Weakly-Supervised Multimodal Learning on MIMIC-CXR

Multimodal data integration and label scarcity pose significant challenges for machine learning in medical settings. To address these issues, we conduct an in-depth evaluation of the newly proposed Multimodal Variational Mixture-of-Experts (MMVM) VAE on the challenging MIMIC-CXR dataset. Our analysis demonstrates that the MMVM VAE consistently outperforms other multimodal VAEs and fully supervised approaches, highlighting its strong potential for real-world medical applications.

Optimal Transport for Latent Integration with An Application to Heterogeneous Neuronal Activity Data

Detecting dynamic patterns of task-specific responses shared across heterogeneous datasets is an essential and challenging problem in many scientific applications in medical science and neuroscience. In our motivating example of rodent electrophysiological data, identifying the dynamical patterns in neuronal activity associated with ongoing cognitive demands and behavior is key to uncovering the neural mechanisms of memory. One of the greatest challenges in investigating a cross-subject biological process is that the systematic heterogeneity across individuals could significantly undermine the power of existing machine learning methods to identify the underlying biological dynamics. In addition, many technically challenging neurobiological experiments are conducted on only a handful of subjects where rich longitudinal data are available for each subject. The low sample sizes of such experiments could further reduce the power to detect common dynamic patterns among subjects. In this paper, we propose a novel heterogeneous data integration framework based on optimal transport to extract shared patterns in complex biological processes. The key advantages of the proposed method are that it can increase discriminating power in identifying common patterns by reducing heterogeneity unrelated to the signal by aligning the extracted latent spatiotemporal information across subjects. Our approach is effective even with a small number of subjects, and does not require auxiliary matching information for the alignment. In particular, our method can align longitudinal data across heterogeneous subjects in a common latent space to capture the dynamics of shared patterns while utilizing temporal dependency within subjects.

A Model-Agnostic Graph Neural Network for Integrating Local and Global Information

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, existing GNNs suffer from two significant limitations: a lack of interpretability in results due to their black-box nature, and an inability to learn representations of varying orders. To tackle these issues, we propose a novel Model-agnostic Graph Neural Network (MaGNet) framework, which is able to sequentially integrate information of various orders, extract knowledge from high-order neighbors, and provide meaningful and interpretable results by identifying influential compact graph structures. In particular, MaGNet consists of two components: an estimation model for the latent representation of complex relationships under graph topology, and an interpretation model that identifies influential nodes, edges, and important node features. Theoretically, we establish the generalization error bound for MaGNet via empirical Rademacher complexity, and showcase its power to represent layer-wise neighborhood mixing. We conduct comprehensive numerical studies using simulated data to demonstrate the superior performance of MaGNet in comparison to several state-of-the-art alternatives. Furthermore, we apply MaGNet to a real-world case study aimed at extracting task-critical information from brain activity data, thereby highlighting its effectiveness in advancing scientific research.

Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes

Autoencoders and their variants are among the most widely used models in representation learning and generative modeling. However, autoencoder-based models usually assume that the learned representations are i.i.d. and fail to capture the correlations between the data samples. To address this issue, we propose a novel Sparse Gaussian Process Bayesian Autoencoder (SGPBAE) model in which we impose fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder. We perform posterior estimation for this model via stochastic gradient Hamiltonian Monte Carlo. We evaluate our approach qualitatively and quantitatively on a wide range of representation learning and generative modeling tasks and show that our approach consistently outperforms multiple alternatives relying on Variational Autoencoders.

Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks

Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov Chain Monte Carlo (MCMC) tend to be computationally intensive and inefficient for such high dimensional problems. To address this issue, several methods based on surrogate models have been proposed to speed up the inference process. More specifically, the calibration-emulation-sampling (CES) scheme has been proven to be successful in large dimensional UQ problems. In this work, we propose a novel CES approach for Bayesian inference based on deep neural network (DNN) models for the emulation phase. The resulting algorithm is not only computationally more efficient, but also less sensitive to the training set. Further, by using an Autoencoder (AE) for dimension reduction, we have been able to speed up our Bayesian inference method up to three orders of magnitude. Overall, our method, henceforth called \emph{Dimension-Reduced Emulative Autoencoder Monte Carlo (DREAM)} algorithm, is able to scale Bayesian UQ up to thousands of dimensions in physics-constrained inverse problems. Using two low-dimensional (linear and nonlinear) inverse problems we illustrate the validity this approach. Next, we apply our method to two high-dimensional numerical examples (elliptic and advection-diffussion) to demonstrate its computational advantage over existing algorithms.

Conjoined Dirichlet Process

Biclustering is a class of techniques that simultaneously clusters the rows and columns of a matrix to sort heterogeneous data into homogeneous blocks. Although many algorithms have been proposed to find biclusters, existing methods suffer from the pre-specification of the number of biclusters or place constraints on the model structure. To address these issues, we develop a novel, non-parametric probabilistic biclustering method based on Dirichlet processes to identify biclusters with strong co-occurrence in both rows and columns. The proposed method utilizes dual Dirichlet process mixture models to learn row and column clusters, with the number of resulting clusters determined by the data rather than pre-specified. Probabilistic biclusters are identified by modeling the mutual dependence between the row and column clusters. We apply our method to two different applications, text mining and gene expression analysis, and demonstrate that our method improves bicluster extraction in many settings compared to existing approaches.

Bayesian Neural Decoding Using A Diversity-Encouraging Latent Representation Learning Method

It is well established that temporal organization is critical to memory, and that the ability to temporally organize information is fundamental to many perceptual, cognitive, and motor processes. While our understanding of how the brain processes the spatial context of memories has advanced considerably, our understanding of their temporal organization lags far behind. In this paper, we propose a new approach for elucidating the neural basis of complex behaviors and temporal organization of memories. More specifically, we focus on neural decoding - the prediction of behavioral or experimental conditions based on observed neural data. In general, this is a challenging classification problem, which is of immense interest in neuroscience. Our goal is to develop a new framework that not only improves the overall accuracy of decoding, but also provides a clear latent representation of the decoding process. To accomplish this, our approach uses a Variational Auto-encoder (VAE) model with a diversity-encouraging prior based on determinantal point processes (DPP) to improve latent representation learning by avoiding redundancy in the latent space. We apply our method to data collected from a novel rat experiment that involves presenting repeated sequences of odors at a single port and testing the rats' ability to identify each odor. We show that our method leads to substantially higher accuracy rate for neural decoding and allows to discover novel biological phenomena by providing a clear latent representation of the decoding process.

Variational Hamiltonian Monte Carlo via Score Matching

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining variational Bayesian inference and MCMC simulation in order to improve their overall accuracy and computational efficiency. This marriage of fast evaluation and flexible approximation provides a promising means of designing scalable Bayesian inference methods. In this paper, we explore the possibility of incorporating variational approximation into a state-of-the-art MCMC method, Hamiltonian Monte Carlo (HMC), to reduce the required gradient computation in the simulation of Hamiltonian flow, which is the bottleneck for many applications of HMC in big data problems. To this end, we use a {\it free-form} approximation induced by a fast and flexible surrogate function based on single-hidden layer feedforward neural networks. The surrogate provides sufficiently accurate approximation while allowing for fast exploration of parameter space, resulting in an efficient approximate inference algorithm. We demonstrate the advantages of our method on both synthetic and real data problems.

Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian Monte Carlo (HMC). The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the art methods.

Bayesian Inference on Matrix Manifolds for Linear Dimensionality Reduction

We reframe linear dimensionality reduction as a problem of Bayesian inference on matrix manifolds. This natural paradigm extends the Bayesian framework to dimensionality reduction tasks in higher dimensions with simpler models at greater speeds. Here an orthogonal basis is treated as a single point on a manifold and is associated with a linear subspace on which observations vary maximally. Throughout this paper, we employ the Grassmann and Stiefel manifolds for various dimensionality reduction problems, explore the connection between the two manifolds, and use Hybrid Monte Carlo for posterior sampling on the Grassmannian for the first time. We delineate in which situations either manifold should be considered. Further, matrix manifold models are used to yield scientific insight in the context of cognitive neuroscience, and we conclude that our methods are suitable for basic inference as well as accurate prediction.