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## Abstract

Normalising flows (NFs) map two density functions via a differentiable bijection whose Jacobian determinant can be computed efficiently. Recently, as an alternative to handcrafted bijections, Huang et al. (2018) proposed neural autoregressive flow (NAF) which is a universal approximator for density functions. Their flow is a neural network (NN) whose parameters are predicted by another NN. The latter grows quadratically with the size of the former and thus an efficient technique for parametrization is needed.

We propose block neural autoregressive flow (BNAF), a much more compact universal approximator of density functions, where we model a bijection directly using a single feedforward network. Invertibility is ensured by carefully designing each affine transformation with block matrices that make the flow autoregressive and (strictly) monotone. We compare B-NAF to NAF and other established flows on density estimation and approximate inference for latent variable models. Our proposed flow is competitive across datasets while using orders of magnitude fewer parameters.

We propose block neural autoregressive flow (BNAF), a much more compact universal approximator of density functions, where we model a bijection directly using a single feedforward network. Invertibility is ensured by carefully designing each affine transformation with block matrices that make the flow autoregressive and (strictly) monotone. We compare B-NAF to NAF and other established flows on density estimation and approximate inference for latent variable models. Our proposed flow is competitive across datasets while using orders of magnitude fewer parameters.

Original language | English |
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Title of host publication | Proceedings of the Thirty-Fifth Conference on Uncertainty in Artificial Intelligence, UAI 2019 |

Subtitle of host publication | Tel Aviv, Israel, July 22-25, 2019 |

Place of Publication | Tel Aviv, Israel |

Number of pages | 13 |

Publication status | Published - 22 Jul 2019 |

Event | 35th Conference on Uncertainty in Artificial Intelligence, UAI 2019 - Tel Aviv, Israel Duration: 22 Jul 2019 → 25 Jul 2019 http://auai.org/uai2019/ |

### Conference

Conference | 35th Conference on Uncertainty in Artificial Intelligence, UAI 2019 |
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Abbreviated title | UAI 2019 |

Country/Territory | Israel |

City | Tel Aviv |

Period | 22/07/19 → 25/07/19 |

Internet address |

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