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Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…
Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…
The Euclidean Directed Spanning Forest is a random forest in $\mathbb{R}^d$ introduced by Baccelli and Bordenave in 2007 and we introduce and study here the analogous tree in the hyperbolic space. The topological properties of the Euclidean…
Cross-lingual word embeddings can be applied to several natural language processing applications across multiple languages. Unlike prior works that use word embeddings based on the Euclidean space, this short paper presents a simple and…
Natural language text exhibits hierarchical structure in a variety of respects. Ideally, we could incorporate our prior knowledge of this hierarchical structure into unsupervised learning algorithms that work on text data. Recent work by…
The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
Learning fine-grained embeddings from coarse labels is a challenging task due to limited label granularity supervision, i.e., lacking the detailed distinctions required for fine-grained tasks. The task becomes even more demanding when…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to…
We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…
Modern training and inference pipelines in statistical learning and deep learning repeatedly invoke linear-system solves as inner loops, yet high-accuracy deterministic solvers can be prohibitively expensive when solves must be repeated…
Biological diversity has evolved despite the essentially infinite complexity of protein sequence space. We present a hierarchical approach to the efficient searching of this space and quantify the evolutionary potential of our approach with…
Reconstructing the evolutionary history relating a collection of molecular sequences is the main subject of modern Bayesian phylogenetic inference. However, the commonly used Markov chain Monte Carlo methods can be inefficient due to the…
Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically…
Hyperbolic space has become a popular choice of manifold for representation learning of various datatypes from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical…
Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to…
Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…
Hyperbolic geometry has been successfully applied in modeling brain cortical and subcortical surfaces with general topological structures. However such approaches, similar to other surface based brain morphology analysis methods, usually…