arXiv subjects

Ullrich Köthe

Publications and source records attributed to Ullrich Köthe.

At least 37 records · Page 2Linked to original sources

arXiv2024

Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference

We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the marginal likelihood based on approximate representations of the joint model. Upon perfect approximation, the marginal likelihood is constant across all parameter values by definition. However, errors in approximate inference lead to undesirable variance in the marginal likelihood estimates across different parameter values. We penalize violations of this symmetry with a \textit{self-consistency loss} which significantly improves the quality of approximate inference in low data regimes and can be used to augment the training of popular neural density estimators. We apply our method to a number of synthetic problems and realistic scientific models, discovering notable advantages in the context of both neural posterior and likelihood approximation.

cs.LG↗

arXiv2024

Lifting Architectural Constraints of Injective Flows

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise. Injective Flows fix this by jointly learning a manifold and the distribution on it. So far, they have been limited by restrictive architectures and/or high computational cost. We lift both constraints by a new efficient estimator for the maximum likelihood loss, compatible with free-form bottleneck architectures. We further show that naively learning both the data manifold and the distribution on it can lead to divergent solutions, and use this insight to motivate a stable maximum likelihood training objective. We perform extensive experiments on toy, tabular and image data, demonstrating the competitive performance of the resulting model.

cs.LG↗

arXiv2024

Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigation

Recent advances in probabilistic deep learning enable efficient amortized Bayesian inference in settings where the likelihood function is only implicitly defined by a simulation program (simulation-based inference; SBI). But how faithful is such inference if the simulation represents reality somewhat inaccurately, that is, if the true system behavior at test time deviates from the one seen during training? We conceptualize the types of such model misspecification arising in SBI and systematically investigate how the performance of neural posterior approximators gradually deteriorates as a consequence, making inference results less and less trustworthy. To notify users about this problem, we propose a new misspecification measure that can be trained in an unsupervised fashion (i.e., without training data from the true distribution) and reliably detects model misspecification at test time. Our experiments clearly demonstrate the utility of our new measure both on toy examples with an analytical ground-truth and on representative scientific tasks in cell biology, cognitive decision making, disease outbreak dynamics, and computer vision. We show how the proposed misspecification test warns users about suspicious outputs, raises an alarm when predictions are not trustworthy, and guides model designers in their search for better simulators.

cs.LG↗

arXiv2024

Free-form Flows: Make Any Architecture a Normalizing Flow

Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure that uses an efficient estimator for the gradient of the change of variables formula. This enables any dimension-preserving neural network to serve as a generative model through maximum likelihood training. Our approach allows placing the emphasis on tailoring inductive biases precisely to the task at hand. Specifically, we achieve excellent results in molecule generation benchmarks utilizing $E(n)$-equivariant networks. Moreover, our method is competitive in an inverse problem benchmark, while employing off-the-shelf ResNet architectures.

cs.LG↗

arXiv2024

DALSA: Domain Adaptation for Supervised Learning From Sparsely Annotated MR Images

We propose a new method that employs transfer learning techniques to effectively correct sampling selection errors introduced by sparse annotations during supervised learning for automated tumor segmentation. The practicality of current learning-based automated tissue classification approaches is severely impeded by their dependency on manually segmented training databases that need to be recreated for each scenario of application, site, or acquisition setup. The comprehensive annotation of reference datasets can be highly labor-intensive, complex, and error-prone. The proposed method derives high-quality classifiers for the different tissue classes from sparse and unambiguous annotations and employs domain adaptation techniques for effectively correcting sampling selection errors introduced by the sparse sampling. The new approach is validated on labeled, multi-modal MR images of 19 patients with malignant gliomas and by comparative analysis on the BraTS 2013 challenge data sets. Compared to training on fully labeled data, we reduced the time for labeling and training by a factor greater than 70 and 180 respectively without sacrificing accuracy. This dramatically eases the establishment and constant extension of large annotated databases in various scenarios and imaging setups and thus represents an important step towards practical applicability of learning-based approaches in tissue classification.

eess.IV↗

arXiv2023

Neural Superstatistics for Bayesian Estimation of Dynamic Cognitive Models

Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension and estimate the resulting dynamics from a superstatistics perspective. Such a model entails a hierarchy between a low-level observation model and a high-level transition model. The observation model describes the local behavior of a system, and the transition model specifies how the parameters of the observation model evolve over time. To overcome the estimation challenges resulting from the complexity of superstatistical models, we develop and validate a simulation-based deep learning method for Bayesian inference, which can recover both time-varying and time-invariant parameters. We first benchmark our method against two existing frameworks capable of estimating time-varying parameters. We then apply our method to fit a dynamic version of the diffusion decision model to long time series of human response times data. Our results show that the deep learning approach is very efficient in capturing the temporal dynamics of the model. Furthermore, we show that the erroneous assumption of static or homogeneous parameters will hide important temporal information.

stat.ME↗

arXiv2023

A Review of Change of Variable Formulas for Generative Modeling

Change-of-variables (CoV) formulas allow to reduce complicated probability densities to simpler ones by a learned transformation with tractable Jacobian determinant. They are thus powerful tools for maximum-likelihood learning, Bayesian inference, outlier detection, model selection, etc. CoV formulas have been derived for a large variety of model types, but this information is scattered over many separate works. We present a systematic treatment from the unifying perspective of encoder/decoder architectures, which collects 28 CoV formulas in a single place, reveals interesting relationships between seemingly diverse methods, emphasizes important distinctions that are not always clear in the literature, and identifies surprising gaps for future research.

cs.LG↗

arXiv2023

BayesFlow: Amortized Bayesian Workflows With Neural Networks

Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis. Typical problems in Bayesian workflows are the approximation of intractable posterior distributions for diverse model types and the comparison of competing models of the same process in terms of their complexity and predictive performance. This manuscript introduces the Python library BayesFlow for simulation-based training of established neural network architectures for amortized data compression and inference. Amortized Bayesian inference, as implemented in BayesFlow, enables users to train custom neural networks on model simulations and re-use these networks for any subsequent application of the models. Since the trained networks can perform inference almost instantaneously, the upfront neural network training is quickly amortized.

cs.LG↗

arXiv2023

On the Convergence Rate of Gaussianization with Random Rotations

Gaussianization is a simple generative model that can be trained without backpropagation. It has shown compelling performance on low dimensional data. As the dimension increases, however, it has been observed that the convergence speed slows down. We show analytically that the number of required layers scales linearly with the dimension for Gaussian input. We argue that this is because the model is unable to capture dependencies between dimensions. Empirically, we find the same linear increase in cost for arbitrary input $p(x)$, but observe favorable scaling for some distributions. We explore potential speed-ups and formulate challenges for further research.

cs.LG↗

arXiv2023

Finding Competence Regions in Domain Generalization

We investigate a "learning to reject" framework to address the problem of silent failures in Domain Generalization (DG), where the test distribution differs from the training distribution. Assuming a mild distribution shift, we wish to accept out-of-distribution (OOD) data from a new domain whenever a model's estimated competence foresees trustworthy responses, instead of rejecting OOD data outright. Trustworthiness is then predicted via a proxy incompetence score that is tightly linked to the performance of a classifier. We present a comprehensive experimental evaluation of existing proxy scores as incompetence scores for classification and highlight the resulting trade-offs between rejection rate and accuracy gain. For comparability with prior work, we focus on standard DG benchmarks and consider the effect of measuring incompetence via different learned representations in a closed versus an open world setting. Our results suggest that increasing incompetence scores are indeed predictive of reduced accuracy, leading to significant improvements of the average accuracy below a suitable incompetence threshold. However, the scores are not yet good enough to allow for a favorable accuracy/rejection trade-off in all tested domains. Surprisingly, our results also indicate that classifiers optimized for DG robustness do not outperform a naive Empirical Risk Minimization (ERM) baseline in the competence region, that is, where test samples elicit low incompetence scores.

cs.LG↗

arXiv2023

JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models

This work proposes ``jointly amortized neural approximation'' (JANA) of intractable likelihood functions and posterior densities arising in Bayesian surrogate modeling and simulation-based inference. We train three complementary networks in an end-to-end fashion: 1) a summary network to compress individual data points, sets, or time series into informative embedding vectors; 2) a posterior network to learn an amortized approximate posterior; and 3) a likelihood network to learn an amortized approximate likelihood. Their interaction opens a new route to amortized marginal likelihood and posterior predictive estimation -- two important ingredients of Bayesian workflows that are often too expensive for standard methods. We benchmark the fidelity of JANA on a variety of simulation models against state-of-the-art Bayesian methods and propose a powerful and interpretable diagnostic for joint calibration. In addition, we investigate the ability of recurrent likelihood networks to emulate complex time series models without resorting to hand-crafted summary statistics.

cs.LG↗

arXiv2023

Positive Difference Distribution for Image Outlier Detection using Normalizing Flows and Contrastive Data

Detecting test data deviating from training data is a central problem for safe and robust machine learning. Likelihoods learned by a generative model, e.g., a normalizing flow via standard log-likelihood training, perform poorly as an outlier score. We propose to use an unlabelled auxiliary dataset and a probabilistic outlier score for outlier detection. We use a self-supervised feature extractor trained on the auxiliary dataset and train a normalizing flow on the extracted features by maximizing the likelihood on in-distribution data and minimizing the likelihood on the contrastive dataset. We show that this is equivalent to learning the normalized positive difference between the in-distribution and the contrastive feature density. We conduct experiments on benchmark datasets and compare to the likelihood, the likelihood ratio and state-of-the-art anomaly detection methods.

cs.LG↗

arXiv2023

Training Invertible Neural Networks as Autoencoders

Autoencoders are able to learn useful data representations in an unsupervised matter and have been widely used in various machine learning and computer vision tasks. In this work, we present methods to train Invertible Neural Networks (INNs) as (variational) autoencoders which we call INN (variational) autoencoders. Our experiments on MNIST, CIFAR and CelebA show that for low bottleneck sizes our INN autoencoder achieves results similar to the classical autoencoder. However, for large bottleneck sizes our INN autoencoder outperforms its classical counterpart. Based on the empirical results, we hypothesize that INN autoencoders might not have any intrinsic information loss and thereby are not bounded to a maximal number of layers (depth) after which only suboptimal results can be achieved.

cs.LG↗

arXiv2023

Unsupervised Domain Transfer with Conditional Invertible Neural Networks

Synthetic medical image generation has evolved as a key technique for neural network training and validation. A core challenge, however, remains in the domain gap between simulations and real data. While deep learning-based domain transfer using Cycle Generative Adversarial Networks and similar architectures has led to substantial progress in the field, there are use cases in which state-of-the-art approaches still fail to generate training images that produce convincing results on relevant downstream tasks. Here, we address this issue with a domain transfer approach based on conditional invertible neural networks (cINNs). As a particular advantage, our method inherently guarantees cycle consistency through its invertible architecture, and network training can efficiently be conducted with maximum likelihood training. To showcase our method's generic applicability, we apply it to two spectral imaging modalities at different scales, namely hyperspectral imaging (pixel-level) and photoacoustic tomography (image-level). According to comprehensive experiments, our method enables the generation of realistic spectral data and outperforms the state of the art on two downstream classification tasks (binary and multi-class). cINN-based domain transfer could thus evolve as an important method for realistic synthetic data generation in the field of spectral imaging and beyond.

eess.IV↗

arXiv2023

Towards Learned Emulation of Interannual Water Isotopologue Variations in General Circulation Models

Simulating abundances of stable water isotopologues, i.e. molecules differing in their isotopic composition, within climate models allows for comparisons with proxy data and, thus, for testing hypotheses about past climate and validating climate models under varying climatic conditions. However, many models are run without explicitly simulating water isotopologues. We investigate the possibility to replace the explicit physics-based simulation of oxygen isotopic composition in precipitation using machine learning methods. These methods estimate isotopic composition at each time step for given fields of surface temperature and precipitation amount. We implement convolutional neural networks (CNNs) based on the successful UNet architecture and test whether a spherical network architecture outperforms the naive approach of treating Earth's latitude-longitude grid as a flat image. Conducting a case study on a last millennium run with the iHadCM3 climate model, we find that roughly 40\% of the temporal variance in the isotopic composition is explained by the emulations on interannual and monthly timescale, with spatially varying emulation quality. A modified version of the standard UNet architecture for flat images yields results that are equally good as the predictions by the spherical CNN. We test generalization to last millennium runs of other climate models and find that while the tested deep learning methods yield the best results on iHadCM3 data, the performance drops when predicting on other models and is comparable to simple pixel-wise linear regression. An extended choice of predictor variables and improving the robustness of learned climate--oxygen isotope relationships should be explored in future work.

physics.ao-ph↗

arXiv2022

Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks

Neural density estimators have proven remarkably powerful in performing efficient simulation-based Bayesian inference in various research domains. In particular, the BayesFlow framework uses a two-step approach to enable amortized parameter estimation in settings where the likelihood function is implicitly defined by a simulation program. But how faithful is such inference when simulations are poor representations of reality? In this paper, we conceptualize the types of model misspecification arising in simulation-based inference and systematically investigate the performance of the BayesFlow framework under these misspecifications. We propose an augmented optimization objective which imposes a probabilistic structure on the latent data space and utilize maximum mean discrepancy (MMD) to detect potentially catastrophic misspecifications during inference undermining the validity of the obtained results. We verify our detection criterion on a number of artificial and realistic misspecifications, ranging from toy conjugate models to complex models of decision making and disease outbreak dynamics applied to real data. Further, we show that posterior inference errors increase as a function of the distance between the true data-generating distribution and the typical set of simulations in the latent summary space. Thus, we demonstrate the dual utility of MMD as a method for detecting model misspecification and as a proxy for verifying the faithfulness of amortized Bayesian inference.

stat.ME↗

arXiv2022

Whitening Convergence Rate of Coupling-based Normalizing Flows

Coupling-based normalizing flows (e.g. RealNVP) are a popular family of normalizing flow architectures that work surprisingly well in practice. This calls for theoretical understanding. Existing work shows that such flows weakly converge to arbitrary data distributions. However, they make no statement about the stricter convergence criterion used in practice, the maximum likelihood loss. For the first time, we make a quantitative statement about this kind of convergence: We prove that all coupling-based normalizing flows perform whitening of the data distribution (i.e. diagonalize the covariance matrix) and derive corresponding convergence bounds that show a linear convergence rate in the depth of the flow. Numerical experiments demonstrate the implications of our theory and point at open questions.

cs.LG↗

arXiv2022

Content-Aware Differential Privacy with Conditional Invertible Neural Networks

Differential privacy (DP) has arisen as the gold standard in protecting an individual's privacy in datasets by adding calibrated noise to each data sample. While the application to categorical data is straightforward, its usability in the context of images has been limited. Contrary to categorical data the meaning of an image is inherent in the spatial correlation of neighboring pixels making the simple application of noise infeasible. Invertible Neural Networks (INN) have shown excellent generative performance while still providing the ability to quantify the exact likelihood. Their principle is based on transforming a complicated distribution into a simple one e.g. an image into a spherical Gaussian. We hypothesize that adding noise to the latent space of an INN can enable differentially private image modification. Manipulation of the latent space leads to a modified image while preserving important details. Further, by conditioning the INN on meta-data provided with the dataset we aim at leaving dimensions important for downstream tasks like classification untouched while altering other parts that potentially contain identifying information. We term our method content-aware differential privacy (CADP). We conduct experiments on publicly available benchmarking datasets as well as dedicated medical ones. In addition, we show the generalizability of our method to categorical data. The source code is publicly available at https://github.com/Cardio-AI/CADP.

cs.CR↗