Jonathan Crabbé

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.

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.

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.

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.

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.

Nabeel Seedat, Jonathan Crabbé, Zhaozhi Qian et al.

Data quality is crucial for robust machine learning algorithms, with the recent interest in data-centric AI emphasizing the importance of training data characterization. However, current data characterization methods are largely focused on classification settings, with regression settings largely understudied. To address this, we introduce TRIAGE, a novel data characterization framework tailored to regression tasks and compatible with a broad class of regressors. TRIAGE utilizes conformal predictive distributions to provide a model-agnostic scoring method, the TRIAGE score. We operationalize the score to analyze individual samples' training dynamics and characterize samples as under-, over-, or well-estimated by the model. We show that TRIAGE's characterization is consistent and highlight its utility to improve performance via data sculpting/filtering, in multiple regression settings. Additionally, beyond sample level, we show TRIAGE enables new approaches to dataset selection and feature acquisition. Overall, TRIAGE highlights the value unlocked by data characterization in real-world regression applications

Jonathan Crabbé, Pau Rodríguez, Vaishaal Shankar et al.

What distinguishes robust models from non-robust ones? While for ImageNet distribution shifts it has been shown that such differences in robustness can be traced back predominantly to differences in training data, so far it is not known what that translates to in terms of what the model has learned. In this work, we bridge this gap by probing the representation spaces of 16 robust zero-shot CLIP vision encoders with various backbones (ResNets and ViTs) and pretraining sets (OpenAI, LAION-400M, LAION-2B, YFCC15M, CC12M and {DataComp}), and comparing them to the representation spaces of less robust models with identical backbones, but different (pre)training sets or objectives (CLIP pretraining on ImageNet-Captions, and supervised training or finetuning on ImageNet).Through this analysis, we generate three novel insights. Firstly, we detect the presence of outlier features in robust zero-shot CLIP vision encoders, which to the best of our knowledge is the first time these are observed in non-language and non-transformer models. Secondly, we find the existence of outlier features to be an indication of ImageNet shift robustness in models, since we only find them in robust models in our analysis. Lastly, we also investigate the number of unique encoded concepts in the representation space and find zero-shot CLIP models to encode a higher number of unique concepts in their representation space. However, we do not find this to be an indicator of ImageNet shift robustness and hypothesize that it is rather related to the language supervision. Since the presence of outlier features can be detected without access to any data from shifted datasets, we believe that they could be a useful tool for practitioners to get a feeling for the distribution shift robustness of a pretrained model during deployment.

Claudio Zeni, Robert Pinsler, Daniel Zügner et al. · cambridge

The design of functional materials with desired properties is essential in driving technological advances in areas like energy storage, catalysis, and carbon capture. Generative models provide a new paradigm for materials design by directly generating entirely novel materials given desired property constraints. Despite recent progress, current generative models have low success rate in proposing stable crystals, or can only satisfy a very limited set of property constraints. Here, we present MatterGen, a model that generates stable, diverse inorganic materials across the periodic table and can further be fine-tuned to steer the generation towards a broad range of property constraints. To enable this, we introduce a new diffusion-based generative process that produces crystalline structures by gradually refining atom types, coordinates, and the periodic lattice. We further introduce adapter modules to enable fine-tuning towards any given property constraints with a labeled dataset. Compared to prior generative models, structures produced by MatterGen are more than twice as likely to be novel and stable, and more than 15 times closer to the local energy minimum. After fine-tuning, MatterGen successfully generates stable, novel materials with desired chemistry, symmetry, as well as mechanical, electronic and magnetic properties. Finally, we demonstrate multi-property materials design capabilities by proposing structures that have both high magnetic density and a chemical composition with low supply-chain risk. We believe that the quality of generated materials and the breadth of MatterGen's capabilities represent a major advancement towards creating a universal generative model for materials design.

Jonathan Crabbé, Nicolas Huynh, Jan Stanczuk et al. · cambridge

Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope of time series diffusion models. More specifically, we analyze whether representing time series in the frequency domain is a useful inductive bias for score-based diffusion models. By starting from the canonical SDE formulation of diffusion in the time domain, we show that a dual diffusion process occurs in the frequency domain with an important nuance: Brownian motions are replaced by what we call mirrored Brownian motions, characterized by mirror symmetries among their components. Building on this insight, we show how to adapt the denoising score matching approach to implement diffusion models in the frequency domain. This results in frequency diffusion models, which we compare to canonical time diffusion models. Our empirical evaluation on real-world datasets, covering various domains like healthcare and finance, shows that frequency diffusion models better capture the training distribution than time diffusion models. We explain this observation by showing that time series from these datasets tend to be more localized in the frequency domain than in the time domain, which makes them easier to model in the former case. All our observations point towards impactful synergies between Fourier analysis and diffusion models.

Nicolas Huynh, Jeroen Berrevoets, Nabeel Seedat et al. · cambridge

Identification and appropriate handling of inconsistencies in data at deployment time is crucial to reliably use machine learning models. While recent data-centric methods are able to identify such inconsistencies with respect to the training set, they suffer from two key limitations: (1) suboptimality in settings where features exhibit statistical independencies, due to their usage of compressive representations and (2) lack of localization to pin-point why a sample might be flagged as inconsistent, which is important to guide future data collection. We solve these two fundamental limitations using directed acyclic graphs (DAGs) to encode the training set's features probability distribution and independencies as a structure. Our method, called DAGnosis, leverages these structural interactions to bring valuable and insightful data-centric conclusions. DAGnosis unlocks the localization of the causes of inconsistencies on a DAG, an aspect overlooked by previous approaches. Moreover, we show empirically that leveraging these interactions (1) leads to more accurate conclusions in detecting inconsistencies, as well as (2) provides more detailed insights into why some samples are flagged.

Boris van Breugel, Jonathan Crabbé, Rob Davis et al.

Tabular data is one of the most ubiquitous modalities, yet the literature on tabular generative foundation models is lagging far behind its text and vision counterparts. Creating such a model is hard, due to the heterogeneous feature spaces of different tabular datasets, tabular metadata (e.g. dataset description and feature headers), and tables lacking prior knowledge (e.g. feature order). In this work we propose LaTable: a novel tabular diffusion model that addresses these challenges and can be trained across different datasets. Through extensive experiments we find that LaTable outperforms baselines on in-distribution generation, and that finetuning LaTable can generate out-of-distribution datasets better with fewer samples. On the other hand, we explore the poor zero-shot performance of LaTable, and what it may teach us about building generative tabular foundation models with better zero- and few-shot generation capabilities.

Nabeel Seedat, Jonathan Crabbé, Mihaela van der Schaar

Systematic quantification of data quality is critical for consistent model performance. Prior works have focused on out-of-distribution data. Instead, we tackle an understudied yet equally important problem of characterizing incongruous regions of in-distribution (ID) data, which may arise from feature space heterogeneity. To this end, we propose a paradigm shift with Data-SUITE: a data-centric AI framework to identify these regions, independent of a task-specific model. Data-SUITE leverages copula modeling, representation learning, and conformal prediction to build feature-wise confidence interval estimators based on a set of training instances. These estimators can be used to evaluate the congruence of test instances with respect to the training set, to answer two practically useful questions: (1) which test instances will be reliably predicted by a model trained with the training instances? and (2) can we identify incongruous regions of the feature space so that data owners understand the data's limitations or guide future data collection? We empirically validate Data-SUITE's performance and coverage guarantees and demonstrate on cross-site medical data, biased data, and data with concept drift, that Data-SUITE best identifies ID regions where a downstream model may be reliable (independent of said model). We also illustrate how these identified regions can provide insights into datasets and highlight their limitations.

Jonathan Crabbé, Zhaozhi Qian, Fergus Imrie et al.

Modern machine learning models are complicated. Most of them rely on convoluted latent representations of their input to issue a prediction. To achieve greater transparency than a black-box that connects inputs to predictions, it is necessary to gain a deeper understanding of these latent representations. To that aim, we propose SimplEx: a user-centred method that provides example-based explanations with reference to a freely selected set of examples, called the corpus. SimplEx uses the corpus to improve the user's understanding of the latent space with post-hoc explanations answering two questions: (1) Which corpus examples explain the prediction issued for a given test example? (2) What features of these corpus examples are relevant for the model to relate them to the test example? SimplEx provides an answer by reconstructing the test latent representation as a mixture of corpus latent representations. Further, we propose a novel approach, the Integrated Jacobian, that allows SimplEx to make explicit the contribution of each corpus feature in the mixture. Through experiments on tasks ranging from mortality prediction to image classification, we demonstrate that these decompositions are robust and accurate. With illustrative use cases in medicine, we show that SimplEx empowers the user by highlighting relevant patterns in the corpus that explain model representations. Moreover, we demonstrate how the freedom in choosing the corpus allows the user to have personalized explanations in terms of examples that are meaningful for them.

Jonathan Crabbé, Mihaela van der Schaar

How can we explain the predictions of a machine learning model? When the data is structured as a multivariate time series, this question induces additional difficulties such as the necessity for the explanation to embody the time dependency and the large number of inputs. To address these challenges, we propose dynamic masks (Dynamask). This method produces instance-wise importance scores for each feature at each time step by fitting a perturbation mask to the input sequence. In order to incorporate the time dependency of the data, Dynamask studies the effects of dynamic perturbation operators. In order to tackle the large number of inputs, we propose a scheme to make the feature selection parsimonious (to select no more feature than necessary) and legible (a notion that we detail by making a parallel with information theory). With synthetic and real-world data, we demonstrate that the dynamic underpinning of Dynamask, together with its parsimony, offer a neat improvement in the identification of feature importance over time. The modularity of Dynamask makes it ideal as a plug-in to increase the transparency of a wide range of machine learning models in areas such as medicine and finance, where time series are abundant.

Jonathan Crabbé, Yao Zhang, William Zame et al.

Machine Learning has proved its ability to produce accurate models but the deployment of these models outside the machine learning community has been hindered by the difficulties of interpreting these models. This paper proposes an algorithm that produces a continuous global interpretation of any given continuous black-box function. Our algorithm employs a variation of projection pursuit in which the ridge functions are chosen to be Meijer G-functions, rather than the usual polynomial splines. Because Meijer G-functions are differentiable in their parameters, we can tune the parameters of the representation by gradient descent; as a consequence, our algorithm is efficient. Using five familiar data sets from the UCI repository and two familiar machine learning algorithms, we demonstrate that our algorithm produces global interpretations that are both highly accurate and parsimonious (involve a small number of terms). Our interpretations permit easy understanding of the relative importance of features and feature interactions. Our interpretation algorithm represents a leap forward from the previous state of the art.