Ömer Deniz Akyıldız

Lecture notes

• Stochastic Simulation: From Uniform Random Numbers to Generative Models (Draft), O. D. Akyildiz, 2023 [PDF], [Jupyter Book].

Working papers

• Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics, J. Marks, T. Y. J. Wang, O. D. Akyildiz. 2025, [arXiv].
• Uniform-in-time convergence bounds for Persistent Contrastive Divergence Algorithms, P. F. V. Oliva, O. D. Akyildiz, A. B. Duncan. 2025, [arXiv].
• Training Latent Diffusion Models with Interacting Particle Algorithms, T. Y. J. Wang, J. Kuntz, O. D. Akyildiz. 2025, [arXiv].
• On the contraction properties of Sinkhorn semigroups, O. D. Akyildiz, P. Del Moral, J. Miguez. 2025, [arXiv].
• Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modelling, P. Cordero-Encinar, O. D. Akyildiz, A. B. Duncan. 2025, [arXiv].
• Gaussian entropic optimal transport: Schrödinger bridges and the Sinkhorn algorithm, O. D. Akyildiz, P. Del Moral, J. Miguez. 2024, [arXiv].
• Kinetic Interacting Particle Langevin Monte Carlo, P. F. Valsecchi Oliva, O. D. Akyildiz, 2024, [arXiv].
• A Multiscale Perspective on Maximum Marginal Likelihood Estimation, O. D. Akyildiz, M. Ottobre, I. Souttar, 2024, [arXiv].

Selected Publications

• Sampling by averaging: A multiscale approach to score estimation, P. Cordero-Encinar, A. B. Duncan, S. Reich, O. D. Akyildiz. NeurIPS 2025, [arXiv].
• Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm, J. Cuin, D. Carbone, O. D. Akyildiz. NeurIPS 2025, [arXiv].
• On diffusion posterior sampling via sequential Monte Carlo for zero-shot scaffolding of protein motifs, J. M. Young, O. D. Akyildiz. Transactions on Machine Learning Research (TMLR), 2025, [journal], [arXiv].
• Statistical Finite Elements via Interacting Particle Langevin Dynamics, A. Glyn-Davies, C. Duffin, I. Kazlauskaite, M. Girolami, O. D. Akyildiz. SIAM Journal on Uncertainty Quantification, 2025, [journal], [arXiv].
• Nudging state-space models for Bayesian filtering under misspecified dynamics, F. Gonzalez, O. D. Akyildiz, D. Crisan, J. Miguez. Statistics and Computing, 2025, [journal], [arXiv].
• Efficient Prior Calibration From Indirect Data, O. D. Akyildiz, M. Girolami, A. M. Stuart, A. Vadeboncoeur. SIAM Journal on Scientific Computing, 2025, [journal], [arXiv].
• Proximal Interacting Particle Langevin Algorithms, P. C. Encinar, F. R. Crucinio, O. D. Akyildiz, Uncertainty in Artificial Intelligence (UAI), Best Student Paper Award, 2025, [proceedings], [arXiv].
• A Primer on Variational Inference for Physics-Informed Deep Generative Modelling, A. Glyn-Davies, A. Vadeboncoeur, O. D. Akyildiz, I. Kazlauskaite, M. Girolami, Philosophical Transactions of the Royal Society A, 2025, [journal], [arXiv].
• A Proximal Newton Adaptive Importance Sampler, V. Elvira, É. Chouzenoux, O. D. Akyildiz. IEEE Signal Processing Letters, 2025, [journal], [arXiv].
• Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation, Ö. D. Akyildiz, F. R. Crucinio, M. Girolami, T. Johnston, S. Sabanis. ESAIM: Probability and Statistics, 2025, [journal], [arXiv].
• On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates, S. Bruno, Y. Zhang, D. Lim, O. D. Akyildiz, S. Sabanis. Transactions on Machine Learning Research (TMLR), 2025, [journal], [arXiv].
• Global convergence of optimized adaptive importance samplers, Ö. D. Akyildiz, 2024 (to appear), Foundations of Data Science (FoDS), 2025, [journal], [arXiv].
• Tweedie Moment Projected Diffusions For Inverse Problems, B. Boys, M. Girolami, J. Pidstrigach, S. Reich, A. Mosca, O. D. Akyildiz, Transactions on Machine Learning Research (TMLR), 2024, Featured Certification, ICLR 2025 Journal Track, [journal], [arXiv].
• $\Phi$-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation, A. Glyn-Davies, C. Duffin, Ö. D. Akyildiz, M. Girolami, Journal of Computational Physics, 2024, [journal], [arXiv].
• Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization, Ö. D. Akyildiz, S. Sabanis, Journal of Machine Learning Research (JMLR), 2024, [journal], [arXiv].
• Sequential discretisation schemes for a class of stochastic differential equations and their application to Bayesian filtering, Ö. D. Akyildiz, D. Crisan, J. Miguez, SIAM Journal on Numerical Analysis, 2024, [journal], [arXiv].
• Fully probabilistic deep models for forward and inverse problems in parametric PDEs, A. Vadeboncoeur, Ö. D. Akyildiz, I. Kazlauskaite, M. Girolami, F. Cirak, Journal of Computational Physics (2023), [arXiv], [journal].
• Gradient-based Adaptive Importance Samplers, V. Elvira, E. Chouzenoux, Ö. D. Akyildiz, L. Martino, Journal of the Franklin Institute, 2023 [arXiv], [journal].
• Random Grid Neural Processes for Parametric Partial Differential Equations, A. Vadeboncoeur, I. Kazlauskaite, F. Cirak, M. Girolami, Ö. D. Akyildiz, International Conference of Machine Learning (ICML), 2023, [arXiv].
• Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization, Y. Zhang, Ö. D. Akyildiz, T. Damoulas, S. Sabanis, Journal of Applied Mathematics and Optimization, 2023, [journal, arXiv].
• Statistical Finite Elements via Langevin Dynamics, Ö. D. Akyildiz*, C. Duffin*, S. Sabanis, M. Girolami, SIAM/ASA Journal of Uncertainty Quantification, 2022 [journal].
• Probabilistic sequential matrix factorization, Ö. D. Akyildiz*, G. J.J. van den Burg*, T. Damoulas, M. F. J. Steel, AISTATS 2021, [arXiv], [code] (*joint first authors).
• Convergence rates for optimised adaptive importance samplers, Ö. D. Akyıldız, J. Miguez. Statistics and Computing, 31, 12 (2021), [journal] [arXiv].
• VarGrad: A Low Variance Gradient Estimator for Variational Inference, L. Richter, A. Boustati, N. Nuesken, F. J. Ruiz, Ö. D. Akyildiz, NeurIPS 2020, [arXiv].
• Generalized Bayesian Filtering via Sequential Monte Carlo, A. Boustati*, Ö. D. Akyildiz*, T. Damoulas, A. M. Johansen, NeurIPS 2020, [arXiv].
• Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization, Ö. D. Akyildiz, D. Crisan, J. Miguez. Statistics and Computing, 2020, [journal].
• Nudging the particle filter, Ö. D. Akyıldız, J. Miguez. Statistics and Computing, 2020, [journal], [arXiv], [poster].
• A probabilistic incremental proximal gradient method, Ö. D. Akyildiz, E. Chouzenoux, V. Elvira, J. Miguez. IEEE Signal Processing Letters, [IEEExplore], [arXiv], 2019.
• Dictionary filtering: A probabilistic approach to online matrix factorisation, Ö. D. Akyildiz, J. Miguez. Signal, Image, and Video Processing, June 2019, 13(4):737-744. [journal], [pdf].
• The Incremental Proximal Method: A Probabilistic Perspective, Ö. D. Akyıldız, V. Elvira, J. Miguez. ICASSP 2018, [arXiv] .
• Adaptive noisy importance sampling for stochastic optimization, Ö. D. Akyıldız, I. P. Marino, J. Miguez. IEEE CAMSAP 2017, [pdf], [IEEExplore].

Workshop Papers

• A Gradient Flow approach to Solving Inverse Problems with Latent Diffusion Models, Tim Y. J. Wang, O. D. Akyildiz. NeurIPS Workshop Frontiers in Probabilistic Inference: Sampling Meets Learning, 2025, [arXiv].
• On the relationship between online optimizers and recursive filters, Ö. D. Akyıldız, V. Elvira, J. F. Bes, J. Miguez. NIPS Workshop on Optimizing the Optimizers, December 2016, Barcelona, Spain, [pdf], [poster].

Others

• Adaptively Optimised Adaptive Importance Samplers, C. A. C. C. Perello, Ö. D. Akyildiz, 2023, [arXiv].
• A probabilistic interpretation of replicator-mutator dynamics, Ö. D. Akyıldız, December 2017, [arXiv].
• Matrix Factorisation with Linear Filters, Ö. D. Akyıldız, September 2015, [arXiv], [discussion], [slides].
• Online Matrix Factorisation via Broyden Updates, Ö. D. Akyıldız, June 2015, [arXiv], [MLSS poster].
• Primal-Dual Algorithms for Audio Decomposition Using Mixed Norms, İ. Bayram and Ö. D. Akyıldız. Signal, Image and Video Processing, 8(1):95-110, January 2014. [pdf].
• An EM Algorithm for Learning in Controlled Linear Dynamical Systems, O. D. Akyildiz, 2013, [pdf].
• An Analysis Prior Based Decomposition Method for Audio Signals, Ö. D. Akyıldız, İ. Bayram, EUSIPCO 2012.

Thesis

• Sequential and adaptive Bayesian computation for inference and optimization, PhD thesis, Ö. D. Akyıldız, March 2019, Universidad Carlos III de Madrid, [pdf], [bibtex], [slides].