Related papers: Variational Barycentric Coordinates
Many real-world optimisation problems are defined over both categorical and continuous variables, yet efficient optimisation methods such asBayesian Optimisation (BO) are not designed tohandle such mixed-variable search spaces. Recent…
We introduce and study a variant of the Wasserstein distance on the space of probability measures, specially designed to deal with measures whose support has a dendritic, or treelike structure with a particular direction of orientation. Our…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…
We propose a single neural probabilistic model based on variational autoencoder that can be conditioned on an arbitrary subset of observed features and then sample the remaining features in "one shot". The features may be both real-valued…
We propose a method to approximate the distribution of robot configurations satisfying multiple objectives. Our approach uses variational inference, a popular method in Bayesian computation, which has several advantages over sampling-based…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a…
Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
We investigate the barycentric associativity property for functions with indefinite arities and discuss the more general property of barycentric preassociativity, a generalization of barycentric associativity which does not involve any…
We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
Correlative computational microscopy can accelerate imaging and modeling of cellular dynamics by relaxing trade-offs inherent to dynamic imaging. Existing computational microscopy frameworks are either specialized or overly generic,…
Computing the unregularized Wasserstein barycenter for measure-valued data is a challenging optimization task. Recent algorithms have been tailored to either discrete measures as point clouds or continuous measures discretized on regular…
We introduce a novel numerical framework for the exploration of Blaschke--Santal\'o diagrams, which are efficient tools characterizing the possible inequalities relating some given shape functionals. We introduce a parametrization of convex…
How does the brain predict physical outcomes while acting in the world? Machine learning world models compress visual input into latent spaces, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world…
Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations…
In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…
Large-scale neuronal activity recordings with fluorescent calcium indicators are increasingly common, yielding high-resolution 2D or 3D videos. Traditional analysis pipelines reduce this data to 1D traces by segmenting regions of interest,…