@conference {Radev2020,
	title = {BayesFlow: Learning complex stochastic models with invertible neural networks},
	year = {2020},
	abstract = {Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit likelihood function is not available. With this work, we propose a novel method for globally amortized Bayesian inference based on invertible neural networks which we call BayesFlow. The method uses simulation to learn a global estimator for the probabilistic mapping from observed data to underlying model parameters. A neural network pre-trained in this way can then, without additional training or optimization, infer full posteriors on arbitrary many real data sets involving the same model family. In addition, our method incorporates a summary network trained to embed the observed data into maximally informative summary statistics. Learning summary statistics from data makes the method applicable to modeling scenarios where standard inference techniques with hand-crafted summary statistics fail. We demonstrate the utility of BayesFlow on challenging intractable models from population dynamics, epidemiology, cognitive science and ecology. We argue that BayesFlow provides a general framework for building reusable Bayesian parameter estimation machines for any process model from which data can be simulated.},
	url = {http://arxiv.org/abs/2003.06281},
	author = {Radev, Stefan T. and Mertens, Ulf K. and Voss, Andreass and Lynton Ardizzone and K{\"o}the, Ullrich}
}
@article {Ardizzone2020,
	title = {Exact Information Bottleneck with Invertible Neural Networks: Getting the Best of Discriminative and Generative Modeling},
	year = {2020},
	month = {jan},
	abstract = {Generative models are more informative about underlying phenomena than discriminative ones and offer superior uncertainty quantification and out-of-distribution robustness. However, these advantages often come at the expense of reduced classification accuracy. The Information Bottleneck objective (IB) formulates this trade-off in a clean information-theoretic way, but its practical application is hampered by a lack of accurate high-dimensional estimators of mutual information (MI), its main constituent. To overcome this limitation, we develop the theory and methodology of IB-INNs, which optimize the IB objective by means of Invertible Neural Networks (INNs), without the need for approximations of MI. Our experiments show that IB-INNs allow for a precise adjustment of the generative/discriminative trade-off: They learn accurate models of the class conditional likelihoods, generalize well to unseen data and reliably detect out-of-distribution examples, while at the same time exhibiting classification accuracy close to purely discriminative feed-forward networks.},
	url = {http://arxiv.org/abs/2001.06448},
	author = {Lynton Ardizzone and Mackowiak, Radek and Carsten Rother and Ullrich K{\"o}the}
}
@techreport {Kruse2019,
	title = {Benchmarking Invertible Architectures on Inverse Problems},
	number = {i},
	year = {2019},
	abstract = {Recent work demonstrated that flow-based invert-ible neural networks are promising tools for solving ambiguous inverse problems. Following up on this, we investigate how ten invertible archi-tectures and related models fare on two intuitive, low-dimensional benchmark problems, obtaining the best results with coupling layers and simple autoencoders. We hope that our initial efforts inspire other researchers to evaluate their invertible architectures in the same setting and put forth additional benchmarks, so our evaluation may eventually grow into an official community challenge.},
	author = {Kruse, Jakob and Lynton Ardizzone and Carsten Rother and Ullrich K{\"o}the}
}
@article {Ardizzone2019,
	title = {Guided Image Generation with Conditional Invertible Neural Networks},
	year = {2019},
	abstract = {In this work, we address the task of natural image generation guided by a conditioning input. We introduce a new architecture called conditional invertible neural network (cINN). The cINN combines the purely generative INN model with an unconstrained feed-forward network, which efficiently preprocesses the conditioning input into useful features. All parameters of the cINN are jointly optimized with a stable, maximum likelihood-based training procedure. By construction, the cINN does not experience mode collapse and generates diverse samples, in contrast to e.g. cGANs. At the same time our model produces sharp images since no reconstruction loss is required, in contrast to e.g. VAEs. We demonstrate these properties for the tasks of MNIST digit generation and image colorization. Furthermore, we take advantage of our bi-directional cINN architecture to explore and manipulate emergent properties of the latent space, such as changing the image style in an intuitive way.},
	url = {http://arxiv.org/abs/1907.02392},
	author = {Lynton Ardizzone and Carsten L{\"u}th and Kruse, Jakob and Carsten Rother and Ullrich K{\"o}the}
}
@article {Ardizzone2019a,
	title = {Guided Image Generation with Conditional Invertible Neural Networks},
	year = {2019},
	abstract = {In this work, we address the task of natural image generation guided by a conditioning input. We introduce a new architecture called conditional invertible neural network (cINN). The cINN combines the purely generative INN model with an unconstrained feed-forward network, which efficiently preprocesses the conditioning input into useful features. All parameters of the cINN are jointly optimized with a stable, maximum likelihood-based training procedure. By construction, the cINN does not experience mode collapse and generates diverse samples, in contrast to e.g. cGANs. At the same time our model produces sharp images since no reconstruction loss is required, in contrast to e.g. VAEs. We demonstrate these properties for the tasks of MNIST digit generation and image colorization. Furthermore, we take advantage of our bi-directional cINN architecture to explore and manipulate emergent properties of the latent space, such as changing the image style in an intuitive way.},
	url = {http://arxiv.org/abs/1907.02392},
	author = {Lynton Ardizzone and Carsten L{\"u}th and Kruse, Jakob and Carsten Rother and Ullrich K{\"o}the}
}
@conference {Adler2019,
	title = {Out of Distribution Detection for Intra-operative Functional Imaging},
	booktitle = {MICCAI UNSURE Workshop 2019},
	volume = {11840 LNCS},
	year = {2019},
	pages = {75{\textendash}82},
	abstract = {Multispectral optical imaging is becoming a key tool in the operating room. Recent research has shown that machine learning algorithms can be used to convert pixel-wise reflectance measurements to tissue parameters, such as oxygenation. However, the accuracy of these algorithms can only be guaranteed if the spectra acquired during surgery match the ones seen during training. It is therefore of great interest to detect so-called out of distribution (OoD) spectra to prevent the algorithm from presenting spurious results. In this paper we present an information theory based approach to OoD detection based on the widely applicable information criterion (WAIC). Our work builds upon recent methodology related to invertible neural networks (INN). Specifically, we make use of an ensemble of INNs as we need their tractable Jacobians in order to compute the WAIC. Comprehensive experiments with in silico, and in vivo multispectral imaging data indicate that our approach is well-suited for OoD detection. Our method could thus be an important step towards reliable functional imaging in the operating room.},
	issn = {16113349},
	doi = {10.1007/978-3-030-32689-0_8},
	author = {Adler, Tim J and Ayala, Leonardo and Lynton Ardizzone and Kenngott, Hannes G and Vemuri, Anant and M{\"u}ller-Stich, Beat P and Carsten Rother and Ullrich K{\"o}the and Maier-Hein, Lena}
}
