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The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…

3D contrastive representation learning has exhibited remarkable efficacy across various downstream tasks. However, existing contrastive learning paradigms based on cosine similarity fail to deeply explore the potential intra-modal…

Retrieval-augmented generation (RAG) for biomedical knowledge faces a hierarchy-aware ontology grounding challenge: resources like HPO, DO, and MeSH use deep ``is-a" taxonomies, yet production stacks rely on Euclidean embeddings and ANN…

Genomic sequence analysis plays a crucial role in various scientific and medical domains. Traditional machine-learning approaches often struggle to capture the complex relationships and hierarchical structures of sequence data when working…

This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…

This position paper summarizes a recently developed research program focused on inference in the context of data centric science and engineering applications, and forecasts its trajectory forward over the next decade. Often one endeavours…

We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…

How can we represent hierarchical information present in large type inventories for entity typing? We study the ability of hyperbolic embeddings to capture hierarchical relations between mentions in context and their target types in a…

Many real-world networks exhibit hierarchical, tree-like structure and heavy-tailed degree distributions, phenomena not readily captured by standard statistical models for network data. Extensions of the popular continuous latent space…

In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…

The rapid growth in genomic pathogen data spurs the need for efficient inference techniques, such as Hamiltonian Monte Carlo (HMC) in a Bayesian framework, to estimate parameters of these phylogenetic models where the dimensions of the…

We show an efficient algorithm for generating geodesic regular tree structures for periodic hyperbolic and Euclidean tessellations and experimentally verify its performance on tessellations.

Hyperbolic space is quickly gaining traction as a promising geometry for hierarchical and robust representation learning. A core open challenge is the development of a mathematical formulation of hyperbolic neural networks that is both…

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

Hyperbolic space can naturally embed hierarchies, unlike Euclidean space. Hyperbolic Neural Networks (HNNs) exploit such representational power by lifting Euclidean features into hyperbolic space for classification, outperforming Euclidean…

In this article we consider a Bayesian inverse problem associated to elliptic partial differential equations (PDEs) in two and three dimensions. This class of inverse problems is important in applications such as hydrology, but the…

Homologous proteins evolve from a common ancestral sequence, constrained by intricate patterns of co-evolving residues. Accurate reconstruction of evolutionary histories remains a challenge, primarily due to the inability of the existing…

Recent research in representation learning has shown that hierarchical data lends itself to low-dimensional and highly informative representations in hyperbolic space. However, even if hyperbolic embeddings have gathered attention in image…

Continual learning has traditionally focused on classifying either instances or classes, but real-world applications, such as robotics and self-driving cars, require models to handle both simultaneously. To mirror real-life scenarios, we…

Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts,…