Mihaela van der Schaar

Zhaozhi Qian, Bogdan-Constantin Cebere, Mihaela van der Schaar

Synthcity is an open-source software package for innovative use cases of synthetic data in ML fairness, privacy and augmentation across diverse tabular data modalities, including static data, regular and irregular time series, data with censoring, multi-source data, composite data, and more. Synthcity provides the practitioners with a single access point to cutting edge research and tools in synthetic data. It also offers the community a playground for rapid experimentation and prototyping, a one-stop-shop for SOTA benchmarks, and an opportunity for extending research impact. The library can be accessed on GitHub (https://github.com/vanderschaarlab/synthcity) and pip (https://pypi.org/project/synthcity/). We warmly invite the community to join the development effort by providing feedback, reporting bugs, and contributing code.

Fergus Imrie, Bogdan Cebere, Eoin F. McKinney et al.

Diagnostic and prognostic models are increasingly important in medicine and inform many clinical decisions. Recently, machine learning approaches have shown improvement over conventional modeling techniques by better capturing complex interactions between patient covariates in a data-driven manner. However, the use of machine learning introduces a number of technical and practical challenges that have thus far restricted widespread adoption of such techniques in clinical settings. To address these challenges and empower healthcare professionals, we present a machine learning framework, AutoPrognosis 2.0, to develop diagnostic and prognostic models. AutoPrognosis leverages state-of-the-art advances in automated machine learning to develop optimized machine learning pipelines, incorporates model explainability tools, and enables deployment of clinical demonstrators, without requiring significant technical expertise. Our framework eliminates the major technical obstacles to predictive modeling with machine learning that currently impede clinical adoption. To demonstrate AutoPrognosis 2.0, we provide an illustrative application where we construct a prognostic risk score for diabetes using the UK Biobank, a prospective study of 502,467 individuals. The models produced by our automated framework achieve greater discrimination for diabetes than expert clinical risk scores. Our risk score has been implemented as a web-based decision support tool and can be publicly accessed by patients and clinicians worldwide. In addition, AutoPrognosis 2.0 is provided as an open-source python package. By open-sourcing our framework as a tool for the community, clinicians and other medical practitioners will be able to readily develop new risk scores, personalized diagnostics, and prognostics using modern machine learning techniques.

Luis Oala, Manil Maskey, Lilith Bat-Leah et al. · mit

Drawing from discussions at the inaugural DMLR workshop at ICML 2023 and meetings prior, in this report we outline the relevance of community engagement and infrastructure development for the creation of next-generation public datasets that will advance machine learning science. We chart a path forward as a collective effort to sustain the creation and maintenance of these datasets and methods towards positive scientific, societal and business impact.

Jonathan Crabbé, Mihaela van der Schaar · cambridge

Concept-based explanations permit to understand the predictions of a deep neural network (DNN) through the lens of concepts specified by users. Existing methods assume that the examples illustrating a concept are mapped in a fixed direction of the DNN's latent space. When this holds true, the concept can be represented by a concept activation vector (CAV) pointing in that direction. In this work, we propose to relax this assumption by allowing concept examples to be scattered across different clusters in the DNN's latent space. Each concept is then represented by a region of the DNN's latent space that includes these clusters and that we call concept activation region (CAR). To formalize this idea, we introduce an extension of the CAV formalism that is based on the kernel trick and support vector classifiers. This CAR formalism yields global concept-based explanations and local concept-based feature importance. We prove that CAR explanations built with radial kernels are invariant under latent space isometries. In this way, CAR assigns the same explanations to latent spaces that have the same geometry. We further demonstrate empirically that CARs offer (1) more accurate descriptions of how concepts are scattered in the DNN's latent space; (2) global explanations that are closer to human concept annotations and (3) concept-based feature importance that meaningfully relate concepts with each other. Finally, we use CARs to show that DNNs can autonomously rediscover known scientific concepts, such as the prostate cancer grading system.

Zahra Atashgahi, Tennison Liu, Mykola Pechenizkiy et al.

Sparse Neural Networks (SNNs) have emerged as powerful tools for efficient feature selection. Leveraging the dynamic sparse training (DST) algorithms within SNNs has demonstrated promising feature selection capabilities while drastically reducing computational overheads. Despite these advancements, several critical aspects remain insufficiently explored for feature selection. Questions persist regarding the choice of the DST algorithm for network training, the choice of metric for ranking features/neurons, and the comparative performance of these methods across diverse datasets when compared to dense networks. This paper addresses these gaps by presenting a comprehensive systematic analysis of feature selection with sparse neural networks. Moreover, we introduce a novel metric considering sparse neural network characteristics, which is designed to quantify feature importance within the context of SNNs. Our findings show that feature selection with SNNs trained with DST algorithms can achieve, on average, more than $50\%$ memory and $55\%$ FLOPs reduction compared to the dense networks, while outperforming them in terms of the quality of the selected features. Our code and the supplementary material are available on GitHub (\url{https://github.com/zahraatashgahi/Neuron-Attribution}).

Evgeny S. Saveliev, Mihaela van der Schaar

TemporAI is an open source Python software library for machine learning (ML) tasks involving data with a time component, focused on medicine and healthcare use cases. It supports data in time series, static, and eventmodalities and provides an interface for prediction, causal inference, and time-to-event analysis, as well as common preprocessing utilities and model interpretability methods. The library aims to facilitate innovation in the medical ML space by offering a standardized temporal setting toolkit for model development, prototyping and benchmarking, bridging the gaps in the ML research, healthcare professional, medical/pharmacological industry, and data science communities. TemporAI is available on GitHub (https://github.com/vanderschaarlab/temporai) and we welcome community engagement through use, feedback, and code contributions.

Alan Jeffares, Tennison Liu, Jonathan Crabbé et al. · cambridge

Despite their success with unstructured data, deep neural networks are not yet a panacea for structured tabular data. In the tabular domain, their efficiency crucially relies on various forms of regularization to prevent overfitting and provide strong generalization performance. Existing regularization techniques include broad modelling decisions such as choice of architecture, loss functions, and optimization methods. In this work, we introduce Tabular Neural Gradient Orthogonalization and Specialization (TANGOS), a novel framework for regularization in the tabular setting built on latent unit attributions. The gradient attribution of an activation with respect to a given input feature suggests how the neuron attends to that feature, and is often employed to interpret the predictions of deep networks. In TANGOS, we take a different approach and incorporate neuron attributions directly into training to encourage orthogonalization and specialization of latent attributions in a fully-connected network. Our regularizer encourages neurons to focus on sparse, non-overlapping input features and results in a set of diverse and specialized latent units. In the tabular domain, we demonstrate that our approach can lead to improved out-of-sample generalization performance, outperforming other popular regularization methods. We provide insight into why our regularizer is effective and demonstrate that TANGOS can be applied jointly with existing methods to achieve even greater generalization performance.

Nabeel Seedat, Jonathan Crabbé, Ioana Bica et al. · cambridge, oxford

High model performance, on average, can hide that models may systematically underperform on subgroups of the data. We consider the tabular setting, which surfaces the unique issue of outcome heterogeneity - this is prevalent in areas such as healthcare, where patients with similar features can have different outcomes, thus making reliable predictions challenging. To tackle this, we propose Data-IQ, a framework to systematically stratify examples into subgroups with respect to their outcomes. We do this by analyzing the behavior of individual examples during training, based on their predictive confidence and, importantly, the aleatoric (data) uncertainty. Capturing the aleatoric uncertainty permits a principled characterization and then subsequent stratification of data examples into three distinct subgroups (Easy, Ambiguous, Hard). We experimentally demonstrate the benefits of Data-IQ on four real-world medical datasets. We show that Data-IQ's characterization of examples is most robust to variation across similarly performant (yet different) models, compared to baselines. Since Data-IQ can be used with any ML model (including neural networks, gradient boosting etc.), this property ensures consistency of data characterization, while allowing flexible model selection. Taking this a step further, we demonstrate that the subgroups enable us to construct new approaches to both feature acquisition and dataset selection. Furthermore, we highlight how the subgroups can inform reliable model usage, noting the significant impact of the Ambiguous subgroup on model generalization.

Daniel Jarrett, Ioana Bica, Mihaela van der Schaar · oxford

Consider learning a generative model for time-series data. The sequential setting poses a unique challenge: Not only should the generator capture the conditional dynamics of (stepwise) transitions, but its open-loop rollouts should also preserve the joint distribution of (multi-step) trajectories. On one hand, autoregressive models trained by MLE allow learning and computing explicit transition distributions, but suffer from compounding error during rollouts. On the other hand, adversarial models based on GAN training alleviate such exposure bias, but transitions are implicit and hard to assess. In this work, we study a generative framework that seeks to combine the strengths of both: Motivated by a moment-matching objective to mitigate compounding error, we optimize a local (but forward-looking) transition policy, where the reinforcement signal is provided by a global (but stepwise-decomposable) energy model trained by contrastive estimation. At training, the two components are learned cooperatively, avoiding the instabilities typical of adversarial objectives. At inference, the learned policy serves as the generator for iterative sampling, and the learned energy serves as a trajectory-level measure for evaluating sample quality. By expressly training a policy to imitate sequential behavior of time-series features in a dataset, this approach embodies "generation by imitation". Theoretically, we illustrate the correctness of this formulation and the consistency of the algorithm. Empirically, we evaluate its ability to generate predictively useful samples from real-world datasets, verifying that it performs at the standard of existing benchmarks.

Alan Jeffares, Tennison Liu, Jonathan Crabbé et al. · cambridge

Ensembles of machine learning models have been well established as a powerful method of improving performance over a single model. Traditionally, ensembling algorithms train their base learners independently or sequentially with the goal of optimizing their joint performance. In the case of deep ensembles of neural networks, we are provided with the opportunity to directly optimize the true objective: the joint performance of the ensemble as a whole. Surprisingly, however, directly minimizing the loss of the ensemble appears to rarely be applied in practice. Instead, most previous research trains individual models independently with ensembling performed post hoc. In this work, we show that this is for good reason - joint optimization of ensemble loss results in degenerate behavior. We approach this problem by decomposing the ensemble objective into the strength of the base learners and the diversity between them. We discover that joint optimization results in a phenomenon in which base learners collude to artificially inflate their apparent diversity. This pseudo-diversity fails to generalize beyond the training data, causing a larger generalization gap. We proceed to comprehensively demonstrate the practical implications of this effect on a range of standard machine learning tasks and architectures by smoothly interpolating between independent training and joint optimization.

Ioana Bica, Mihaela van der Schaar · oxford

Consider the problem of improving the estimation of conditional average treatment effects (CATE) for a target domain of interest by leveraging related information from a source domain with a different feature space. This heterogeneous transfer learning problem for CATE estimation is ubiquitous in areas such as healthcare where we may wish to evaluate the effectiveness of a treatment for a new patient population for which different clinical covariates and limited data are available. In this paper, we address this problem by introducing several building blocks that use representation learning to handle the heterogeneous feature spaces and a flexible multi-task architecture with shared and private layers to transfer information between potential outcome functions across domains. Then, we show how these building blocks can be used to recover transfer learning equivalents of the standard CATE learners. On a new semi-synthetic data simulation benchmark for heterogeneous transfer learning we not only demonstrate performance improvements of our heterogeneous transfer causal effect learners across datasets, but also provide insights into the differences between these learners from a transfer perspective.

Jonathan Crabbé, Mihaela van der Schaar · cambridge

Unsupervised black-box models are challenging to interpret. Indeed, most existing explainability methods require labels to select which component(s) of the black-box's output to interpret. In the absence of labels, black-box outputs often are representation vectors whose components do not correspond to any meaningful quantity. Hence, choosing which component(s) to interpret in a label-free unsupervised/self-supervised setting is an important, yet unsolved problem. To bridge this gap in the literature, we introduce two crucial extensions of post-hoc explanation techniques: (1) label-free feature importance and (2) label-free example importance that respectively highlight influential features and training examples for a black-box to construct representations at inference time. We demonstrate that our extensions can be successfully implemented as simple wrappers around many existing feature and example importance methods. We illustrate the utility of our label-free explainability paradigm through a qualitative and quantitative comparison of representation spaces learned by various autoencoders trained on distinct unsupervised tasks.

Jonathan Crabbé, Alicia Curth, Ioana Bica et al. · cambridge, oxford

Estimating personalized effects of treatments is a complex, yet pervasive problem. To tackle it, recent developments in the machine learning (ML) literature on heterogeneous treatment effect estimation gave rise to many sophisticated, but opaque, tools: due to their flexibility, modularity and ability to learn constrained representations, neural networks in particular have become central to this literature. Unfortunately, the assets of such black boxes come at a cost: models typically involve countless nontrivial operations, making it difficult to understand what they have learned. Yet, understanding these models can be crucial -- in a medical context, for example, discovered knowledge on treatment effect heterogeneity could inform treatment prescription in clinical practice. In this work, we therefore use post-hoc feature importance methods to identify features that influence the model's predictions. This allows us to evaluate treatment effect estimators along a new and important dimension that has been overlooked in previous work: We construct a benchmarking environment to empirically investigate the ability of personalized treatment effect models to identify predictive covariates -- covariates that determine differential responses to treatment. Our benchmarking environment then enables us to provide new insight into the strengths and weaknesses of different types of treatment effects models as we modulate different challenges specific to treatment effect estimation -- e.g. the ratio of prognostic to predictive information, the possible nonlinearity of potential outcomes and the presence and type of confounding.

Evgeny Saveliev, Tim Schubert, Thomas Pouplin et al.

Despite its significant promise and continuous technical advances, real-world applications of artificial intelligence (AI) remain limited. We attribute this to the "domain expert-AI-conundrum": while domain experts, such as clinician scientists, should be able to build predictive models such as risk scores, they face substantial barriers in accessing state-of-the-art (SOTA) tools. While automated machine learning (AutoML) has been proposed as a partner in clinical predictive modeling, many additional requirements need to be fulfilled to make machine learning accessible for clinician scientists. To address this gap, we introduce CliMB, a no-code AI-enabled partner designed to empower clinician scientists to create predictive models using natural language. CliMB guides clinician scientists through the entire medical data science pipeline, thus empowering them to create predictive models from real-world data in just one conversation. CliMB also creates structured reports and interpretable visuals. In evaluations involving clinician scientists and systematic comparisons against a baseline GPT-4, CliMB consistently demonstrated superior performance in key areas such as planning, error prevention, code execution, and model performance. Moreover, in blinded assessments involving 45 clinicians from diverse specialties and career stages, more than 80% preferred CliMB over GPT-4. Overall, by providing a no-code interface with clear guidance and access to SOTA methods in the fields of data-centric AI, AutoML, and interpretable ML, CliMB empowers clinician scientists to build robust predictive models. The proof-of-concept version of CliMB is available as open-source software on GitHub: https://github.com/vanderschaarlab/climb.

Jeroen Berrevoets, Krzysztof Kacprzyk, Zhaozhi Qian et al.

Causal deep learning (CDL) is a new and important research area in the larger field of machine learning. With CDL, researchers aim to structure and encode causal knowledge in the extremely flexible representation space of deep learning models. Doing so will lead to more informed, robust, and general predictions and inference -- which is important! However, CDL is still in its infancy. For example, it is not clear how we ought to compare different methods as they are so different in their output, the way they encode causal knowledge, or even how they represent this knowledge. This is a living paper that categorises methods in causal deep learning beyond Pearl's ladder of causation. We refine the rungs in Pearl's ladder, while also adding a separate dimension that categorises the parametric assumptions of both input and representation, arriving at the map of causal deep learning. Our map covers machine learning disciplines such as supervised learning, reinforcement learning, generative modelling and beyond. Our paradigm is a tool which helps researchers to: find benchmarks, compare methods, and most importantly: identify research gaps. With this work we aim to structure the avalanche of papers being published on causal deep learning. While papers on the topic are being published daily, our map remains fixed. We open-source our map for others to use as they see fit: perhaps to offer guidance in a related works section, or to better highlight the contribution of their paper.

Jonathan Crabbé, Mihaela van der Schaar · cambridge

Interpretability methods are valuable only if their explanations faithfully describe the explained model. In this work, we consider neural networks whose predictions are invariant under a specific symmetry group. This includes popular architectures, ranging from convolutional to graph neural networks. Any explanation that faithfully explains this type of model needs to be in agreement with this invariance property. We formalize this intuition through the notion of explanation invariance and equivariance by leveraging the formalism from geometric deep learning. Through this rigorous formalism, we derive (1) two metrics to measure the robustness of any interpretability method with respect to the model symmetry group; (2) theoretical robustness guarantees for some popular interpretability methods and (3) a systematic approach to increase the invariance of any interpretability method with respect to a symmetry group. By empirically measuring our metrics for explanations of models associated with various modalities and symmetry groups, we derive a set of 5 guidelines to allow users and developers of interpretability methods to produce robust explanations.

Eleonora Giunchiglia, Fergus Imrie, Mihaela van der Schaar et al. · oxford

In the recent years, machine learning has made great advancements that have been at the root of many breakthroughs in different application domains. However, it is still an open issue how make them applicable to high-stakes or safety-critical application domains, as they can often be brittle and unreliable. In this paper, we argue that requirements definition and satisfaction can go a long way to make machine learning models even more fitting to the real world, especially in critical domains. To this end, we present two problems in which (i) requirements arise naturally, (ii) machine learning models are or can be fruitfully deployed, and (iii) neglecting the requirements can have dramatic consequences. We show how the requirements specification can be fruitfully integrated into the standard machine learning development pipeline, proposing a novel pyramid development process in which requirements definition may impact all the subsequent phases in the pipeline, and viceversa.

Daniel Jarrett, Bogdan Cebere, Tennison Liu et al.

Consider the problem of imputing missing values in a dataset. One the one hand, conventional approaches using iterative imputation benefit from the simplicity and customizability of learning conditional distributions directly, but suffer from the practical requirement for appropriate model specification of each and every variable. On the other hand, recent methods using deep generative modeling benefit from the capacity and efficiency of learning with neural network function approximators, but are often difficult to optimize and rely on stronger data assumptions. In this work, we study an approach that marries the advantages of both: We propose *HyperImpute*, a generalized iterative imputation framework for adaptively and automatically configuring column-wise models and their hyperparameters. Practically, we provide a concrete implementation with out-of-the-box learners, optimizers, simulators, and extensible interfaces. Empirically, we investigate this framework via comprehensive experiments and sensitivities on a variety of public datasets, and demonstrate its ability to generate accurate imputations relative to a strong suite of benchmarks. Contrary to recent work, we believe our findings constitute a strong defense of the iterative imputation paradigm.

Hao Sun, Boris van Breugel, Jonathan Crabbe et al. · cambridge

Uncertainty Quantification (UQ) is essential for creating trustworthy machine learning models. Recent years have seen a steep rise in UQ methods that can flag suspicious examples, however, it is often unclear what exactly these methods identify. In this work, we propose a framework for categorizing uncertain examples flagged by UQ methods in classification tasks. We introduce the confusion density matrix -- a kernel-based approximation of the misclassification density -- and use this to categorize suspicious examples identified by a given uncertainty method into three classes: out-of-distribution (OOD) examples, boundary (Bnd) examples, and examples in regions of high in-distribution misclassification (IDM). Through extensive experiments, we show that our framework provides a new and distinct perspective for assessing differences between uncertainty quantification methods, thereby forming a valuable assessment benchmark.

Boris van Breugel, Hao Sun, Zhaozhi Qian et al.

Data is the foundation of most science. Unfortunately, sharing data can be obstructed by the risk of violating data privacy, impeding research in fields like healthcare. Synthetic data is a potential solution. It aims to generate data that has the same distribution as the original data, but that does not disclose information about individuals. Membership Inference Attacks (MIAs) are a common privacy attack, in which the attacker attempts to determine whether a particular real sample was used for training of the model. Previous works that propose MIAs against generative models either display low performance -- giving the false impression that data is highly private -- or need to assume access to internal generative model parameters -- a relatively low-risk scenario, as the data publisher often only releases synthetic data, not the model. In this work we argue for a realistic MIA setting that assumes the attacker has some knowledge of the underlying data distribution. We propose DOMIAS, a density-based MIA model that aims to infer membership by targeting local overfitting of the generative model. Experimentally we show that DOMIAS is significantly more successful at MIA than previous work, especially at attacking uncommon samples. The latter is disconcerting since these samples may correspond to underrepresented groups. We also demonstrate how DOMIAS' MIA performance score provides an interpretable metric for privacy, giving data publishers a new tool for achieving the desired privacy-utility trade-off in their synthetic data.

Nabeel Seedat, Fergus Imrie, Alexis Bellot et al.

Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer ''what-iF'' questions. Existing causal inference approaches typically consider regular, discrete-time intervals between observations and treatment decisions and hence are unable to naturally model irregularly sampled data, which is the common setting in practice. To handle arbitrary observation patterns, we interpret the data as samples from an underlying continuous-time process and propose to model its latent trajectory explicitly using the mathematics of controlled differential equations. This leads to a new approach, the Treatment Effect Neural Controlled Differential Equation (TE-CDE), that allows the potential outcomes to be evaluated at any time point. In addition, adversarial training is used to adjust for time-dependent confounding which is critical in longitudinal settings and is an added challenge not encountered in conventional time-series. To assess solutions to this problem, we propose a controllable simulation environment based on a model of tumor growth for a range of scenarios with irregular sampling reflective of a variety of clinical scenarios. TE-CDE consistently outperforms existing approaches in all simulated scenarios with irregular sampling.

Fergus Imrie, Stefan Denner, Lucas S. Brunschwig et al.

The application of machine learning in medicine and healthcare has led to the creation of numerous diagnostic and prognostic models. However, despite their success, current approaches generally issue predictions using data from a single modality. This stands in stark contrast with clinician decision-making which employs diverse information from multiple sources. While several multimodal machine learning approaches exist, significant challenges in developing multimodal systems remain that are hindering clinical adoption. In this paper, we introduce a multimodal framework, AutoPrognosis-M, that enables the integration of structured clinical (tabular) data and medical imaging using automated machine learning. AutoPrognosis-M incorporates 17 imaging models, including convolutional neural networks and vision transformers, and three distinct multimodal fusion strategies. In an illustrative application using a multimodal skin lesion dataset, we highlight the importance of multimodal machine learning and the power of combining multiple fusion strategies using ensemble learning. We have open-sourced our framework as a tool for the community and hope it will accelerate the uptake of multimodal machine learning in healthcare and spur further innovation.

Daniel Jarrett, Jinsung Yoon, Ioana Bica et al.

Time-series learning is the bread and butter of data-driven *clinical decision support*, and the recent explosion in ML research has demonstrated great potential in various healthcare settings. At the same time, medical time-series problems in the wild are challenging due to their highly *composite* nature: They entail design choices and interactions among components that preprocess data, impute missing values, select features, issue predictions, estimate uncertainty, and interpret models. Despite exponential growth in electronic patient data, there is a remarkable gap between the potential and realized utilization of ML for clinical research and decision support. In particular, orchestrating a real-world project lifecycle poses challenges in engineering (i.e. hard to build), evaluation (i.e. hard to assess), and efficiency (i.e. hard to optimize). Designed to address these issues simultaneously, Clairvoyance proposes a unified, end-to-end, autoML-friendly pipeline that serves as a (i) software toolkit, (ii) empirical standard, and (iii) interface for optimization. Our ultimate goal lies in facilitating transparent and reproducible experimentation with complex inference workflows, providing integrated pathways for (1) personalized prediction, (2) treatment-effect estimation, and (3) information acquisition. Through illustrative examples on real-world data in outpatient, general wards, and intensive-care settings, we illustrate the applicability of the pipeline paradigm on core tasks in the healthcare journey. To the best of our knowledge, Clairvoyance is the first to demonstrate viability of a comprehensive and automatable pipeline for clinical time-series ML.

Boris van Breugel, Mihaela van der Schaar

Generating synthetic data through generative models is gaining interest in the ML community and beyond. In the past, synthetic data was often regarded as a means to private data release, but a surge of recent papers explore how its potential reaches much further than this -- from creating more fair data to data augmentation, and from simulation to text generated by ChatGPT. In this perspective we explore whether, and how, synthetic data may become a dominant force in the machine learning world, promising a future where datasets can be tailored to individual needs. Just as importantly, we discuss which fundamental challenges the community needs to overcome for wider relevance and application of synthetic data -- the most important of which is quantifying how much we can trust any finding or prediction drawn from synthetic data.

Boris van Breugel, Nabeel Seedat, Fergus Imrie et al.

Evaluating the performance of machine learning models on diverse and underrepresented subgroups is essential for ensuring fairness and reliability in real-world applications. However, accurately assessing model performance becomes challenging due to two main issues: (1) a scarcity of test data, especially for small subgroups, and (2) possible distributional shifts in the model's deployment setting, which may not align with the available test data. In this work, we introduce 3S Testing, a deep generative modeling framework to facilitate model evaluation by generating synthetic test sets for small subgroups and simulating distributional shifts. Our experiments demonstrate that 3S Testing outperforms traditional baselines -- including real test data alone -- in estimating model performance on minority subgroups and under plausible distributional shifts. In addition, 3S offers intervals around its performance estimates, exhibiting superior coverage of the ground truth compared to existing approaches. Overall, these results raise the question of whether we need a paradigm shift away from limited real test data towards synthetic test data.

Lasse Hansen, Nabeel Seedat, Mihaela van der Schaar et al.

Synthetic data serves as an alternative in training machine learning models, particularly when real-world data is limited or inaccessible. However, ensuring that synthetic data mirrors the complex nuances of real-world data is a challenging task. This paper addresses this issue by exploring the potential of integrating data-centric AI techniques which profile the data to guide the synthetic data generation process. Moreover, we shed light on the often ignored consequences of neglecting these data profiles during synthetic data generation -- despite seemingly high statistical fidelity. Subsequently, we propose a novel framework to evaluate the integration of data profiles to guide the creation of more representative synthetic data. In an empirical study, we evaluate the performance of five state-of-the-art models for tabular data generation on eleven distinct tabular datasets. The findings offer critical insights into the successes and limitations of current synthetic data generation techniques. Finally, we provide practical recommendations for integrating data-centric insights into the synthetic data generation process, with a specific focus on classification performance, model selection, and feature selection. This study aims to reevaluate conventional approaches to synthetic data generation and promote the application of data-centric AI techniques in improving the quality and effectiveness of synthetic data.

Alicia Curth, Mihaela van der Schaar

Personalized treatment effect estimates are often of interest in high-stakes applications -- thus, before deploying a model estimating such effects in practice, one needs to be sure that the best candidate from the ever-growing machine learning toolbox for this task was chosen. Unfortunately, due to the absence of counterfactual information in practice, it is usually not possible to rely on standard validation metrics for doing so, leading to a well-known model selection dilemma in the treatment effect estimation literature. While some solutions have recently been investigated, systematic understanding of the strengths and weaknesses of different model selection criteria is still lacking. In this paper, instead of attempting to declare a global `winner', we therefore empirically investigate success- and failure modes of different selection criteria. We highlight that there is a complex interplay between selection strategies, candidate estimators and the data used for comparing them, and provide interesting insights into the relative (dis)advantages of different criteria alongside desiderata for the design of further illuminating empirical studies in this context.

Samuel Holt, Zhaozhi Qian, Mihaela van der Schaar

Neural Ordinary Differential Equations model dynamical systems with ODEs learned by neural networks. However, ODEs are fundamentally inadequate to model systems with long-range dependencies or discontinuities, which are common in engineering and biological systems. Broader classes of differential equations (DE) have been proposed as remedies, including delay differential equations and integro-differential equations. Furthermore, Neural ODE suffers from numerical instability when modelling stiff ODEs and ODEs with piecewise forcing functions. In this work, we propose Neural Laplace, a unified framework for learning diverse classes of DEs including all the aforementioned ones. Instead of modelling the dynamics in the time domain, we model it in the Laplace domain, where the history-dependencies and discontinuities in time can be represented as summations of complex exponentials. To make learning more efficient, we use the geometrical stereographic map of a Riemann sphere to induce more smoothness in the Laplace domain. In the experiments, Neural Laplace shows superior performance in modelling and extrapolating the trajectories of diverse classes of DEs, including the ones with complex history dependency and abrupt changes.

Daniel Jarrett, Alihan Hüyük, Mihaela van der Schaar

Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive, unifying perspective on inverse decision modeling: a framework for learning parameterized representations of sequential decision behavior. First, we formalize the forward problem (as a normative standard), subsuming common classes of control behavior. Second, we use this to formalize the inverse problem (as a descriptive model), generalizing existing work on imitation/reward learning -- while opening up a much broader class of research problems in behavior representation. Finally, we instantiate this approach with an example (inverse bounded rational control), illustrating how this structure enables learning (interpretable) representations of (bounded) rationality -- while naturally capturing intuitive notions of suboptimal actions, biased beliefs, and imperfect knowledge of environments.

Alicia Curth, Alan Jeffares, Mihaela van der Schaar

Conventional statistical wisdom established a well-understood relationship between model complexity and prediction error, typically presented as a U-shaped curve reflecting a transition between under- and overfitting regimes. However, motivated by the success of overparametrized neural networks, recent influential work has suggested this theory to be generally incomplete, introducing an additional regime that exhibits a second descent in test error as the parameter count p grows past sample size n - a phenomenon dubbed double descent. While most attention has naturally been given to the deep-learning setting, double descent was shown to emerge more generally across non-neural models: known cases include linear regression, trees, and boosting. In this work, we take a closer look at evidence surrounding these more classical statistical machine learning methods and challenge the claim that observed cases of double descent truly extend the limits of a traditional U-shaped complexity-generalization curve therein. We show that once careful consideration is given to what is being plotted on the x-axes of their double descent plots, it becomes apparent that there are implicitly multiple complexity axes along which the parameter count grows. We demonstrate that the second descent appears exactly (and only) when and where the transition between these underlying axes occurs, and that its location is thus not inherently tied to the interpolation threshold p=n. We then gain further insight by adopting a classical nonparametric statistics perspective. We interpret the investigated methods as smoothers and propose a generalized measure for the effective number of parameters they use on unseen examples, using which we find that their apparent double descent curves indeed fold back into more traditional convex shapes - providing a resolution to tensions between double descent and statistical intuition.

Jeroen Berrevoets, Krzysztof Kacprzyk, Zhaozhi Qian et al.

Causality has the potential to truly transform the way we solve a large number of real-world problems. Yet, so far, its potential largely remains to be unlocked as causality often requires crucial assumptions which cannot be tested in practice. To address this challenge, we propose a new way of thinking about causality -- we call this causal deep learning. Our causal deep learning framework spans three dimensions: (1) a structural dimension, which incorporates partial yet testable causal knowledge rather than assuming either complete or no causal knowledge among the variables of interest; (2) a parametric dimension, which encompasses parametric forms that capture the type of relationships among the variables of interest; and (3) a temporal dimension, which captures exposure times or how the variables of interest interact (possibly causally) over time. Causal deep learning enables us to make progress on a variety of real-world problems by leveraging partial causal knowledge (including independencies among variables) and quantitatively characterising causal relationships among variables of interest (possibly over time). Our framework clearly identifies which assumptions are testable and which ones are not, such that the resulting solutions can be judiciously adopted in practice. Using our formulation we can combine or chain together causal representations to solve specific problems without losing track of which assumptions are required to build these solutions, pushing real-world impact in healthcare, economics and business, environmental sciences and education, through causal deep learning.

Yangming Li, Mihaela van der Schaar

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

Aleksa Bisercic, Mladen Nikolic, Mihaela van der Schaar et al.

Tabular data is often hidden in text, particularly in medical diagnostic reports. Traditional machine learning (ML) models designed to work with tabular data, cannot effectively process information in such form. On the other hand, large language models (LLMs) which excel at textual tasks, are probably not the best tool for modeling tabular data. Therefore, we propose a novel, simple, and effective methodology for extracting structured tabular data from textual medical reports, called TEMED-LLM. Drawing upon the reasoning capabilities of LLMs, TEMED-LLM goes beyond traditional extraction techniques, accurately inferring tabular features, even when their names are not explicitly mentioned in the text. This is achieved by combining domain-specific reasoning guidelines with a proposed data validation and reasoning correction feedback loop. By applying interpretable ML models such as decision trees and logistic regression over the extracted and validated data, we obtain end-to-end interpretable predictions. We demonstrate that our approach significantly outperforms state-of-the-art text classification models in medical diagnostics. Given its predictive performance, simplicity, and interpretability, TEMED-LLM underscores the potential of leveraging LLMs to improve the performance and trustworthiness of ML models in medical applications.

Samuel Holt, Max Ruiz Luyten, Mihaela van der Schaar

Transformer-based large language models (LLMs) are constrained by the fixed context window of the underlying transformer architecture, hindering their ability to produce long and coherent outputs. Memory-augmented LLMs are a promising solution, but current approaches cannot handle long output generation tasks since they (1) only focus on reading memory and reduce its evolution to the concatenation of new memories or (2) use very specialized memories that cannot adapt to other domains. This paper presents L2MAC, the first practical LLM-based general-purpose stored-program automatic computer (von Neumann architecture) framework, an LLM-based multi-agent system, for long and consistent output generation. Its memory has two components: the instruction registry, which is populated with a prompt program to solve the user-given task, and a file store, which will contain the final and intermediate outputs. Each instruction in turn is executed by a separate LLM agent, whose context is managed by a control unit capable of precise memory reading and writing to ensure effective interaction with the file store. These components enable L2MAC to generate extensive outputs, bypassing the constraints of the finite context window while producing outputs that fulfill a complex user-specified task. We empirically demonstrate that L2MAC achieves state-of-the-art performance in generating large codebases for system design tasks, significantly outperforming other coding methods in implementing the detailed user-specified task; we show that L2MAC works for general-purpose extensive text-based tasks, such as writing an entire book; and we provide valuable insights into L2MAC's performance improvement over existing methods.

Ioana Bica, Daniel Jarrett, Mihaela van der Schaar · oxford

Consider learning an imitation policy on the basis of demonstrated behavior from multiple environments, with an eye towards deployment in an unseen environment. Since the observable features from each setting may be different, directly learning individual policies as mappings from features to actions is prone to spurious correlations -- and may not generalize well. However, the expert's policy is often a function of a shared latent structure underlying those observable features that is invariant across settings. By leveraging data from multiple environments, we propose Invariant Causal Imitation Learning (ICIL), a novel technique in which we learn a feature representation that is invariant across domains, on the basis of which we learn an imitation policy that matches expert behavior. To cope with transition dynamics mismatch, ICIL learns a shared representation of causal features (for all training environments), that is disentangled from the specific representations of noise variables (for each of those environments). Moreover, to ensure that the learned policy matches the observation distribution of the expert's policy, ICIL estimates the energy of the expert's observations and uses a regularization term that minimizes the imitator policy's next state energy. Experimentally, we compare our methods against several benchmarks in control and healthcare tasks and show its effectiveness in learning imitation policies capable of generalizing to unseen environments.

Alihan Hüyük, Daniel Jarrett, Mihaela van der Schaar

Understanding human behavior from observed data is critical for transparency and accountability in decision-making. Consider real-world settings such as healthcare, in which modeling a decision-maker's policy is challenging -- with no access to underlying states, no knowledge of environment dynamics, and no allowance for live experimentation. We desire learning a data-driven representation of decision-making behavior that (1) inheres transparency by design, (2) accommodates partial observability, and (3) operates completely offline. To satisfy these key criteria, we propose a novel model-based Bayesian method for interpretable policy learning ("Interpole") that jointly estimates an agent's (possibly biased) belief-update process together with their (possibly suboptimal) belief-action mapping. Through experiments on both simulated and real-world data for the problem of Alzheimer's disease diagnosis, we illustrate the potential of our approach as an investigative device for auditing, quantifying, and understanding human decision-making behavior.

Alexander Norcliffe, Bogdan Cebere, Fergus Imrie et al.

Synthetic data is becoming an increasingly promising technology, and successful applications can improve privacy, fairness, and data democratization. While there are many methods for generating synthetic tabular data, the task remains non-trivial and unexplored for specific scenarios. One such scenario is survival data. Here, the key difficulty is censoring: for some instances, we are not aware of the time of event, or if one even occurred. Imbalances in censoring and time horizons cause generative models to experience three new failure modes specific to survival analysis: (1) generating too few at-risk members; (2) generating too many at-risk members; and (3) censoring too early. We formalize these failure modes and provide three new generative metrics to quantify them. Following this, we propose SurvivalGAN, a generative model that handles survival data firstly by addressing the imbalance in the censoring and event horizons, and secondly by using a dedicated mechanism for approximating time-to-event/censoring. We evaluate this method via extensive experiments on medical datasets. SurvivalGAN outperforms multiple baselines at generating survival data, and in particular addresses the failure modes as measured by the new metrics, in addition to improving downstream performance of survival models trained on the synthetic data.

Nabeel Seedat, Alan Jeffares, Fergus Imrie et al.

Conformal prediction is a powerful distribution-free tool for uncertainty quantification, establishing valid prediction intervals with finite-sample guarantees. To produce valid intervals which are also adaptive to the difficulty of each instance, a common approach is to compute normalized nonconformity scores on a separate calibration set. Self-supervised learning has been effectively utilized in many domains to learn general representations for downstream predictors. However, the use of self-supervision beyond model pretraining and representation learning has been largely unexplored. In this work, we investigate how self-supervised pretext tasks can improve the quality of the conformal regressors, specifically by improving the adaptability of conformal intervals. We train an auxiliary model with a self-supervised pretext task on top of an existing predictive model and use the self-supervised error as an additional feature to estimate nonconformity scores. We empirically demonstrate the benefit of the additional information using both synthetic and real data on the efficiency (width), deficit, and excess of conformal prediction intervals.

Nabeel Seedat, Fergus Imrie, Mihaela van der Schaar

While there have been a number of remarkable breakthroughs in machine learning (ML), much of the focus has been placed on model development. However, to truly realize the potential of machine learning in real-world settings, additional aspects must be considered across the ML pipeline. Data-centric AI is emerging as a unifying paradigm that could enable such reliable end-to-end pipelines. However, this remains a nascent area with no standardized framework to guide practitioners to the necessary data-centric considerations or to communicate the design of data-centric driven ML systems. To address this gap, we propose DC-Check, an actionable checklist-style framework to elicit data-centric considerations at different stages of the ML pipeline: Data, Training, Testing, and Deployment. This data-centric lens on development aims to promote thoughtfulness and transparency prior to system development. Additionally, we highlight specific data-centric AI challenges and research opportunities. DC-Check is aimed at both practitioners and researchers to guide day-to-day development. As such, to easily engage with and use DC-Check and associated resources, we provide a DC-Check companion website (https://www.vanderschaar-lab.com/dc-check/). The website will also serve as an updated resource as methods and tooling evolve over time.

Alizée Pace, Alex J. Chan, Mihaela van der Schaar

Building models of human decision-making from observed behaviour is critical to better understand, diagnose and support real-world policies such as clinical care. As established policy learning approaches remain focused on imitation performance, they fall short of explaining the demonstrated decision-making process. Policy Extraction through decision Trees (POETREE) is a novel framework for interpretable policy learning, compatible with fully-offline and partially-observable clinical decision environments -- and builds probabilistic tree policies determining physician actions based on patients' observations and medical history. Fully-differentiable tree architectures are grown incrementally during optimization to adapt their complexity to the modelling task, and learn a representation of patient history through recurrence, resulting in decision tree policies that adapt over time with patient information. This policy learning method outperforms the state-of-the-art on real and synthetic medical datasets, both in terms of understanding, quantifying and evaluating observed behaviour as well as in accurately replicating it -- with potential to improve future decision support systems.

Toon Vanderschueren, Alicia Curth, Wouter Verbeke et al.

Machine learning (ML) holds great potential for accurately forecasting treatment outcomes over time, which could ultimately enable the adoption of more individualized treatment strategies in many practical applications. However, a significant challenge that has been largely overlooked by the ML literature on this topic is the presence of informative sampling in observational data. When instances are observed irregularly over time, sampling times are typically not random, but rather informative -- depending on the instance's characteristics, past outcomes, and administered treatments. In this work, we formalize informative sampling as a covariate shift problem and show that it can prohibit accurate estimation of treatment outcomes if not properly accounted for. To overcome this challenge, we present a general framework for learning treatment outcomes in the presence of informative sampling using inverse intensity-weighting, and propose a novel method, TESAR-CDE, that instantiates this framework using Neural CDEs. Using a simulation environment based on a clinical use case, we demonstrate the effectiveness of our approach in learning under informative sampling.

Jaeok Park, Mihaela van der Schaar

We propose an incentive scheme based on intervention to sustain cooperation among self-interested users. In the proposed scheme, an intervention device collects imperfect signals about the actions of the users for a test period, and then chooses the level of intervention that degrades the performance of the network for the remaining time period. We analyze the problems of designing an optimal intervention rule given a test period and choosing an optimal length of the test period. The intervention device can provide the incentive for cooperation by exerting intervention following signals that involve a high likelihood of deviation. Increasing the length of the test period has two counteracting effects on the performance: It improves the quality of signals, but at the same time it weakens the incentive for cooperation due to increased delay.

Yanke Li, Hatt Tobias, Ioana Bica et al. · oxford

Leveraging labelled data from multiple domains to enable prediction in another domain without labels is a significant, yet challenging problem. To address this problem, we introduce the framework DAPDAG (\textbf{D}omain \textbf{A}daptation via \textbf{P}erturbed \textbf{DAG} Reconstruction) and propose to learn an auto-encoder that undertakes inference on population statistics given features and reconstructing a directed acyclic graph (DAG) as an auxiliary task. The underlying DAG structure is assumed invariant among observed variables whose conditional distributions are allowed to vary across domains led by a latent environmental variable $E$. The encoder is designed to serve as an inference device on $E$ while the decoder reconstructs each observed variable conditioned on its graphical parents in the DAG and the inferred $E$. We train the encoder and decoder jointly in an end-to-end manner and conduct experiments on synthetic and real datasets with mixed variables. Empirical results demonstrate that reconstructing the DAG benefits the approximate inference. Furthermore, our approach can achieve competitive performance against other benchmarks in prediction tasks, with better adaptation ability, especially in the target domain significantly different from the source domains.

Dennis Frauen, Fergus Imrie, Alicia Curth et al.

Unobserved confounding is common in many applications, making causal inference from observational data challenging. As a remedy, causal sensitivity analysis is an important tool to draw causal conclusions under unobserved confounding with mathematical guarantees. In this paper, we propose NeuralCSA, a neural framework for generalized causal sensitivity analysis. Unlike previous work, our framework is compatible with (i) a large class of sensitivity models, including the marginal sensitivity model, f-sensitivity models, and Rosenbaum's sensitivity model; (ii) different treatment types (i.e., binary and continuous); and (iii) different causal queries, including (conditional) average treatment effects and simultaneous effects on multiple outcomes. The generality of NeuralCSA is achieved by learning a latent distribution shift that corresponds to a treatment intervention using two conditional normalizing flows. We provide theoretical guarantees that NeuralCSA is able to infer valid bounds on the causal query of interest and also demonstrate this empirically using both simulated and real-world data.

Fergus Imrie, Alexander Norcliffe, Pietro Lio et al.

In many real world problems, features do not act alone but in combination with each other. For example, in genomics, diseases might not be caused by any single mutation but require the presence of multiple mutations. Prior work on feature selection either seeks to identify individual features or can only determine relevant groups from a predefined set. We investigate the problem of discovering groups of predictive features without predefined grouping. To do so, we define predictive groups in terms of linear and non-linear interactions between features. We introduce a novel deep learning architecture that uses an ensemble of feature selection models to find predictive groups, without requiring candidate groups to be provided. The selected groups are sparse and exhibit minimum overlap. Furthermore, we propose a new metric to measure similarity between discovered groups and the ground truth. We demonstrate the utility of our model on multiple synthetic tasks and semi-synthetic chemistry datasets, where the ground truth structure is known, as well as an image dataset and a real-world cancer dataset.

Samuel Holt, Alihan Hüyük, Zhaozhi Qian et al.

Many real-world offline reinforcement learning (RL) problems involve continuous-time environments with delays. Such environments are characterized by two distinctive features: firstly, the state x(t) is observed at irregular time intervals, and secondly, the current action a(t) only affects the future state x(t + g) with an unknown delay g > 0. A prime example of such an environment is satellite control where the communication link between earth and a satellite causes irregular observations and delays. Existing offline RL algorithms have achieved success in environments with irregularly observed states in time or known delays. However, environments involving both irregular observations in time and unknown delays remains an open and challenging problem. To this end, we propose Neural Laplace Control, a continuous-time model-based offline RL method that combines a Neural Laplace dynamics model with a model predictive control (MPC) planner--and is able to learn from an offline dataset sampled with irregular time intervals from an environment that has a inherent unknown constant delay. We show experimentally on continuous-time delayed environments it is able to achieve near expert policy performance.

Hao Sun, Alihan Hüyük, Daniel Jarrett et al.

Learning controllers with offline data in decision-making systems is an essential area of research due to its potential to reduce the risk of applications in real-world systems. However, in responsibility-sensitive settings such as healthcare, decision accountability is of paramount importance, yet has not been adequately addressed by the literature. This paper introduces the Accountable Offline Controller (AOC) that employs the offline dataset as the Decision Corpus and performs accountable control based on a tailored selection of examples, referred to as the Corpus Subset. AOC operates effectively in low-data scenarios, can be extended to the strictly offline imitation setting, and displays qualities of both conservation and adaptability. We assess AOC's performance in both simulated and real-world healthcare scenarios, emphasizing its capability to manage offline control tasks with high levels of performance while maintaining accountability.

Elisabeth R. M. Heremans, Nabeel Seedat, Bertien Buyse et al.

As machine learning becomes increasingly prevalent in critical fields such as healthcare, ensuring the safety and reliability of machine learning systems becomes paramount. A key component of reliability is the ability to estimate uncertainty, which enables the identification of areas of high and low confidence and helps to minimize the risk of error. In this study, we propose a machine learning pipeline called U-PASS tailored for clinical applications that incorporates uncertainty estimation at every stage of the process, including data acquisition, training, and model deployment. The training process is divided into a supervised pre-training step and a semi-supervised finetuning step. We apply our uncertainty-guided deep learning pipeline to the challenging problem of sleep staging and demonstrate that it systematically improves performance at every stage. By optimizing the training dataset, actively seeking informative samples, and deferring the most uncertain samples to an expert, we achieve an expert-level accuracy of 85% on a challenging clinical dataset of elderly sleep apnea patients, representing a significant improvement over the baseline accuracy of 75%. U-PASS represents a promising approach to incorporating uncertainty estimation into machine learning pipelines, thereby improving their reliability and unlocking their potential in clinical settings.

Yuchao Qin, Mihaela van der Schaar, Changhee Lee

Clustering time-series data in healthcare is crucial for clinical phenotyping to understand patients' disease progression patterns and to design treatment guidelines tailored to homogeneous patient subgroups. While rich temporal dynamics enable the discovery of potential clusters beyond static correlations, two major challenges remain outstanding: i) discovery of predictive patterns from many potential temporal correlations in the multi-variate time-series data and ii) association of individual temporal patterns to the target label distribution that best characterizes the underlying clinical progression. To address such challenges, we develop a novel temporal clustering method, T-Phenotype, to discover phenotypes of predictive temporal patterns from labeled time-series data. We introduce an efficient representation learning approach in frequency domain that can encode variable-length, irregularly-sampled time-series into a unified representation space, which is then applied to identify various temporal patterns that potentially contribute to the target label using a new notion of path-based similarity. Throughout the experiments on synthetic and real-world datasets, we show that T-Phenotype achieves the best phenotype discovery performance over all the evaluated baselines. We further demonstrate the utility of T-Phenotype by uncovering clinically meaningful patient subgroups characterized by unique temporal patterns.

Alex J. Chan, Alicia Curth, Mihaela van der Schaar

Human decision making is well known to be imperfect and the ability to analyse such processes individually is crucial when attempting to aid or improve a decision-maker's ability to perform a task, e.g. to alert them to potential biases or oversights on their part. To do so, it is necessary to develop interpretable representations of how agents make decisions and how this process changes over time as the agent learns online in reaction to the accrued experience. To then understand the decision-making processes underlying a set of observed trajectories, we cast the policy inference problem as the inverse to this online learning problem. By interpreting actions within a potential outcomes framework, we introduce a meaningful mapping based on agents choosing an action they believe to have the greatest treatment effect. We introduce a practical algorithm for retrospectively estimating such perceived effects, alongside the process through which agents update them, using a novel architecture built upon an expressive family of deep state-space models. Through application to the analysis of UNOS organ donation acceptance decisions, we demonstrate that our approach can bring valuable insights into the factors that govern decision processes and how they change over time.