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Marcus Brubaker

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3 papers

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NeurIPS Conference 2025 Conference Paper

Reconstructing Heterogeneous Biomolecules via Hierarchical Gaussian Mixtures and Part Discovery

Shayan Shekarforoush
David Lindell
Marcus Brubaker
David Fleet

Cryo-EM is a transformational paradigm in molecular biology where computational methods are used to infer 3D molecular structure at atomic resolution from extremely noisy 2D electron microscope images. At the forefront of research is how to model the structure when the imaged particles exhibit non-rigid conformational flexibility and compositional variation where parts are sometimes missing. We introduce a novel 3D reconstruction framework with a hierarchical Gaussian mixture model, inspired in part by Gaussian Splatting for 4D scene reconstruction. In particular, the structure of the model is grounded in an initial process that infers a part-based segmentation of the particle, providing essential inductive bias in order to handle both conformational and compositional variability. The framework, called \methodName, is shown to reveal biologically meaningful structures on complex experimental datasets, and establishes a new state-of-the-art on CryoBench, a benchmark for cryo-EM heterogeneity methods.

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AAAI Conference 2020 Conference Paper

Diachronic Embedding for Temporal Knowledge Graph Completion

Rishab Goel
Seyed Mehran Kazemi
Marcus Brubaker
Pascal Poupart

Knowledge graphs (KGs) typically contain temporal facts indicating relationships among entities at different times. Due to their incompleteness, several approaches have been proposed to infer new facts for a KG based on the existing ones– a problem known as KG completion. KG embedding approaches have proved effective for KG completion, however, they have been developed mostly for static KGs. Developing temporal KG embedding models is an increasingly important problem. In this paper, we build novel models for temporal KG completion through equipping static models with a diachronic entity embedding function which provides the characteristics of entities at any point in time. This is in contrast to the existing temporal KG embedding approaches where only static entity features are provided. The proposed embedding function is model-agnostic and can be potentially combined with any static model. We prove that combining it with SimplE, a recent model for static KG embedding, results in a fully expressive model for temporal KG completion. Our experiments indicate the superiority of our proposal compared to existing baselines.

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NeurIPS Conference 2013 Conference Paper

Efficient Optimization for Sparse Gaussian Process Regression

Yanshuai Cao
Marcus Brubaker
David Fleet
Aaron Hertzmann

We propose an efficient discrete optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates this inducing set and the hyperparameters using a single objective, either the marginal likelihood or a variational free energy. The space and time complexity are linear in the training set size, and the algorithm can be applied to large regression problems on discrete or continuous domains. Empirical evaluation shows state-of-art performance in the discrete case and competitive results in the continuous case.

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