Provable learning of noisy-or networks

Conference Paper

Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding parameters with the maximum likelihood is NP-hard even in very simple settings. In recent years, provably efficient algorithms were nevertheless developed for models with linear structures: topic models, mixture models, hidden Markov models, etc. These algorithms use matrix or tensor decomposition, and make some reasonable assumptions about the parameters of the underlying model. But matrix or tensor decomposition seems of little use when the latent variable model has nonlinearities. The current paper shows how to make progress: tensor decomposition is applied for learning the single-layer noisy or network, which is a textbook example of a Bayes net, and used for example in the classic QMR-DT software for diagnosing which disease(s) a patient may have by observing the symptoms he/she exhibits. The technical novelty here, which should be useful in other settings in future, is analysis of tensor decomposition in presence of systematic error (i.e., where the noise/error is correlated with the signal, and doesn't decrease as number of samples goes to infinity). This requires rethinking all steps of tensor decomposition methods from the ground up. For simplicity our analysis is stated assuming that the network parameters were chosen from a probability distribution but the method seems more generally applicable.

Full Text

Duke Authors

Cited Authors

  • Arora, S; Ge, R; Ma, T; Risteski, A

Published Date

  • June 19, 2017

Published In

Volume / Issue

  • Part F128415 /

Start / End Page

  • 1057 - 1066

International Standard Serial Number (ISSN)

  • 0737-8017

International Standard Book Number 13 (ISBN-13)

  • 9781450345286

Digital Object Identifier (DOI)

  • 10.1145/3055399.3055482

Citation Source

  • Scopus