Blind regression: Nonparametric regression for latent variable models via collaborative filtering
© 2016 NIPS Foundation - All Rights Reserved. We introduce the framework of blind regression motivated by matrix completion for recommendation systems: given m users, n movies, and a subset of user-movie ratings, the goal is to predict the unobserved user-movie ratings given the data, i.e., to compl...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2021
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| Online Access: | https://hdl.handle.net/1721.1/137181 |
| _version_ | 1811082252679905280 |
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| author | Shah, Devavrat Song, Dogyoon Lee, Christina E. Li, Yihua |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Shah, Devavrat Song, Dogyoon Lee, Christina E. Li, Yihua |
| author_sort | Shah, Devavrat |
| collection | MIT |
| description | © 2016 NIPS Foundation - All Rights Reserved. We introduce the framework of blind regression motivated by matrix completion for recommendation systems: given m users, n movies, and a subset of user-movie ratings, the goal is to predict the unobserved user-movie ratings given the data, i.e., to complete the partially observed matrix. Following the framework of non-parametric statistics, we posit that user u and movie i have features x1(u) and x2 (i) respectively, and their corresponding rating y(u, i) is a noisy measurement of f(x1(u), x2(i)) for some unknown function f. In contrast with classical regression, the features x = (x1(u), x2(i)) are not observed, making it challenging to apply standard regression methods to predict the unobserved ratings. Inspired by the classical Taylor's expansion for differentiable functions, we provide a prediction algorithm that is consistent for all Lipschitz functions. In fact, the analysis through our framework naturally leads to a variant of collaborative filtering, shedding insight into the widespread success of collaborative filtering in practice. Assuming each entry is sampled independently with probability at least max(m-1+δ,n-1/2+δ) with δ > 0, we prove that the expected fraction of our estimates with error greater than e is less than γ2/ϵ2 plus a polynomially decaying term, where γ2 is the variance of the additive entry-wise noise term. Experiments with the MovieLens and Netflix datasets suggest that our algorithm provides principled improvements over basic collaborative filtering and is competitive with matrix factorization methods. |
| first_indexed | 2024-09-23T12:00:09Z |
| format | Article |
| id | mit-1721.1/137181 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:00:09Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | mit-1721.1/1371812023-02-06T20:32:04Z Blind regression: Nonparametric regression for latent variable models via collaborative filtering Shah, Devavrat Song, Dogyoon Lee, Christina E. Li, Yihua Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science © 2016 NIPS Foundation - All Rights Reserved. We introduce the framework of blind regression motivated by matrix completion for recommendation systems: given m users, n movies, and a subset of user-movie ratings, the goal is to predict the unobserved user-movie ratings given the data, i.e., to complete the partially observed matrix. Following the framework of non-parametric statistics, we posit that user u and movie i have features x1(u) and x2 (i) respectively, and their corresponding rating y(u, i) is a noisy measurement of f(x1(u), x2(i)) for some unknown function f. In contrast with classical regression, the features x = (x1(u), x2(i)) are not observed, making it challenging to apply standard regression methods to predict the unobserved ratings. Inspired by the classical Taylor's expansion for differentiable functions, we provide a prediction algorithm that is consistent for all Lipschitz functions. In fact, the analysis through our framework naturally leads to a variant of collaborative filtering, shedding insight into the widespread success of collaborative filtering in practice. Assuming each entry is sampled independently with probability at least max(m-1+δ,n-1/2+δ) with δ > 0, we prove that the expected fraction of our estimates with error greater than e is less than γ2/ϵ2 plus a polynomially decaying term, where γ2 is the variance of the additive entry-wise noise term. Experiments with the MovieLens and Netflix datasets suggest that our algorithm provides principled improvements over basic collaborative filtering and is competitive with matrix factorization methods. 2021-11-03T14:11:53Z 2021-11-03T14:11:53Z 2016 2019-07-16T14:34:36Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/137181 Shah, Devavrat, Song, Dogyoon, Lee, Christina E. and Li, Yihua. 2016. "Blind regression: Nonparametric regression for latent variable models via collaborative filtering." en https://papers.nips.cc/paper/2016/hash/678a1491514b7f1006d605e9161946b1-Abstract.html Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Neural Information Processing Systems (NIPS) |
| spellingShingle | Shah, Devavrat Song, Dogyoon Lee, Christina E. Li, Yihua Blind regression: Nonparametric regression for latent variable models via collaborative filtering |
| title | Blind regression: Nonparametric regression for latent variable models via collaborative filtering |
| title_full | Blind regression: Nonparametric regression for latent variable models via collaborative filtering |
| title_fullStr | Blind regression: Nonparametric regression for latent variable models via collaborative filtering |
| title_full_unstemmed | Blind regression: Nonparametric regression for latent variable models via collaborative filtering |
| title_short | Blind regression: Nonparametric regression for latent variable models via collaborative filtering |
| title_sort | blind regression nonparametric regression for latent variable models via collaborative filtering |
| url | https://hdl.handle.net/1721.1/137181 |
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