The goal of this work is to develop principled techniques to extract information from high dimensional data sets with complex dependencies in areas such as medicine that can provide insight into individual as well as population level variation. We develop $\texttt{LucidAtlas}$, an approach that can represent spatially varying information, and can capture the influence of covariates as well as population uncertainty. As a versatile atlas representation, $\texttt{LucidAtlas}$ offers robust capabilities for covariate interpretation, individualized prediction, population trend analysis, and uncertainty estimation, with the flexibility to incorporate prior knowledge. Additionally, we discuss the trustworthiness and potential risks of neural additive models for analyzing dependent covariates and then introduce a marginalization approach to explain the dependence of an individual predictor on the models' response (the atlas). To validate our method, we demonstrate its generalizability on two medical datasets. Our findings underscore the critical role of by-construction interpretable models in advancing scientific discovery. Our code will be publicly available upon acceptance.

Artificial intelligence has significantly impacted medical applications, particularly with the advent of Medical Large Vision Language Models (Med-LVLMs), sparking optimism for the future of automated and personalized healthcare. However, the trustworthiness of Med-LVLMs remains unverified, posing significant risks for future model deployment. In this paper, we introduce CARES and aim to Comprehensively evAluate the tRustworthinESs of Med-LVLMs across the medical domain. We assess the trustworthiness of Med-LVLMs across five dimensions, including trustfulness, fairness, safety, privacy, and robustness. CARES comprises about 41K question-answer pairs in both closed and open-ended formats, covering 16 medical image modalities and 27 anatomical regions. Our analysis reveals that the models consistently exhibit concerns regarding trustworthiness, often displaying factual inaccuracies and failing to maintain fairness across different demographic groups. Furthermore, they are vulnerable to attacks and demonstrate a lack of privacy awareness.

Medical records often consist of different modalities, such as images, text, and tabular information. Integrating all modalities offers a holistic view of a patient's condition, while analyzing them longitudinally provides a better understanding of disease progression. However, real-world longitudinal medical records present challenges: 1) patients may lack some or all of the data for a specific timepoint, and 2) certain modalities or views might be absent for all patients during a particular period. In this work, we introduce a unified model for longitudinal multi-modal multi-view prediction with missingness. Our method allows as many timepoints as desired for input, and aims to leverage all available data, regardless of their availability. We conduct extensive experiments on the knee osteoarthritis dataset from the Osteoarthritis Initiative for pain and Kellgren-Lawrence grade prediction at a future timepoint. We demonstrate the effectiveness of our method by comparing results from our unified model to specific models that use the same modality and view combinations during training and evaluation. We also show the benefit of having extended temporal data and provide post-hoc analysis for a deeper understanding of each modality/view's importance for different tasks.

We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class -- in our case, Rademacher complexity -- how much can we (a-priori) constrain this class while maintaining an empirical error comparable to the unconstrained setting. To assess excess capacity in modern architectures, we first extend an existing generalization bound to accommodate function composition and addition, as well as the specific structure of convolutions. This then facilitates studying residual networks through the lens of the accompanying capacity measure. The key quantities driving this measure are the Lipschitz constants of the layers and the (2,1) group norm distance to the initializations of the convolution weights. We show that these quantities (1) can be kept surprisingly small and, (2) since excess capacity unexpectedly increases with task difficulty, this points towards an unnecessarily large capacity of unconstrained models.

Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.

Mitigating bias in machine learning is a challenging task, due in large part to the presence of competing objectives. Namely, a fair algorithm often comes at the cost of lower predictive accuracy, and vice versa, a highly predictive algorithm may be one that incurs high bias. This work presents a methodology for estimating the fairness-accuracy Pareto front of a fully-connected feedforward neural network, for any accuracy measure and any fairness measure. Our experiments firstly reveal that for training data already exhibiting disparities, a newly introduced causal notion of fairness may be capable of traversing a greater part of the fairness-accuracy space, relative to more standard measures such as demographic parity and conditional parity. The experiments also reveal that tools from multi-objective optimisation are crucial in efficiently estimating the Pareto front (i.e., by finding more non-dominated points), relative to other sensible but ad-hoc approaches. Finally, the work serves to highlight possible synergy between deep learning and multi-objective optimisation. Given that deep learning is increasingly deployed in real-world decision making, the Pareto front can provide a formal way to reason about inherent conflicts.

Clustering and prediction are two primary tasks in the fields of unsupervised and supervised learning, respectively. Although much of the recent advances in machine learning have been centered around those two tasks, the interdependent, mutually beneficial relationship between them is rarely explored. One could reasonably expect appropriately clustering the data would aid the downstream prediction task and, conversely, a better prediction performance for the downstream task could potentially inform a more appropriate clustering strategy. In this work, we focus on the latter part of this mutually beneficial relationship. To this end, we introduce Deep Goal-Oriented Clustering (DGC), a probabilistic framework that clusters the data by jointly using supervision via side-information and unsupervised modeling of the inherent data structure in an end-to-end fashion. We show the effectiveness of our model on a range of datasets by achieving prediction accuracies comparable to the state-of-the-art, while, more importantly in our setting, simultaneously learning congruent clustering strategies.

Modern methods for learning over graph input data have shown the fruitfulness of accounting for relationships among elements in a collection. However, most methods that learn over set input data use only rudimentary approaches to exploit intra-collection relationships. In this work we introduce Deep Message Passing on Sets (DMPS), a novel method that incorporates relational learning for sets. DMPS not only connects learning on graphs with learning on sets via deep kernel learning, but it also bridges message passing on sets and traditional diffusion dynamics commonly used in denoising models. Based on these connections, we develop two new blocks for relational learning on sets: the set-denoising block and the set-residual block . The former is motivated by the connection between message passing on general graphs and diffusion-based denoising models, whereas the latter is inspired by the well-known residual network. In addition to demonstrating the interpretability of our model by learning the true underlying relational structure experimentally, we also show the effectiveness of our approach on both synthetic and real-world datasets by achieving results that are competitive with or outperform the state-of-the-art.

Canonical Correlation Analysis (CCA) is widely used for multimodal data analysis and, more recently, for discriminative tasks such as multi-view learning; however, it makes no use of class labels. Recent CCA methods have started to address this weakness but are limited in that they do not simultaneously optimize the CCA projection for discrimination and the CCA projection itself, or they are linear only. We address these deficiencies by simultaneously optimizing a CCA-based and a task objective in an end-to-end manner. Together, these two objectives learn a non-linear CCA projection to a shared latent space that is highly correlated and discriminative. Our method shows a significant improvement over previous state-of-the-art (including deep supervised approaches) for cross-view classification, regularization with a second view, and semi-supervised learning on real data.

We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an autoencoder's latent space via a novel type of loss, operating on information from persistent homology. Under mild conditions, this loss is differentiable and we present a theoretical analysis of the properties induced by the loss. We choose one-class learning as our upstream task and demonstrate that the imposed structure enables informed parameter selection for modeling the in-class distribution via kernel density estimators. Evaluated on computer vision data, these one-class models exhibit competitive performance and, in a low sample size regime, outperform other methods by a large margin. Notably, our results indicate that a single autoencoder, trained on auxiliary (unlabeled) data, yields a mapping into latent space that can be reused across datasets for one-class learning.