4 citations · 10 across the 17 of their papers we have counts for
18 papers
Particle-based Generalised Stochastic Optimisation
Jiechen Jackie Zhang, O. Deniz Akyildiz
We develop a class of general diffusion-based stochastic particle optimisation methods for loss functions with intractable gradients. Specifically, we consider problems in which th…
An Operator-Theoretic Analysis of Nonlinear Filtering under Model Misspecification
Fabián González, Ömer Deniz Akyildiz, Dan Crisan +1
We study nonlinear filtering with misspecified initial distributions and dynamics, but a correctly specified observation model. Observations are treated as a random process generat…
Momentum SVGD-EM for Accelerated Maximum Marginal Likelihood Estimation
Adam Rozzio, Rafael Athanasiades, O. Deniz Akyildiz
Maximum marginal likelihood estimation (MMLE) can be formulated as the optimization of a free energy functional. From this viewpoint, the Expectation-Maximisation (EM) algorithm ad…
Efficient Stochastic Optimisation via Sequential Monte Carlo
James Cuin, Davide Carbone, Yanbo Tang +1
The problem of optimising functions with intractable gradients frequently arises in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures…
Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics
Joanna Marks, Tim Y. J. Wang, O. Deniz Akyildiz
We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for sol…
A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
Tim Y. J. Wang, O. Deniz Akyildiz
Solving ill-posed inverse problems requires powerful and flexible priors. We propose leveraging pretrained latent diffusion models for this task through a new training-free approac…
Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm
James Cuin, Davide Carbone, O. Deniz Akyildiz
We utilise a sampler originating from nonequilibrium statistical mechanics, termed here Jarzynski-adjusted Langevin algorithm (JALA), to build statistical estimation methods in lat…
Training Latent Diffusion Models with Interacting Particle Algorithms
Tim Y. J. Wang, Juan Kuntz, O. Deniz Akyildiz
We introduce a novel particle-based algorithm for end-to-end training of latent diffusion models. We reformulate the training task as minimizing a free energy functional and obtain…
On the contraction properties of Sinkhorn semigroups
O. Deniz Akyildiz, Pierre del Moral, Joaquin Miguez
We develop a novel stability theory for Sinkhorn semigroups based on Lyapunov techniques and quantitative contraction coefficients, and establish exponential convergence of Sinkhor…
Statistical Finite Elements via Interacting Particle Langevin Dynamics
Alex Glyn-Davies, Connor Duffin, Ieva Kazlauskaite +2
In this paper, we develop a class of interacting particle Langevin algorithms to solve inverse problems for partial differential equations (PDEs). In particular, we leverage the st…
A Primer on Variational Inference for Physics-Informed Deep Generative Modelling
Alex Glyn-Davies, Arnaud Vadeboncoeur, O. Deniz Akyildiz +2
Variational inference (VI) is a computationally efficient and scalable methodology for approximate Bayesian inference. It strikes a balance between accuracy of uncertainty quantifi…
Kinetic Interacting Particle Langevin Monte Carlo
Paul Felix Valsecchi Oliva, O. Deniz Akyildiz
This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods, for statistical inference…
A Multiscale Perspective on Maximum Marginal Likelihood Estimation
O. Deniz Akyildiz, Michela Ottobre, Iain Souttar
In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood e…
Adaptively Optimised Adaptive Importance Samplers
Carlos A. C. C. Perello, Ömer Deniz Akyildiz
We introduce a new class of adaptive importance samplers leveraging adaptive optimisation tools, which we term AdaOAIS. We build on Optimised Adaptive Importance Samplers (OAIS), a…
Random Grid Neural Processes for Parametric Partial Differential Equations
Arnaud Vadeboncoeur, Ieva Kazlauskaite, Yanni Papandreou +3
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 va…
Global convergence of optimized adaptive importance samplers
Ömer Deniz Akyildiz
We analyze the optimized adaptive importance sampler (OAIS) for performing Monte Carlo integration with general proposals. We leverage a classical result which shows that the bias…
A probabilistic interpretation of replicator-mutator dynamics
Ömer Deniz Akyıldız
In this note, we investigate the relationship between probabilistic updating mechanisms and discrete-time replicator-mutator dynamics. We consider the recently shown connection bet…
Online Matrix Factorization via Broyden Updates
Ömer Deniz Akyıldız
In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observat…