25 citations · 63 across the 24 of their papers we have counts for
24 papers
Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?
Pedro C. Vieira, Pedro Ribeiro, Viacheslav Borovitskiy
While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply a…
Omnipresent Yet Overlooked: Heat Kernels in Combinatorial Bayesian Optimization
Colin Doumont, Victor Picheny, Viacheslav Borovitskiy +1
Bayesian Optimization (BO) has the potential to solve various combinatorial tasks, ranging from materials science to neural architecture search. However, BO requires specialized ke…
Residual Deep Gaussian Processes on Manifolds
Kacper Wyrwal, Andreas Krause, Viacheslav Borovitskiy
We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary l…
The GeometricKernels Package: Heat and Matérn Kernels for Geometric Learning on Manifolds, Meshes, and Graphs
Peter Mostowsky, Vincent Dutordoir, Iskander Azangulov +6
Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applicati…
Posterior Contraction Rates for Matérn Gaussian Processes on Riemannian Manifolds
Paul Rosa, Viacheslav Borovitskiy, Alexander Terenin +1
Gaussian processes are used in many machine learning applications that rely on uncertainty quantification. Recently, computational tools for working with these models in geometric…
Hodge-Compositional Edge Gaussian Processes
Maosheng Yang, Viacheslav Borovitskiy, Elvin Isufi
We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form tr…
Implicit Manifold Gaussian Process Regression
Bernardo Fichera, Viacheslav Borovitskiy, Andreas Krause +1
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with h…
Intrinsic Gaussian Vector Fields on Manifolds
Daniel Robert-Nicoud, Andreas Krause, Viacheslav Borovitskiy
Various applications ranging from robotics to climate science require modeling signals on non-Euclidean domains, such as the sphere. Gaussian process models on manifolds have recen…
Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spaces
Iskander Azangulov, Andrei Smolensky, Alexander Terenin +1
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used…
On power sum kernels on symmetric groups
Iskander Azangulov, Viacheslav Borovitskiy, Andrei Smolensky
In this note, we introduce a family of "power sum" kernels and the corresponding Gaussian processes on symmetric groups . Such processes are bi-invariant: the action…
Isotropic Gaussian Processes on Finite Spaces of Graphs
Viacheslav Borovitskiy, Mohammad Reza Karimi, Vignesh Ram Somnath +1
We propose a principled way to define Gaussian process priors on various sets of unweighted graphs: directed or undirected, with or without loops. We endow each of these sets with…
Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifolds
Noémie Jaquier, Leonel Rozo, Miguel González-Duque +2
Human motion taxonomies serve as high-level hierarchical abstractions that classify how humans move and interact with their environment. They have proven useful to analyse grasps,…
Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact case
Iskander Azangulov, Andrei Smolensky, Alexander Terenin +1
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used…
Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels
Michael Hutchinson, Alexander Terenin, Viacheslav Borovitskiy +3
Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-mak…
Geometry-aware Bayesian Optimization in Robotics using Riemannian Matérn Kernels
Noémie Jaquier, Viacheslav Borovitskiy, Andrei Smolensky +3
Bayesian optimization is a data-efficient technique which can be used for control parameter tuning, parametric policy adaptation, and structure design in robotics. Many of these pr…
Littlewood-Paley-Rubio de Francia inequality for multi-parameter Vilenkin systems
Viacheslav Borovitskiy
A version of Littlewood-Paley-Rubio de Francia inequality for bounded multi-parameter Vilenkin systems is proved: for any family of disjoint sets $I_k = I_k^1 \times \ldots \times…
Bellman function method for general operators on martingales
Viacheslav Borovitskiy, Nikolay N. Osipov, Anton Tselishchev
It is shown that the Bellman function method can be applied to study the -norms of general operators on martingales, i.e., of operators that are not necessarily martingale tra…
Littlewood-Paley-Rubio de Francia Inequality for the Two-parameter Walsh System
Viacheslav Borovitskiy
A version of Littlewood-Paley-Rubio de Francia inequality for the two-parameter Walsh system is proved: for any family of disjoint rectangles in ${\mathb…
Quadric Hypersurface Intersection for Manifold Learning in Feature Space
Fedor Pavutnitskiy, Sergei O. Ivanov, Evgeny Abramov +5
The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark an…
Pathwise Conditioning of Gaussian Processes
James T. Wilson, Viacheslav Borovitskiy, Alexander Terenin +2
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connectin…
Matérn Gaussian Processes on Graphs
Viacheslav Borovitskiy, Iskander Azangulov, Alexander Terenin +3
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many differen…
Matérn Gaussian processes on Riemannian manifolds
Viacheslav Borovitskiy, Alexander Terenin, Peter Mostowsky +1
Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance.…
Efficiently Sampling Functions from Gaussian Process Posteriors
James T. Wilson, Viacheslav Borovitskiy, Alexander Terenin +2
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predicti…
K-closedness of weighted Hardy spaces on the two-dimensional torus
V. Borovitskiy
It is proved that, under certain restrictions on weights, a pair of weighted Hardy spaces on the two-dimensional torus is K-closed in the pair of the corresponding weighted Lebesgu…