Multimodal learning has mainly focused on learning large models on, and fusing feature representations from, different modalities for better performances on downstream tasks. In this work, we take a detour from this trend and study the intrinsic nature of multimodal data by asking the following questions: 1) Can we learn more structured latent representations of general multimodal data?; and 2) can we intuitively understand, both mathematically and visually, what the latent representations capture? To answer 1), we propose a general and lightweight framework, Multimodal Understanding Through Correlation Maximization and Minimization (MUCMM), that can be incorporated into any large pre-trained network. MUCMM learns both the common and individual representations. The common representations capture what is common between the modalities; the individual representations capture the unique aspect of the modalities. To answer 2), we propose novel scores that summarize the learned common and individual structures and visualize the score gradients with respect to the input, visually discerning what the different representations capture. We further provide mathematical intuitions of the computed gradients in a linear setting, and demonstrate the effectiveness of our approach through a variety of experiments.

Approaches for rapidly identifying patients at high risk of early breast cancer recurrence are needed. Image-based methods for prescreening hematoxylin and eosin (H&E) stained tumor slides could offer temporal and financial efficiency. We evaluated a data set of 704 1-mm tumor core H&E images (2–4 cores per case), corresponding to 202 participants (101 who recurred; 101 non-recurrent matched on age and follow-up time) from breast cancers diagnosed between 2008–2012 in the Carolina Breast Cancer Study. We leveraged deep learning to extract image information and trained a model to identify recurrence. Cross-validation accuracy for predicting recurrence was 62.4% [95% CI: 55.7, 69.1], similar to grade (65.8% [95% CI: 59.3, 72.3]) and ER status (66.3% [95% CI: 59.8, 72.8]). Interestingly, 70% (19/27) of early-recurrent low-intermediate grade tumors were identified by our image model. Relative to existing markers, image-based analyses provide complementary information for predicting early recurrence.

Mixture models are universal approximators of smooth densities but are difficult to utilize in complicated datasets due to restrictions on typically available modes and challenges with initialiations. We show that by continuously parameterizing a mixture of factor analyzers using a learned ordinary differential equation, we can improve the fit of mixture models over direct methods. Once trained, the mixture components can be extracted and the neural ODE can be discarded, leaving us with an effective, but low-resource model. We additionally explore the use of a training curriculum from an easy-to-model latent space extracted from a normalizing flow to the more complex input space and show that the smooth curriculum helps to stabilize and improve results with and without the continuous parameterization. Finally, we introduce a hierarchical version of the model to enable more flexible, robust classification and clustering, and show substantial improvements against traditional parameterizations of GMMs.

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. For readers who are interested in the detailed derivations of serveral results that we present in this work, please see the supplementary material at: https://arxiv.org/abs/1909.09877.

In this work we develop a novel Bayesian neural network methodology to achieve strong adversarial robustness without the need for online adversarial training. Unlike previous efforts in this direction, we do not rely solely on the stochasticity of network weights by minimizing the divergence between the learned parameter distribution and a prior. Instead, we additionally require that the model maintain some expected uncertainty with respect to all input covariates. We demonstrate that by encouraging the network to distribute evenly across inputs, the network becomes less susceptible to localized, brittle features which imparts a natural robustness to targeted perturbations. We show empirical robustness on several benchmark datasets.