520 research outputs found
Efficient Algorithms and Error Analysis for the Modified Nystrom Method
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
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
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
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