Addressing Misspecification in Simulation-based Inference through Data-driven Calibration

Driven by steady progress in generative modeling, simulation-based inference (SBI) has enabled inference over stochastic simulators. However, recent work has demonstrated that model misspecification can harm SBI's reliability. This work introduces robust posterior estimation (ROPE), a framework that overcomes model misspecification with a small real-world calibration set of ground truth parameter measurements. We formalize the misspecification gap as the solution of an optimal transport problem between learned representations of real-world and simulated observations. Assuming the prior distribution over the parameters of interest is known and well-specified, our method offers a controllable balance between calibrated uncertainty and informative inference under all possible misspecifications of the simulator. Our empirical results on four synthetic tasks and two real-world problems demonstrate that ROPE outperforms baselines and consistently returns informative and calibrated credible intervals.

Simulation-based Inference for Cardiovascular Models

Over the past decades, hemodynamics simulators have steadily evolved and have become tools of choice for studying cardiovascular systems in-silico. While such tools are routinely used to simulate whole-body hemodynamics from physiological parameters, solving the corresponding inverse problem of mapping waveforms back to plausible physiological parameters remains both promising and challenging. Motivated by advances in simulation-based inference (SBI), we cast this inverse problem as statistical inference. In contrast to alternative approaches, SBI provides \textit{posterior distributions} for the parameters of interest, providing a \textit{multi-dimensional} representation of uncertainty for \textit{individual} measurements. We showcase this ability by performing an in-silico uncertainty analysis of five biomarkers of clinical interest comparing several measurement modalities. Beyond the corroboration of known facts, such as the feasibility of estimating heart rate, our study highlights the potential of estimating new biomarkers from standard-of-care measurements. SBI reveals practically relevant findings that cannot be captured by standard sensitivity analyses, such as the existence of sub-populations for which parameter estimation exhibits distinct uncertainty regimes. Finally, we study the gap between in-vivo and in-silico with the MIMIC-III waveform database and critically discuss how cardiovascular simulations can inform real-world data analysis.

Robust Hybrid Learning With Expert Augmentation

Hybrid modelling reduces the misspecification of expert models by combining them with machine learning (ML) components learned from data. Like for many ML algorithms, hybrid model performance guarantees are limited to the training distribution. Leveraging the insight that the expert model is usually valid even outside the training domain, we overcome this limitation by introducing a hybrid data augmentation strategy termed \textit{expert augmentation}. Based on a probabilistic formalization of hybrid modelling, we show why expert augmentation improves generalization. Finally, we validate the practical benefits of augmented hybrid models on a set of controlled experiments, modelling dynamical systems described by ordinary and partial differential equations.

Learning Invariant Representations with Missing Data

Spurious correlations allow flexible models to predict well during training but poorly on related test populations. Recent work has shown that models that satisfy particular independencies involving correlation-inducing \textit{nuisance} variables have guarantees on their test performance. Enforcing such independencies requires nuisances to be observed during training. However, nuisances, such as demographics or image background labels, are often missing. Enforcing independence on just the observed data does not imply independence on the entire population. Here we derive \acrshort{mmd} estimators used for invariance objectives under missing nuisances. On simulations and clinical data, optimizing through these estimates achieves test performance similar to using estimators that make use of the full data.

Exchanging Lessons Between Algorithmic Fairness and Domain Generalization

Standard learning approaches are designed to perform well on average for the data distribution available at training time. Developing learning approaches that are not overly sensitive to the training distribution is central to research on domain- or out-of-distribution generalization, robust optimization and fairness. In this work we focus on links between research on domain generalization and algorithmic fairness -- where performance under a distinct but related test distributions is studied -- and show how the two fields can be mutually beneficial. While domain generalization methods typically rely on knowledge of disjoint "domains" or "environments", "sensitive" label information indicating which demographic groups are at risk of discrimination is often used in the fairness literature. Drawing inspiration from recent fairness approaches that improve worst-case performance without knowledge of sensitive groups, we propose a novel domain generalization method that handles the more realistic scenario where environment partitions are not provided. We then show theoretically and empirically how different partitioning schemes can lead to increased or decreased generalization performance, enabling us to outperform Invariant Risk Minimization with handcrafted environments in multiple cases. We also show how a re-interpretation of IRMv1 allows us for the first time to directly optimize a common fairness criterion, group-sufficiency, and thereby improve performance on a fair prediction task.

Understanding and mitigating exploding inverses in invertible neural networks

Invertible neural networks (INNs) have been used to design generative models, implement memory-saving gradient computation, and solve inverse problems. In this work, we show that commonly-used INN architectures suffer from exploding inverses and are thus prone to becoming numerically non-invertible. Across a wide range of INN use-cases, we reveal failures including the non-applicability of the change-of-variables formula on in- and out-of-distribution (OOD) data, incorrect gradients for memory-saving backprop, and the inability to sample from normalizing flow models. We further derive bi-Lipschitz properties of atomic building blocks of common architectures. These insights into the stability of INNs then provide ways forward to remedy these failures. For tasks where local invertibility is sufficient, like memory-saving backprop, we propose a flexible and efficient regularizer. For problems where global invertibility is necessary, such as applying normalizing flows on OOD data, we show the importance of designing stable INN building blocks.

Shortcut Learning in Deep Neural Networks

Deep learning has triggered the current rise of artificial intelligence and is the workhorse of today's machine intelligence. Numerous success stories have rapidly spread all over science, industry and society, but its limitations have only recently come into focus. In this perspective we seek to distil how many of deep learning's problem can be seen as different symptoms of the same underlying problem: shortcut learning. Shortcuts are decision rules that perform well on standard benchmarks but fail to transfer to more challenging testing conditions, such as real-world scenarios. Related issues are known in Comparative Psychology, Education and Linguistics, suggesting that shortcut learning may be a common characteristic of learning systems, biological and artificial alike. Based on these observations, we develop a set of recommendations for model interpretation and benchmarking, highlighting recent advances in machine learning to improve robustness and transferability from the lab to real-world applications.

Fundamental Tradeoffs between Invariance and Sensitivity to Adversarial Perturbations

Adversarial examples are malicious inputs crafted to induce misclassification. Commonly studied sensitivity-based adversarial examples introduce semantically-small changes to an input that result in a different model prediction. This paper studies a complementary failure mode, invariance-based adversarial examples, that introduce minimal semantic changes that modify an input's true label yet preserve the model's prediction. We demonstrate fundamental tradeoffs between these two types of adversarial examples. We show that defenses against sensitivity-based attacks actively harm a model's accuracy on invariance-based attacks, and that new approaches are needed to resist both attack types. In particular, we break state-of-the-art adversarially-trained and certifiably-robust models by generating small perturbations that the models are (provably) robust to, yet that change an input's class according to human labelers. Finally, we formally show that the existence of excessively invariant classifiers arises from the presence of overly-robust predictive features in standard datasets.

How to train your neural ODE

Training neural ODEs on large datasets has not been tractable due to the necessity of allowing the adaptive numerical ODE solver to refine its step size to very small values. In practice this leads to dynamics equivalent to many hundreds or even thousands of layers. In this paper, we overcome this apparent difficulty by introducing a theoretically-grounded combination of both optimal transport and stability regularizations which encourage neural ODEs to prefer simpler dynamics out of all the dynamics that solve a problem well. Simpler dynamics lead to faster convergence and to fewer discretizations of the solver, considerably decreasing wall-clock time without loss in performance. Our approach allows us to train neural ODE based generative models to the same performance as the unregularized dynamics in just over a day on one GPU, whereas unregularized dynamics can take up to 4-6 days of training time on multiple GPUs. This brings neural ODEs significantly closer to practical relevance in large-scale applications.

Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One

We propose to reinterpret a standard discriminative classifier of p(y|x) as an energy based model for the joint distribution p(x,y). In this setting, the standard class probabilities can be easily computed as well as unnormalized values of p(x) and p(x|y). Within this framework, standard discriminative architectures may beused and the model can also be trained on unlabeled data. We demonstrate that energy based training of the joint distribution improves calibration, robustness, andout-of-distribution detection while also enabling our models to generate samplesrivaling the quality of recent GAN approaches. We improve upon recently proposed techniques for scaling up the training of energy based models and presentan approach which adds little overhead compared to standard classification training. Our approach is the first to achieve performance rivaling the state-of-the-artin both generative and discriminative learning within one hybrid model.