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Durk Kingma

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8 papers

2 author rows

ICML Conference 2021 Conference Paper

On Linear Identifiability of Learned Representations

Geoffrey Roeder
Luke Metz
Durk Kingma

Identifiability is a desirable property of a statistical model: it implies that the true model parameters may be estimated to any desired precision, given sufficient computational resources and data. We study identifiability in the context of representation learning: discovering nonlinear data representations that are optimal with respect to some downstream task. When parameterized as deep neural networks, such representation functions lack identifiability in parameter space, because they are over-parameterized by design. In this paper, building on recent advances in nonlinear Independent Components Analysis, we aim to rehabilitate identifiability by showing that a large family of discriminative models are in fact identifiable in function space, up to a linear indeterminacy. Many models for representation learning in a wide variety of domains have been identifiable in this sense, including text, images and audio, state-of-the-art at time of publication. We derive sufficient conditions for linear identifiability and provide empirical support for the result on both simulated and real-world data.

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ICLR Conference 2020 Conference Paper

VideoFlow: A Conditional Flow-Based Model for Stochastic Video Generation

Manoj Kumar 0019
Mohammad Babaeizadeh
Dumitru Erhan
Chelsea Finn
Sergey Levine
Laurent Dinh
Durk Kingma

Generative models that can model and predict sequences of future events can, in principle, learn to capture complex real-world phenomena, such as physical interactions. However, a central challenge in video prediction is that the future is highly uncertain: a sequence of past observations of events can imply many possible futures. Although a number of recent works have studied probabilistic models that can represent uncertain futures, such models are either extremely expensive computationally as in the case of pixel-level autoregressive models, or do not directly optimize the likelihood of the data. To our knowledge, our work is the first to propose multi-frame video prediction with normalizing flows, which allows for direct optimization of the data likelihood, and produces high-quality stochastic predictions. We describe an approach for modeling the latent space dynamics, and demonstrate that flow-based generative models offer a viable and competitive approach to generative modeling of video.

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NeurIPS Conference 2018 Conference Paper

Glow: Generative Flow with Invertible 1x1 Convolutions

Durk Kingma
Prafulla Dhariwal

Flow-based generative models are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood and qualitative sample quality. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient synthesis of large and subjectively realistic-looking images.

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NeurIPS Conference 2016 Conference Paper

Improved Variational Inference with Inverse Autoregressive Flow

Durk Kingma
Tim Salimans
Rafal Jozefowicz
Xi Chen
Ilya Sutskever
Max Welling

The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed flow consists of a chain of invertible transformations, where each transformation is based on an autoregressive neural network. In experiments, we show that IAF significantly improves upon diagonal Gaussian approximate posteriors. In addition, we demonstrate that a novel type of variational autoencoder, coupled with IAF, is competitive with neural autoregressive models in terms of attained log-likelihood on natural images, while allowing significantly faster synthesis.

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NeurIPS Conference 2016 Conference Paper

Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks

Tim Salimans
Durk Kingma

We present weight normalization: a reparameterization of the weight vectors in a neural network that decouples the length of those weight vectors from their direction. By reparameterizing the weights in this way we improve the conditioning of the optimization problem and we speed up convergence of stochastic gradient descent. Our reparameterization is inspired by batch normalization but does not introduce any dependencies between the examples in a minibatch. This means that our method can also be applied successfully to recurrent models such as LSTMs and to noise-sensitive applications such as deep reinforcement learning or generative models, for which batch normalization is less well suited. Although our method is much simpler, it still provides much of the speed-up of full batch normalization. In addition, the computational overhead of our method is lower, permitting more optimization steps to be taken in the same amount of time. We demonstrate the usefulness of our method on applications in supervised image recognition, generative modelling, and deep reinforcement learning.

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NeurIPS Conference 2015 Conference Paper

Variational Dropout and the Local Reparameterization Trick

Durk Kingma
Tim Salimans
Max Welling

We explore an as yet unexploited opportunity for drastically improving the efficiency of stochastic gradient variational Bayes (SGVB) with global model parameters. Regular SGVB estimators rely on sampling of parameters once per minibatch of data, and have variance that is constant w. r. t. the minibatch size. The efficiency of such estimators can be drastically improved upon by translating uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such reparameterizations with local noise can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. We find an important connection with regularization by dropout: the original Gaussian dropout objective corresponds to SGVB with local noise, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose \emph{variational dropout}, a generalization of Gaussian dropout, but with a more flexibly parameterized posterior, often leading to better generalization. The method is demonstrated through several experiments.

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NeurIPS Conference 2014 Conference Paper

Semi-supervised Learning with Deep Generative Models

Durk Kingma
Shakir Mohamed
Danilo Jimenez Rezende
Max Welling

The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances in variational methods can be used to provide significant improvements, making generative approaches highly competitive for semi-supervised learning.

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NeurIPS Conference 2010 Conference Paper

Regularized estimation of image statistics by Score Matching

Durk Kingma
Yann Cun

Score Matching is a recently-proposed criterion for training high-dimensional density models for which maximum likelihood training is intractable. It has been applied to learning natural image statistics but has so-far been limited to simple models due to the difficulty of differentiating the loss with respect to the model parameters. We show how this differentiation can be automated with an extended version of the double-backpropagation algorithm. In addition, we introduce a regularization term for the Score Matching loss that enables its use for a broader range of problem by suppressing instabilities that occur with finite training sample sizes and quantized input values. Results are reported for image denoising and super-resolution.

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