Imputation across image inpainting and feature imputation in synthetic and Our models achieve state-of-the-art performance in both single and multiple Extensive empirical evaluations show that Imputation by introducing an auxiliary objective that provides a principled We apply AC-Flow to the imputation ofįeatures, and also develop a unified platform for both multiple and single (AC-Flow), that can be conditioned on arbitrary subsets of observed covariates, Of variables based) flow generative models, arbitrary conditioning flow models Yielding all conditional distributions p(x_u | x_o) (for arbitrary x_u) Instead, in this work we develop a model that is capable of Traditional conditional approaches provide a modelįor a fixed set of covariates conditioned on another fixed set of observedĬovariates. Spurred on by recent impressive results, there has been a surge in interest for generative probabilistic modeling in machine learning. These models learn an approximation of the underlying data distribution and are capable of drawing realistic samples from it. ![]() Generative models have a multitude of potential applications, including image restoration, agent planning, and unsupervised representation learning. In this work, we propose a framework, arbitrary conditioning flow models (AC-Flow), to construct generative models that However, most generative approaches are solely focused on the joint distribution of features, p ( x ), and are opaque in the conditional dependencies that are carried among subsets of features. Yield tractable (analytically available) conditional likelihoods p ( x u ∣ x o ) of an arbitrary subset of covariates, x u, given the remaining observed covariates x o. We focus on the use of AC-Flow for the purpose of imputation, where we infer possible values of x u, given observed values x o both in general real-valued data and images (for inpainting). 1) We propose a novel extension of flow-based generative models to model the conditional distribution of arbitrary unobserved covariates in data imputation tasks. Our method is the first to develop invertible transformations that operate on an arbitrary set of covariates. 2) We strengthen a flow-based model by using a novel autoregressive conditional likelihood. ![]() 3) We propose a novel penalty to generate a single imputed “best guess” for models without an analytically available mean. 4) We run extensive empirical studies and show that AC-Flow achieves state-of-the-art performance for both missing feature imputation and image inpainting on benchmark real-world datasets. (a) general formulationįigure 1: Conditional transformations used in AC-Flow. ![]() ![]() Grayed out boxes represent missing covariates. Checkerboarded boxes in (b) belong to unobserved dimensions, but are used as conditioning in the affine coupling transformation. Where q x o, b is a transformation on the unobserved covariates x u with respect to the observed covariates x o and binary mask b as demonstrated in Fig.
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