520 research outputs found

    Efficient Algorithms and Error Analysis for the Modified Nystrom Method

    Full text link
    Many kernel methods suffer from high time and space complexities and are thus prohibitive in big-data applications. To tackle the computational challenge, the Nystr\"om method has been extensively used to reduce time and space complexities by sacrificing some accuracy. The Nystr\"om method speedups computation by constructing an approximation of the kernel matrix using only a few columns of the matrix. Recently, a variant of the Nystr\"om method called the modified Nystr\"om method has demonstrated significant improvement over the standard Nystr\"om method in approximation accuracy, both theoretically and empirically. In this paper, we propose two algorithms that make the modified Nystr\"om method practical. First, we devise a simple column selection algorithm with a provable error bound. Our algorithm is more efficient and easier to implement than and nearly as accurate as the state-of-the-art algorithm. Second, with the selected columns at hand, we propose an algorithm that computes the approximation in lower time complexity than the approach in the previous work. Furthermore, we prove that the modified Nystr\"om method is exact under certain conditions, and we establish a lower error bound for the modified Nystr\"om method.Comment: 9-page paper plus appendix. In Proceedings of the 17th International Conference on Artificial Intelligence and Statistics (AISTATS) 2014, Reykjavik, Iceland. JMLR: W&CP volume 3

    A Scalable CUR Matrix Decomposition Algorithm: Lower Time Complexity and Tighter Bound

    Full text link
    The CUR matrix decomposition is an important extension of Nystr\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advantages over the existing relative-error CUR algorithms that it possesses tighter theoretical bound and lower time complexity, and that it can avoid maintaining the whole data matrix in main memory. Finally, experiments on several real-world datasets demonstrate significant improvement over the existing relative-error algorithms.Comment: accepted by NIPS 201

    Methodologies for Improving Modern Industrial Recommender Systems

    Full text link
    Recommender system (RS) is an established technology with successful applications in social media, e-commerce, entertainment, and more. RSs are indeed key to the success of many popular APPs, such as YouTube, Tik Tok, Xiaohongshu, Bilibili, and others. This paper explores the methodology for improving modern industrial RSs. It is written for experienced RS engineers who are diligently working to improve their key performance indicators, such as retention and duration. The experiences shared in this paper have been tested in some real industrial RSs and are likely to be generalized to other RSs as well. Most contents in this paper are industry experience without publicly available references
    • …
    corecore