Neural Autoregressive Flows

Huang, Chin-Wei; Krueger, David W.; Lacoste, Alexandre; Courville, Aaron

doi:10.48550/arxiv.1804.00779

Cited by 63 publications

(56 citation statements)

References 24 publications

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“…Learning the Darmois construction. To learn the Darmois construction from data, we use normalising flows, see [35,65]. Since Darmois solutions have triangular Jacobian (Remark 2.4), we use an architecture based on residual flows [16] which we constrain such that the Jacobian of the full model is triangular.…”

Section: Numerical Evaluation Of the C Ima Contrast For Spurious Nonl...mentioning

confidence: 99%

“…We remark that, while the possibility of using normalising flows to "learn" the Darmois construction is mentioned in [35,65], where a similar construction is mentioned in a theoretical argument to prove "universal approximation capacity for densities" for normalising flow models with triangular Jacobian, it has to the best of our knowledge not been tested empirically, since autoregressive modules with triangular Jacobian are typically used in combination with permutation, shuffling or linear layers which overall lead to architectures with a non-triangular Jacobian.…”

Section: E2 How To Implement the Darmois Constructionmentioning

confidence: 99%

“…In order for the Jacobian of g to be triangular, g n (z) should only depend on z n , g n−1 (z) should only depend on z n and z n−1 , and so on. To achieve this, we make the weight matrices block triangular as indicated in (34), (35), and (36).…”

Section: E2 How To Implement the Darmois Constructionmentioning

confidence: 99%

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Independent mechanism analysis, a new concept?

Gresele¹,

Kügelgen²,

Stimper³

et al. 2021

Preprint

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Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof. Unfortunately, when the mixing is nonlinear, the model is provably nonidentifiable, since statistical independence alone does not sufficiently constrain the problem. Identifiability can be recovered in settings where additional, typically observed variables are included in the generative process. We investigate an alternative path and consider instead including assumptions reflecting the principle of independent causal mechanisms exploited in the field of causality. Specifically, our approach is motivated by thinking of each source as independently influencing the mixing process. This gives rise to a framework which we term independent mechanism analysis. We provide theoretical and empirical evidence that our approach circumvents a number of nonidentifiability issues arising in nonlinear blind source separation. * Equal contribution.Preprint. Under review.

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Section: Numerical Evaluation Of the C Ima Contrast For Spurious Nonl...mentioning

confidence: 99%

Section: E2 How To Implement the Darmois Constructionmentioning

confidence: 99%

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Independent mechanism analysis, a new concept?

Gresele¹,

Kügelgen²,

Stimper³

et al. 2021

Preprint

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show abstract

“…Examples of neural architectures for normalizing flow are IAF [39], MAF [54], NICE [19], Real NVP [20], Glow [38], NAF [29] and BNAF [18]. We adapt Block Neural Autoregressive Flow (BNAF) in our implementation.…”

Section: Normalizing Flowmentioning

confidence: 99%

Visual Attention in Imaginative Agents

Rangrej,

Clark

2021

Preprint

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We present a recurrent agent who perceives surroundings through a series of discrete fixations. At each timestep, the agent imagines a variety of plausible scenes consistent with the fixation history. The next fixation is planned using uncertainty in the content of the imagined scenes. As time progresses, the agent becomes more certain about the content of the surrounding, and the variety in the imagined scenes reduces. The agent is built using a variational autoencoder and normalizing flows, and trained in an unsupervised manner on a proxy task of scene-reconstruction. The latent representations of the imagined scenes are found to be useful for performing pixel-level and scene-level tasks by higher-order modules. The agent is tested on various 2D and 3D datasets.

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“…Flow-based models [5,6,19,33,10,18,2,12,9,32,24] aim to learn a bijective mapping between the target space and the latent space. For a high-dimensional random variable (e.g., an image) x with distribution x ∼ p(x) and a latent variable z with simple tractable distribution z ∼ p(z) (e.g., multivariate Gaussian distribution), flow models generally use an invertible neural network f θ to transform x to z: z = f θ (x).…”

Section: Preliminariesmentioning

confidence: 99%

Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling

Liang¹,

Lugmayr²,

Zhang³

et al. 2021

Preprint

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Normalizing flows have recently demonstrated promising results for low-level vision tasks. For image superresolution (SR), it learns to predict diverse photo-realistic high-resolution (HR) images from the low-resolution (LR) image rather than learning a deterministic mapping. For image rescaling, it achieves high accuracy by jointly modelling the downscaling and upscaling processes. While existing approaches employ specialized techniques for these two tasks, we set out to unify them in a single formulation. In this paper, we propose the hierarchical conditional flow (HCFlow) as a unified framework for image SR and image rescaling. More specifically, HCFlow learns a bijective mapping between HR and LR image pairs by modelling the distribution of the LR image and the rest high-frequency component simultaneously. In particular, the high-frequency component is conditional on the LR image in a hierarchical manner. To further enhance the performance, other losses such as perceptual loss and GAN loss are combined with the commonly used negative loglikelihood loss in training. Extensive experiments on general image SR, face image SR and image rescaling have demonstrated that the proposed HCFlow achieves state-ofthe-art performance in terms of both quantitative metrics and visual quality.

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Neural Autoregressive Flows

Cited by 63 publications

References 24 publications

Independent mechanism analysis, a new concept?

Independent mechanism analysis, a new concept?

Visual Attention in Imaginative Agents

Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling

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