Bhattacharyya, C and Kannan, R (2020) Near-optimal sample complexity bounds for learning latent k-polytopes and applications to ad-mixtures. In: 37th International Conference on Machine Learning, ICML 2020, 13-18 July 2020, virtual, online, pp. 831-840.
Full text not available from this repository.Abstract
Deriving Optimal bounds on Sample Complexity of Latent Variable models is an active area of research. Recently such bounds were obtained for Mixture of Gaussians (Ashtiani et al., 2018), no such results are known for Ad-mixtures, a generalization of Mixture distributions. In this paper we show that O*(dk/m) samples are sufficient to learn each of k- topic vectors of LDA, a popular Ad-mixture model, with vocabulary size d and m 2 (1) words per document, to any constant error in L1 norm. The result is a corollary of the major contribution of this paper: The first sample complexity upper bound for the problem (introduced in (Bhattacharyya & Kannan, 2020)) of learning the vertices of a Latent k- Polytope in Rd, given perturbed points from it. The bound, O*(dk/β), is optimal and linear in number of parameters. It applies to many stochastic models including a broad class Ad-mixtures. To demonstrate the generality of the approach we specialize the setting to Mixed Membership Stochastic Block Models(MMSB) and show for the first time that if an MMSB has k blocks, the sample complexity is O*(k2) under usual assumptions. © 2020 37th International Conference on Machine Learning, ICML 2020. All rights reserved.
| Item Type: | Conference Paper |
|---|---|
| Publication: | 37th International Conference on Machine Learning, ICML 2020 |
| Publisher: | International Machine Learning Society (IMLS) |
| Additional Information: | The copyright for this article belongs to International Machine Learning Society (IMLS) |
| Keywords: | Machine learning; Mixtures; Stochastic systems, Latent variable models; Mixture distributions; Mixture of Gaussians; Optimal bounds; Sample complexity; Stochastic block models; Usual assumptions; Vocabulary size, Stochastic models |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation Division of Interdisciplinary Sciences > Robert Bosch Centre for Cyber Physical Systems |
| Date Deposited: | 04 Aug 2021 05:51 |
| Last Modified: | 04 Aug 2021 05:51 |
| URI: | http://eprints.iisc.ac.in/id/eprint/68984 |
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