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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence / EAAI-20

Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee

February 1, 2023

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Authors

Ming Lin

Alibaba Group


Shuang Qiu

University of Michigan


Jieping Ye

University of Michigan


Xiaomin Song

Alibaba Group


Qi Qian

Alibaba Group


Liang Sun

Alibaba Group


Shenghuo Zhu

Alibaba Group


Rong Jin

Alibaba Group


DOI:

10.1609/aaai.v33i01.33014312


Abstract:

Factorization machine (FM) is a popular machine learning model to capture the second order feature interactions. The optimal learning guarantee of FM and its generalized version is not yet developed. For a rank k generalized FM of d dimensional input, the previous best known sampling complexity is O[k3d · polylog(kd)] under Gaussian distribution. This bound is sub-optimal comparing to the information theoretical lower bound O(kd). In this work, we aim to tighten this bound towards optimal and generalize the analysis to sub-gaussian distribution. We prove that when the input data satisfies the so-called τ-Moment Invertible Property, the sampling complexity of generalized FM can be improved to O[k2d · polylog(kd)/τ2]. When the second order self-interaction terms are excluded in the generalized FM, the bound can be improved to the optimal O[kd · polylog(kd)] up to the logarithmic factors. Our analysis also suggests that the positive semi-definite constraint in the conventional FM is redundant as it does not improve the sampling complexity while making the model difficult to optimize. We evaluate our improved FM model in real-time high precision GPS signal calibration task to validate its superiority.

Topics: AAAI

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HOW TO CITE:

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee Proceedings of the AAAI Conference on Artificial Intelligence (2019) 4312-4319.

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee AAAI 2019, 4312-4319.

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin (2019). Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee. Proceedings of the AAAI Conference on Artificial Intelligence, 4312-4319.

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin. Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee. Proceedings of the AAAI Conference on Artificial Intelligence 2019 p.4312-4319.

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin. 2019. Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee. "Proceedings of the AAAI Conference on Artificial Intelligence". 4312-4319.

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin. (2019) "Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee", Proceedings of the AAAI Conference on Artificial Intelligence, p.4312-4319

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin, "Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee", AAAI, p.4312-4319, 2019.

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin. "Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee". Proceedings of the AAAI Conference on Artificial Intelligence, 2019, p.4312-4319.

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin. "Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee". Proceedings of the AAAI Conference on Artificial Intelligence, (2019): 4312-4319.

Ming Lin||Shuang Qiu||Jieping Ye||Xiaomin Song||Qi Qian||Liang Sun||Shenghuo Zhu||Rong Jin. Which Factorization Machine Modeling Is Better: A Theoretical Answer with Optimal Guarantee. AAAI[Internet]. 2019[cited 2023]; 4312-4319.


ISSN: 2374-3468


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