获得$O(Epsilon)$恢复误差，在一遍数据集中消耗$O(Kd)$内存，每次迭代只需要矩阵向量乘积运算.该框架的关键部分是构造一个具有条件独立RIP条件(CI-RIP)的估计序列。作为GFM的特例，我们的框架可以应用于对称或非对称的一阶矩阵感知问题，如感应矩阵补全和相位恢复。
We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the target second order coefficient matrix in gFM is of rank $k$, our algorithm converges linearly, achieves $O(epsilon)$ recovery error after retrieving $O(k^{3}dlog(1/epsilon))$ training instances, consumes $O(kd)$ memory in one-pass of dataset and only requires matrix-vector product operations in each iteration. The key ingredient of our framework is a construction of an estimation sequence endowed with a so-called Conditionally Independent RIP condition (CI-RIP). As special cases of gFM, our framework can be applied to symmetric or asymmetric rank-one matrix sensing problems, such as inductive matrix completion and phase retrieval.
影响因子：
4.300
作者：
Hagar Ibrahim Labouta;Labiba K. El-Khordagui
通讯作者：
Labiba K. El-Khordagui