@InProceedings{8902708,
  author = {P. M. Baggenstoss},
  booktitle = {2019 27th European Signal Processing Conference (EUSIPCO)},
  title = {Applications of Projected Belief Networks (PBN)},
  year = {2019},
  pages = {1-5},
  abstract = {The projected belief network (PBN) is a layered generative network, with tractable likelihood function (LF) that can be trained by gradient ascent as a probability density function (PDF) estimator and classifier. The PBN is derived from a feed-forward neural network (FF-NN) by finding the generative network that implements the probability distribution with maximum entropy (MaxEnt) consistent with the knowledge of the distribution at the output of the FF-NN. The FF-NN, from which the PBN is derived, is a complementary feature extractor that exactly recovers the PBN's hidden variables. This paper presents a multi-layer PBN and a deterministic PBN that are tested using a subset of MNIST data set. When the deterministic PBN is combined with the dual FF-NN, it forms an auto-encoder that achieves much lower reconstruction error on testing data than the equivalent conventional network and functions significantly better as a classifier.},
  keywords = {belief networks;feature extraction;feedforward neural nets;gradient methods;learning (artificial intelligence);maximum entropy methods;maximum likelihood estimation;probability;projected belief networks;layered generative network;tractable likelihood function;probability density function estimator;feed-forward neural network;probability distribution;PBN's hidden variables;multilayer PBN;deterministic PBN;dual FF-NN;equivalent conventional network;maximum entropy;MNIST data set;Neural networks;Feature extraction;Data models;Europe;Signal processing;Entropy;Stochastic processes},
  doi = {10.23919/EUSIPCO.2019.8902708},
  issn = {2076-1465},
  month = {Sep.},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570529856.pdf},
}

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The FF-NN, from which the PBN is derived, is a complementary feature extractor that exactly recovers the PBN's hidden variables. This paper presents a multi-layer PBN and a deterministic PBN that are tested using a subset of MNIST data set. 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M. Baggenstoss},\n booktitle = {2019 27th European Signal Processing Conference (EUSIPCO)},\n title = {Applications of Projected Belief Networks (PBN)},\n year = {2019},\n pages = {1-5},\n abstract = {The projected belief network (PBN) is a layered generative network, with tractable likelihood function (LF) that can be trained by gradient ascent as a probability density function (PDF) estimator and classifier. The PBN is derived from a feed-forward neural network (FF-NN) by finding the generative network that implements the probability distribution with maximum entropy (MaxEnt) consistent with the knowledge of the distribution at the output of the FF-NN. The FF-NN, from which the PBN is derived, is a complementary feature extractor that exactly recovers the PBN's hidden variables. This paper presents a multi-layer PBN and a deterministic PBN that are tested using a subset of MNIST data set. 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