Search Results for author:
Found 17 papers, 3 papers with code
On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates
As a result, we obtain the best known upper bound estimates in terms of key quantities of interest, such as the dimension and rates of convergence, for the Wasserstein-2 distance between the data distribution (Gaussian with unknown mean) and our sampling algorithm.
Adaptively Optimised Adaptive Importance Samplers
We introduce a new class of adaptive importance samplers leveraging adaptive optimisation tools, which we term AdaOAIS.
Random Grid Neural Processes for Parametric Partial Differential Equations
We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes.
Fully probabilistic deep models for forward and inverse problems in parametric PDEs
In the posited probabilistic model, both the forward and inverse maps are approximated as Gaussian distributions with a mean and covariance parameterized by deep neural networks.
Global convergence of optimized adaptive importance samplers
We analyze the optimized adaptive importance sampler (OAIS) for performing Monte Carlo integration with general proposals.
Statistical Finite Elements via Langevin Dynamics
Through embedding uncertainty inside of the governing equations, finite element solutions are updated to give a posterior distribution which quantifies all sources of uncertainty associated with the model.
VarGrad: A Low-Variance Gradient Estimator for Variational Inference
We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates.
Generalized Bayesian Filtering via Sequential Monte Carlo
We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification.
Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization
We provide a nonasymptotic analysis of the convergence of the stochastic gradient Hamiltonian Monte Carlo (SGHMC) to a target measure in Wasserstein-2 distance without assuming log-concavity.
Probabilistic sequential matrix factorization
In particular, we consider nonlinear Gaussian state-space models where sequential approximate inference results in the factorization of a data matrix into a dictionary and time-varying coefficients with potentially nonlinear Markovian dependencies.
Multivariate Time Series Forecasting
Multivariate Time Series Imputation
+1
Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization
In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization.
Convergence rates for optimised adaptive importance samplers
The non-asymptotic bounds derived in this paper imply that when the target belongs to the exponential family, the $L_2$ errors of the optimised samplers converge to the optimal rate of $\mathcal{O}(1/\sqrt{N})$ and the rate of convergence in the number of iterations are explicitly provided.
A probabilistic incremental proximal gradient method
In this paper, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the incremental proximal gradient algorithm.
Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components.
The Incremental Proximal Method: A Probabilistic Perspective
We then carry out this observation to a general sequential setting: We consider the incremental proximal method, which is an algorithm for large-scale optimization, and show that, for a linear-quadratic cost function, it can naturally be realized by the Kalman filter.
Matrix Factorisation with Linear Filters
Using the probabilistic model, we derive a matrix factorisation algorithm as a recursive linear filter.
Online Matrix Factorization via Broyden Updates
In this paper, we propose an online algorithm to compute matrix factorizations.
