Algorithms in High Dimensional Statistics with Low Dimensional Models
The explosively growing size of data in cyberspace with low-value density creates a pressing need for data processing, information extracting, and knowledge refinement. Many applications thus appear, such as personalized recommendation and pinpointing advertisement, by exploring hidden value behind massive amounts of data.
More concretely, my project considers the problem of learning a complete (orthogonal) dictionary from sparsely generated sample signals. Unlike conventional methods that minimize one norm to exploit sparsity and learn the dictionary one column at a time, we propose an alternative sparse promoting operator to learn the entire dictionary over the orthogonal group in a holistic fashion. We give a conceptually simple and yet effective algorithm to justify the proposed formulation, and by combining tools from high dimensional statistics, optimization, and unexpectedly, algebra, we show that it recovers the correct dictionary in fairly very broad conditions, well beyond current theoretical bounds.
Message to Sponsor
- Major: Mathematics, Computer Science and Physics
- Sponsor: Chen Fund
- Mentor: Yi Ma