Babak Shahbaba

Cheng Zhang, Babak Shahbaba, Hongkai Zhao

Markov Chain Monte Carlo (MCMC) algorithms play an important role in statistical inference problems dealing with intractable probability distributions. Recently, many MCMC algorithms such as Hamiltonian Monte Carlo (HMC) and Riemannian Manifold HMC have been proposed to provide distant proposals with high acceptance rate. These algorithms, however, tend to be computationally intensive which could limit their usefulness, especially for big data problems due to repetitive evaluations of functions and statistical quantities that depend on the data. This issue occurs in many statistic computing problems. In this paper, we propose a novel strategy that exploits smoothness (regularity) of parameter space to improve computational efficiency of MCMC algorithms. When evaluation of functions or statistical quantities are needed at a point in parameter space, interpolation from precomputed values or previous computed values is used. More specifically, we focus on Hamiltonian Monte Carlo (HMC) algorithms that use geometric information for faster exploration of probability distributions. Our proposed method is based on precomputing the required geometric information on a set of grids before running sampling information at nearby grids at each iteration of HMC. Sparse grid interpolation method is used for high dimensional problems. Tests on computational examples are shown to illustrate the advantages of our method.

Ba-Hien Tran, Babak Shahbaba, Stephan Mandt et al.

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.

Wenzhuo Zhou, Annie Qu, Keiland W. Cooper et al.

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their 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 effectively 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 node features. Theoretically, we establish the generalization error bound for MaGNet via empirical Rademacher complexity, and demonstrate 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.

Ziyi Liang, Hamed Poursiami, Zhishun Yang et al.

Hyperdimensional Computing (HDC) offers a computationally efficient paradigm for neuromorphic learning. Yet, it lacks rigorous uncertainty quantification, leading to open decision boundaries and, consequently, vulnerability to outliers, adversarial perturbations, and out-of-distribution inputs. To address these limitations, we introduce ConformalHDC, a unified framework that combines the statistical guarantees of conformal prediction with the computational efficiency of HDC. For this framework, we propose two complementary variations. First, the set-valued formulation provides finite-sample, distribution-free coverage guarantees. Using carefully designed conformity scores, it forms enclosed decision boundaries that improve robustness to non-conforming inputs. Second, the point-valued formulation leverages the same conformity scores to produce a single prediction when desired, potentially improving accuracy over traditional HDC by accounting for class interactions. We demonstrate the broad applicability of the proposed framework through evaluations on multiple real-world datasets. In particular, we apply our method to the challenging problem of decoding non-spatial stimulus information from the spiking activity of hippocampal neurons recorded as subjects performed a sequence memory task. Our results show that ConformalHDC not only accurately decodes the stimulus information represented in the neural activity data, but also provides rigorous uncertainty estimates and correctly abstains when presented with data from other behavioral states. Overall, these capabilities position the framework as a reliable, uncertainty-aware foundation for neuromorphic computing.

Zahra Moslemi, Ziyi Liang, Norbert Fortin et al.

Multi-graph learning is crucial for extracting meaningful signals from collections of heterogeneous graphs. However, effectively integrating information across graphs with differing topologies, scales, and semantics, often in the absence of shared node identities, remains a significant challenge. We present the Multi-Graph Meta-Transformer (MGMT), a unified, scalable, and interpretable framework for cross-graph learning. MGMT first applies Graph Transformer encoders to each graph, mapping structure and attributes into a shared latent space. It then selects task-relevant supernodes via attention and builds a meta-graph that connects functionally aligned supernodes across graphs using similarity in the latent space. Additional Graph Transformer layers on this meta-graph enable joint reasoning over intra- and inter-graph structure. The meta-graph provides built-in interpretability: supernodes and superedges highlight influential substructures and cross-graph alignments. Evaluating MGMT on both synthetic datasets and real-world neuroscience applications, we show that MGMT consistently outperforms existing state-of-the-art models in graph-level prediction tasks while offering interpretable representations that facilitate scientific discoveries. Our work establishes MGMT as a unified framework for structured multi-graph learning, advancing representation techniques in domains where graph-based data plays a central role.

Babak Shahbaba, Zahra Moslemi

Humans learn efficiently from their environment by engaging multiple interacting neural systems that support distinct yet complementary forms of control, including model-based (goal-directed) planning, model-free (habitual) responding, and episodic memory-based learning. Model-based mechanisms compute prospective action values using an internal model of the environment, supporting flexible but computationally costly planning; model-free mechanisms cache value estimates and build heuristics that enable fast, efficient habitual responding; and memory-based mechanisms allow rapid adaptation from individual experience. In this work, we aim to elucidate the computational principles underlying this biological efficiency and translate them into a sampling algorithm for scalable Bayesian inference through effective exploration of the posterior distribution. More specifically, our proposed algorithm comprises three components: a model-based module that uses the target distribution for guided but computationally slow sampling; a model-free module that uses previous samples to learn patterns in the parameter space, enabling fast, reflexive sampling without directly evaluating the expensive target distribution; and an episodic-control module that supports rapid sampling by recalling specific past events (i.e., samples). We show that this approach advances Bayesian methods and facilitates their application to large-scale statistical machine learning problems. In particular, we apply our proposed framework to Bayesian deep learning, with an emphasis on proper and principled uncertainty quantification.

Thomas M. Sutter, Yang Meng, Andrea Agostini et al.

Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or both across modalities to learn a shared representation. Such architectures impose hard constraints on the model. In this work, we show that a better latent representation can be obtained by replacing these hard constraints with a soft constraint. We propose a new mixture-of-experts prior, softly guiding each modality's latent representation towards a shared aggregate posterior. This approach results in a superior latent representation and allows each encoding to preserve information better from its uncompressed original features. In extensive experiments on multiple benchmark datasets and two challenging real-world datasets, we show improved learned latent representations and imputation of missing data modalities compared to existing methods.

Andrea Agostini, Daphné Chopard, Yang Meng et al.

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.

Rui Miao, Babak Shahbaba, Annie Qu

Offline reinforcement learning (RL) aims to find optimal policies in dynamic environments in order to maximize the expected total rewards by leveraging pre-collected data. Learning from heterogeneous data is one of the fundamental challenges in offline RL. Traditional methods focus on learning an optimal policy for all individuals with pre-collected data from a single episode or homogeneous batch episodes, and thus, may result in a suboptimal policy for a heterogeneous population. In this paper, we propose an individualized offline policy optimization framework for heterogeneous time-stationary Markov decision processes (MDPs). The proposed heterogeneous model with individual latent variables enables us to efficiently estimate the individual Q-functions, and our Penalized Pessimistic Personalized Policy Learning (P4L) algorithm guarantees a fast rate on the average regret under a weak partial coverage assumption on behavior policies. In addition, our simulation studies and a real data application demonstrate the superior numerical performance of the proposed method compared with existing methods.

Ziyi Liang, Annie Qu, Babak Shahbaba

Developing effective multimodal data fusion strategies has become increasingly essential for improving the predictive power of statistical machine learning methods across a wide range of applications, from autonomous driving to medical diagnosis. Traditional fusion methods, including early, intermediate, and late fusion, integrate data at different stages, each offering distinct advantages and limitations. In this paper, we introduce Meta Fusion, a flexible and principled framework that unifies these existing strategies as special cases. Motivated by deep mutual learning and ensemble learning, Meta Fusion constructs a cohort of models based on various combinations of latent representations across modalities, and further boosts predictive performance through soft information sharing within the cohort. Our approach is model-agnostic in learning the latent representations, allowing it to flexibly adapt to the unique characteristics of each modality. Theoretically, our soft information sharing mechanism reduces the generalization error. Empirically, Meta Fusion consistently outperforms conventional fusion strategies in extensive simulation studies. We further validate our approach on real-world applications, including Alzheimer's disease detection and neural decoding.

Yubai Yuan, Babak Shahbaba, Norbert Fortin et al.

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.

Shiwei Lan, Shuyi Li, Babak Shahbaba

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 models for the emulation phase. The resulting algorithm is computationally more efficient and more robust against variations in 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 (DREAMC)} algorithm, is able to scale Bayesian UQ up to thousands of dimensions for inverse problems. Using two low-dimensional (linear and nonlinear) inverse problems we illustrate the validity of this approach. Next, we apply our method to two high-dimensional numerical examples (elliptic and advection-diffussion) to demonstrate its computational advantages over existing algorithms.

Michelle N. Ngo, Dustin S. Pluta, Alexander N. Ngo et al.

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.

Tian Chen, Lingge Li, Gabriel Elias et al.

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.

Andrew Holbrook, Alexander Vandenberg-Rodes, Babak Shahbaba

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.

Cheng Zhang, Babak Shahbaba, Hongkai Zhao

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.

Shiwei Lan, Babak Shahbaba

Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained domains could be quite challenging for commonly used sampling algorithms. In this paper, we propose a novel augmentation technique that handles a wide range of constraints by mapping the constrained domain to a sphere in the augmented space. By moving freely on the surface of this sphere, sampling algorithms handle constraints implicitly and generate proposals that remain within boundaries when mapped back to the original space. Our proposed method, called {Spherical Augmentation}, provides a mathematically natural and computationally efficient framework for sampling from constrained probability distributions. We show the advantages of our method over state-of-the-art sampling algorithms, such as exact Hamiltonian Monte Carlo, using several examples including truncated Gaussian distributions, Bayesian Lasso, Bayesian bridge regression, reconstruction of quantized stationary Gaussian process, and LDA for topic modeling.

Cheng Zhang, Babak Shahbaba, Hongkai Zhao

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.

Alexander Vandenberg-Rodes, Babak Shahbaba

For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Matérn processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown values. Although similar models have been proposed in the econometric, statistics, and machine learning literature, our approach has several advantages that distinguish it from existing methods: 1) it is flexible to provide high prediction accuracy, yet its complexity is controlled to avoid overfitting; 2) its interpretability separates it from black-box methods; 3) finally, its computational efficiency makes it scalable for high-dimensional time series. In this paper, we use several simulated and real data sets to illustrate these advantages. We will also briefly discuss some extensions of our model.

Shiwei Lan, Babak Shahbaba

In this paper, we discuss an extension of the Split Hamiltonian Monte Carlo (Split HMC) method for Gaussian process model (GPM). This method is based on splitting the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. To this end, we approximate the negative log density (i.e., the energy function) of the distribution of interest by a quadratic function U0 for which Hamiltonian dynamics can be solved analytically. The overall energy function U is then written as U0 + U1, where U1 is the approximation error. The Hamiltonian is then split into two parts; one part is based on U0 is handled analytically, the other part is based on U1 for which we approximate Hamiltonian's equations by discretizing time. We use simulated and real data to compare the performance of our method to the standard HMC. We find that splitting the Hamiltonian for GP models could lead to substantial improvement (up to 10 folds) of sampling efficiency, which is measured in terms of the amount of time required for producing an independent sample with high acceptance probability from posterior distributions.