Generalization Analysis of Deep Non-linear Matrix Completion

Result code in IS VaVaI

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Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Generalization Analysis of Deep Non-linear Matrix Completion

Original language description

We provide generalization bounds for matrix completion with Schatten ???? quasi-norm constraints, which is equivalent to deep matrix factorization with Frobenius constraints. In the uniform sampling regime, the sample complexity scales like ????˜(????????) where ???? is the size of the matrix and ???? is a constraint of the same order as the ground truth rank in the isotropic case. In the distribution-free setting, the bounds scale as ????˜(????1-????2????1+????2), which reduces to the familiar ????root ????32 for ????=1 . Furthermore, we provide an analogue of the weighted trace norm for this setting which brings the sample complexity down to ????˜(????????) in all cases. We then present a non-linear model, Functionally Rescaled Matrix Completion (FRMC) which applies a single trainable function from ℝ->ℝ to each entry of a latent matrix, and prove that this adds only negligible terms of the overall sample complexity, whilst experiments demonstrate that this simple model improvement already leads to significant gains on real data. We also provide extensions of our results to various neural architectures, thereby providing the first comprehensive uniform convergence PAC analysis of neural network matrix completion.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Proceedings of Machine Learning Research

ISBN

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ISSN

2640-3498

e-ISSN

2640-3498

Number of pages

71

Pages from-to

26290-26360

Publisher name

Proceedings of Machine Learning Research

Place of publication

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Event location

Vienna

Event date

Jul 21, 2024

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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