@InProceedings{8081323,
  author = {P. M. Baggenstoss},
  booktitle = {2017 25th European Signal Processing Conference (EUSIPCO)},
  title = {Evaluating the RBM without integration using PDF projection},
  year = {2017},
  pages = {828-832},
  abstract = {In this paper, we apply probability density function (PDF) projection to arrive at an exact closed-form expression for the marginal distribution of the visible data of a restricted Boltzmann machine (RBM) without requiring integrating over the distribution of the hidden variables or needing to know the partition function. We express the visible data marginal as a projected PDF based on a set of sufficient statistics. When a Gaussian mixture model (GMM) is used to estimate the PDF of the sufficient statistics, then we arrive at a combined RBM/GMM model that serves as a general-purpose PDF estimator and Bayesian classifier. The approach extends recusively to compute the input distribution of a multi-layer network. We demonstrate the method using a reduced subset of the MNIST handwritten character data set.},
  keywords = {Bayes methods;Boltzmann machines;data analysis;Gaussian processes;handwritten character recognition;optical character recognition;probability;PDF projection;probability density function projection;closed-form expression;marginal distribution;visible data;restricted Boltzmann machine;hidden variables;partition function;projected PDF;sufficient statistics;Gaussian mixture model;general-purpose PDF estimator;MNIST handwritten character data set;combined RBM-GMM model;multilayer network;Bayes methods;Europe;Signal processing;Probability density function;Computational modeling;Gaussian mixture model},
  doi = {10.23919/EUSIPCO.2017.8081323},
  issn = {2076-1465},
  month = {Aug},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2017/papers/1570342845.pdf},
}

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When a Gaussian mixture model (GMM) is used to estimate the PDF of the sufficient statistics, then we arrive at a combined RBM/GMM model that serves as a general-purpose PDF estimator and Bayesian classifier. The approach extends recusively to compute the input distribution of a multi-layer network. 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Baggenstoss},\n booktitle = {2017 25th European Signal Processing Conference (EUSIPCO)},\n title = {Evaluating the RBM without integration using PDF projection},\n year = {2017},\n pages = {828-832},\n abstract = {In this paper, we apply probability density function (PDF) projection to arrive at an exact closed-form expression for the marginal distribution of the visible data of a restricted Boltzmann machine (RBM) without requiring integrating over the distribution of the hidden variables or needing to know the partition function. We express the visible data marginal as a projected PDF based on a set of sufficient statistics. When a Gaussian mixture model (GMM) is used to estimate the PDF of the sufficient statistics, then we arrive at a combined RBM/GMM model that serves as a general-purpose PDF estimator and Bayesian classifier. The approach extends recusively to compute the input distribution of a multi-layer network. 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