Study on Wasserstein barycenters with computational hardness and fast algorithm development.
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6 results for “fixed-support”
problem Computing Wasserstein barycenters of discrete probability measures with fixed support.
method Developed a deterministic variant of IBP algorithm, FastIBP, with improved complexity.
result Demonstrated favorable performance of FastIBP in practice.
Paper tackles robust optimal transport with improved computational complexity and barycenter approximation.
problem Computing robust optimal transport and its barycenter efficiently.
method Sinkhorn-based algorithms for robust optimal transport and iterative Bregman projections for barycenter approximation.
result Improved computational complexity for robust optimal transport and barycenter approximation.
Paper extends sparse alternatives to softmax for continuous domains, enabling efficient attention mechanisms.
problem Efficiently assigning zero probability to irrelevant categories in continuous domains.
method Extend alpha-entmax to continuous domains, introducing continuous-domain attention mechanisms.
result Continuous attention allows attending to time intervals and compact regions, improving text classification, machine translation, and visual question answering.
New algorithms approximate Rashomon set for sparse models, aiding expert interaction.
problem Lack of interaction between models and domain experts in classical machine learning.
method Approximate Rashomon set of sparse, generalized additive models using ellipsoids.
result Efficiently approximated Rashomon set facilitates model selection and exploration.
Support selection and eventwise decoupling for simultaneous bets proven.
problem Optimizing expected utility for simultaneous independent events with multiple outcomes.
method Proved a support theorem for a broad class of strictly increasing strictly concave utilities, identifying the exact active support and proving independence from utility function.
result The exact active support is the eventwise union of single-event supports, independent of the utility function.
This paper develops sparse alternatives to continuous distributions, including new types of Gaussians and attention mechanisms.
problem Creating flexible continuous distributions with varying support for machine learning applications.
method Defining -regularized prediction maps and Fenchel-Young losses for arbitrary domains, and deriving new types of Gaussians and attention mechanisms.
result Sparse alternatives to continuous distributions, including deformed exponential families and -Gaussians, are introduced.