110 research outputs found
Scalable multi-class sampling via filtered sliced optimal transport
We propose a multi-class point optimization formulation based on continuous
Wasserstein barycenters. Our formulation is designed to handle hundreds to
thousands of optimization objectives and comes with a practical optimization
scheme. We demonstrate the effectiveness of our framework on various sampling
applications like stippling, object placement, and Monte-Carlo integration. We
a derive multi-class error bound for perceptual rendering error which can be
minimized using our optimization. We provide source code at
https://github.com/iribis/filtered-sliced-optimal-transport.Comment: 15 pages, 17 figures, ACM Trans. Graph., Vol. 41, No. 6, Article 261.
Publication date: December 202
Probabilistic Multilevel Clustering via Composite Transportation Distance
We propose a novel probabilistic approach to multilevel clustering problems
based on composite transportation distance, which is a variant of
transportation distance where the underlying metric is Kullback-Leibler
divergence. Our method involves solving a joint optimization problem over
spaces of probability measures to simultaneously discover grouping structures
within groups and among groups. By exploiting the connection of our method to
the problem of finding composite transportation barycenters, we develop fast
and efficient optimization algorithms even for potentially large-scale
multilevel datasets. Finally, we present experimental results with both
synthetic and real data to demonstrate the efficiency and scalability of the
proposed approach.Comment: 25 pages, 3 figure
Healing Products of Gaussian Processes
Gaussian processes (GPs) are nonparametric Bayesian models that have been
applied to regression and classification problems. One of the approaches to
alleviate their cubic training cost is the use of local GP experts trained on
subsets of the data. In particular, product-of-expert models combine the
predictive distributions of local experts through a tractable product
operation. While these expert models allow for massively distributed
computation, their predictions typically suffer from erratic behaviour of the
mean or uncalibrated uncertainty quantification. By calibrating predictions via
a tempered softmax weighting, we provide a solution to these problems for
multiple product-of-expert models, including the generalised product of experts
and the robust Bayesian committee machine. Furthermore, we leverage the optimal
transport literature and propose a new product-of-expert model that combines
predictions of local experts by computing their Wasserstein barycenter, which
can be applied to both regression and classification.Comment: ICML 202
Federated Variational Inference Methods for Structured Latent Variable Models
Federated learning methods enable model training across distributed data
sources without data leaving their original locations and have gained
increasing interest in various fields. However, existing approaches are
limited, excluding many structured probabilistic models. We present a general
and elegant solution based on structured variational inference, widely used in
Bayesian machine learning, adapted for the federated setting. Additionally, we
provide a communication-efficient variant analogous to the canonical FedAvg
algorithm. The proposed algorithms' effectiveness is demonstrated, and their
performance is compared with hierarchical Bayesian neural networks and topic
models
Multi-Marginal Gromov-Wasserstein Transport and Barycenters
Gromov-Wasserstein (GW) distances are combinations of Gromov-Hausdorff and
Wasserstein distances that allow the comparison of two different metric measure
spaces (mm-spaces). Due to their invariance under measure- and
distance-preserving transformations, they are well suited for many applications
in graph and shape analysis. In this paper, we introduce the concept of
multi-marginal GW transport between a set of mm-spaces as well as its
regularized and unbalanced versions. As a special case, we discuss
multi-marginal fused variants, which combine the structure information of an
mm-space with label information from an additional label space. To tackle the
new formulations numerically, we consider the bi-convex relaxation of the
multi-marginal GW problem, which is tight in the balanced case if the cost
function is conditionally negative definite. The relaxed model can be solved by
an alternating minimization, where each step can be performed by a
multi-marginal Sinkhorn scheme. We show relations of our multi-marginal GW
problem to (unbalanced, fused) GW barycenters and present various numerical
results, which indicate the potential of the concept
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