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稀疏编码的非凸优化分析Analyzing Non-Convex Optimization for Sparse Coding |
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| 课程网址: | http://videolectures.net/colt2015_ma_sparse_coding/ |
| 主讲教师: | Tengyu Ma |
| 开课单位: | 普林斯顿大学 |
| 开课时间: | 2015-08-20 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard formulation is as a non-convex optimization problem which is solved in practice by heuristics based on alternating minimization. Recent work has resulted in several algorithms for sparse coding with provable guarantees, but somewhat surprisingly these are outperformed by the simple alternating minimization heuristics. Here we give a general framework for understanding alternating minimization which we leverage to analyze existing heuristics and to design new ones also with provable guarantees. Some of these algorithms seem implementable on simple neural architectures, which was the original motivation of Olshausen and Field cite{OF} in introducing sparse coding. We also give the first efficient algorithm for sparse coding that works almost up to the information theoretic limit for sparse recovery on incoherent dictionaries. All previous algorithms that approached or surpassed this limit run in time exponential in some natural parameter. Finally, our algorithms improve upon the sample complexity of existing approaches. We believe that our analysis framework will have applications in other settings where simple iterative algorithms are used. |
| 关 键 词: | 稀疏编码; 启发式方法; 非凸优化问题 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2022-12-06：chenjy |
| 最后编审: | 2022-12-06：chenjy |
| 阅读次数: | 13 |