图 书 馆
用张量方法学习超完全潜变量模型Learning Overcomplete Latent Variable Models through Tensor Methods |
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| 课程网址: | http://videolectures.net/colt2015_anandkumar_tensor_methods/ |
| 主讲教师: | Animashree Anandkumar |
| 开课单位: | 加州大学欧文分校 |
| 开课时间: | 2015-08-20 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space exceeds the observed dimensionality. In particular, we consider multiview mixtures, ICA, and sparse coding models. Our main tool is a new algorithm for tensor decomposition that works in the overcomplete regime. In the semi-supervised setting, we exploit label information to get a rough estimate of the model parameters, and then refine it using the tensor method on unlabeled samples. We establish learning guarantees when the number of components scales as $k=o(d^{p/2})$, where $d$ is the observed dimension, and $p$ is the order of the observed moment employed in the tensor method (usually $p=3,4$). In the unsupervised setting, a simple initialization algorithm based on SVD of the tensor slices is proposed, and the guarantees are provided under the stricter condition that $k\le \beta d$ (where constant $\beta$ can be larger than $1$). For the learning applications, we provide tight sample complexity bounds through novel covering arguments. |
| 关 键 词: | 张量方法; 变量模型; 样本边界 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2023-06-11：chenxin01 |
| 最后编审: | 2023-06-11：chenxin01 |
| 阅读次数: | 32 |