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Found 12 papers, 2 papers with code
A hybrid tau-leap for simulating chemical kinetics with applications to parameter estimation
We consider the problem of efficiently simulating stochastic models of chemical kinetics.
Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling
This discretisation is asymptotically unbiased for Gaussian targets and shown to converge in an accelerated manner for any target that is $\kappa$-strongly log-concave (i. e., requiring in the order of $\sqrt{\kappa}$ iterations to converge, similarly to accelerated optimisation schemes), comparing favorably to [M. Pereyra, L. Vargas Mieles, K. C.
Gaussian processes for Bayesian inverse problems associated with linear partial differential equations
This work is concerned with the use of Gaussian surrogate models for Bayesian inverse problems associated with linear partial differential equations.
The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distribution
Additionally, instead of viewing the augmented posterior distribution as an approximation of the original model, we propose to consider it as a generalisation of this model.
Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations
We present a framework that allows for the non-asymptotic study of the $2$-Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation and the distribution of its numerical approximation in the strongly log-concave case.
Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms
Bayesian computation is performed by using a parallel tempered version of the preconditioned Crank-Nicolson algorithm on the manifold, which is shown to be ergodic and robust to the non-convex nature of these data-driven models.
A Linear Transportation $\mathrm{L}^p$ Distance for Pattern Recognition
The transportation $\mathrm{L}^p$ distance, denoted $\mathrm{TL}^p$, has been proposed as a generalisation of Wasserstein $\mathrm{W}^p$ distances motivated by the property that it can be applied directly to colour or multi-channelled images, as well as multivariate time-series without normalisation or mass constraints.
The connections between Lyapunov functions for some optimization algorithms and differential equations
In the appropriate limit, this family of methods may be seen as a discretization of a family of second-order ordinary differential equations for which we construct(continuous) Lyapunov functions by means of the LMI framework.
Constructing Gradient Controllable Recurrent Neural Networks Using Hamiltonian Dynamics
The key benefit of this approach is that the corresponding RNN inherits the favorable long time properties of the Hamiltonian system, which in turn allows us to control the hidden states gradient with a hyperparameter of the Hamiltonian RNN architecture.
PDE-Inspired Algorithms for Semi-Supervised Learning on Point Clouds
In this paper we extend the labels by minimising the constrained discrete $p$-Dirichlet energy.
Uncertainty quantification in graph-based classification of high dimensional data
In this paper we introduce, develop algorithms for, and investigate the properties of, a variety of Bayesian models for the task of binary classification; via the posterior distribution on the classification labels, these methods automatically give measures of uncertainty.
(Non-) asymptotic properties of Stochastic Gradient Langevin Dynamics
For this toy model we study the gain of the SGLD over the standard Euler method in the limit of large data sets.
