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06/09/2023
Domain-Agnostic Batch Bayesian Optimization with Diverse Constraints via Bayesian Quadrature
Real-world optimisation problems often feature complex combinations of (...
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05/08/2023
The Signature Kernel
The signature kernel is a positive definite kernel for sequential data. ...
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01/29/2023
Kernelized Cumulants: Beyond Kernel Mean Embeddings
In ℝ^d, it is well-known that cumulants provide an alternative to moment...
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01/27/2023
SOBER: Highly Parallel Bayesian Optimization and Bayesian Quadrature over Discrete and Mixed Spaces
Batch Bayesian optimisation and Bayesian quadrature have been shown to b...
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01/23/2023
Sampling-based Nyström Approximation and Kernel Quadrature
We analyze the Nyström approximation of a positive definite kernel assoc...
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10/11/2022
Hypercontractivity Meets Random Convex Hulls: Analysis of Randomized Multivariate Cubatures
Given a probability measure μ on a set 𝒳 and a vector-valued function φ,...
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06/09/2022
Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination
Calculation of Bayesian posteriors and model evidences typically require...
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05/27/2022
Capturing Graphs with Hypo-Elliptic Diffusions
Convolutional layers within graph neural networks operate by aggregating...
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11/11/2021
Proper Scoring Rules, Gradients, Divergences, and Entropies for Paths and Time Series
Many forecasts consist not of point predictions but concern the evolutio...
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10/12/2021
Tangent Space and Dimension Estimation with the Wasserstein Distance
We provide explicit bounds on the number of sample points required to es...
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07/20/2021
Positively Weighted Kernel Quadrature via Subsampling
We study kernel quadrature rules with positive weights for probability m...
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04/29/2021
Grid-Free Computation of Probabilistic Safety with Malliavin Calculus
We work with continuous-time, continuous-space stochastic dynamical syst...
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02/06/2021
Neural SDEs as Infinite-Dimensional GANs
Stochastic differential equations (SDEs) are a staple of mathematical mo...
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02/04/2021
Nonlinear Independent Component Analysis for Continuous-Time Signals
We study the classical problem of recovering a multidimensional source p...
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01/12/2021
Estimating the probability that a given vector is in the convex hull of a random sample
For a d-dimensional random vector X, let p_n, X be the probability that ...
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01/10/2021
The shifted ODE method for underdamped Langevin MCMC
In this paper, we consider the underdamped Langevin diffusion (ULD) and ...
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06/12/2020
Seq2Tens: An Efficient Representation of Sequences by Low-Rank Tensor Projections
Sequential data such as time series, video, or text can be challenging t...
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06/02/2020
Acceleration of Descent-based Optimization Algorithms via Carathéodory's Theorem
We propose a new technique to accelerate algorithms based on Gradient De...
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06/02/2020
A Randomized Algorithm to Reduce the Support of Discrete Measures
Given a discrete probability measure supported on N atoms and a set of n...
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08/18/2019
Signature Cumulants, Ordered Partitions, and Independence of Stochastic Processes
The sequence of so-called signature moments describes the laws of many s...
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06/19/2019
Variational Gaussian Processes with Signature Covariances
We introduce a Bayesian approach to learn from stream-valued data by usi...
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10/25/2018
Signature moments to characterize laws of stochastic processes
The normalized sequence of moments characterizes the law of any finite-d...
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06/01/2018
Persistence paths and signature features in topological data analysis
We introduce a new feature map for barcodes that arise in persistent hom...
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01/02/2018
Probabilistic supervised learning
Predictive modelling and supervised learning are central to modern data ...
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08/31/2017
Sketching the order of events
We introduce features for massive data streams. These stream features ca...
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01/29/2016
