16 citations · 40 across the 18 of their papers we have counts for
23 papers
Diffusion Path Samplers via Sequential Monte Carlo
James Matthew Young, Paula Cordero-Encinar, Sebastian Reich +2
We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates be…
Sampling by averaging: A multiscale approach to score estimation
Paula Cordero-Encinar, Andrew B. Duncan, Sebastian Reich +1
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods ei…
Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modelling
Paula Cordero-Encinar, O. Deniz Akyildiz, Andrew B. Duncan
We investigate the theoretical properties of general diffusion (interpolation) paths and their Langevin Monte Carlo implementation, referred to as diffusion annealed Langevin Monte…
Gaussian entropic optimal transport: Schrödinger bridges and the Sinkhorn algorithm
O. Deniz Akyildiz, Pierre Del Moral, Joaquín Miguez
Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative mode…
A Proximal Newton Adaptive Importance Sampler
Víctor Elvira, Émilie Chouzenoux, O. Deniz Akyildiz
Adaptive importance sampling (AIS) algorithms are a rising methodology in signal processing, statistics, and machine learning. An effective adaptation of the proposals is key for t…
On diffusion posterior sampling via sequential Monte Carlo for zero-shot scaffolding of protein motifs
James Matthew Young, O. Deniz Akyildiz
With the advent of diffusion models, new proteins can be generated at an unprecedented rate. The motif scaffolding problem requires steering this generative process to yield protei…
Nudging state-space models for Bayesian filtering under misspecified dynamics
Fabian Gonzalez, O. Deniz Akyildiz, Dan Crisan +1
Nudging is a popular algorithmic strategy in numerical filtering to deal with the problem of inference in high-dimensional dynamical systems. We demonstrate in this paper that gene…
Proximal Interacting Particle Langevin Algorithms
Paula Cordero Encinar, Francesca R. Crucinio, O. Deniz Akyildiz
We introduce a class of algorithms, termed proximal interacting particle Langevin algorithms (PIPLA), for inference and learning in latent variable models whose joint probability d…
Efficient Prior Calibration From Indirect Data
O. Deniz Akyildiz, Mark Girolami, Andrew M. Stuart +1
Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four in…
On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates
Stefano Bruno, Ying Zhang, Dong-Young Lim +2
We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our…
Tweedie Moment Projected Diffusions For Inverse Problems
Benjamin Boys, Mark Girolami, Jakiw Pidstrigach +3
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusio…
-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation
Alex Glyn-Davies, Connor Duffin, Ö. Deniz Akyildiz +1
Incorporating unstructured data into physical models is a challenging problem that is emerging in data assimilation. Traditional approaches focus on well-defined observation operat…
Statistical Finite Elements via Langevin Dynamics
Ömer Deniz Akyildiz, Connor Duffin, Sotirios Sabanis +1
The recent statistical finite element method (statFEM) provides a coherent statistical framework to synthesise finite element models with observed data. Through embedding uncertain…
VarGrad: A Low-Variance Gradient Estimator for Variational Inference
Lorenz Richter, Ayman Boustati, Nikolas Nüsken +2
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. We show t…
Generalized Bayesian Filtering via Sequential Monte Carlo
Ayman Boustati, Ömer Deniz Akyildiz, Theodoros Damoulas +1
We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification. In particular, we leverage the loss-theoretic perspecti…
Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization
Ömer Deniz Akyildiz, Sotirios Sabanis
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…
Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization
Ying Zhang, Ömer Deniz Akyildiz, Theodoros Damoulas +1
In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserste…
Convergence rates for optimised adaptive importance samplers
Ömer Deniz Akyildiz, Joaquín Míguez
Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which \textit{adapt} themselves to obtain better…
A probabilistic incremental proximal gradient method
Ömer Deniz Akyildiz, Émilie Chouzenoux, Víctor Elvira +1
In this paper, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the…
Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization
Ömer Deniz Akyildiz, Dan Crisan, Joaquín Míguez
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 con…
The Incremental Proximal Method: A Probabilistic Perspective
Ömer Deniz Akyildiz, Victor Elvira, Joaquin Miguez
In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be r…
Nudging the particle filter
Ömer Deniz Akyıldız, Joaquín Míguez
We investigate a new sampling scheme aimed at improving the performance of particle filters whenever (a) there is a significant mismatch between the assumed model dynamics and the…
Matrix Factorisation with Linear Filters
Ömer Deniz Akyıldız
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which appro…