Omar Rivasplata's Webpage

Omar Rivasplata

Centre for AI Fundamentals
and Department of Computer Science
University of Manchester

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Topics of Interest

Statistical Learning Theory. Machine Learning. AI. Mathematics. Probability and Statistics.

About me and what I do

I certify AI predictions with high confidence.

My research is on machine learning, theory and practice. That said, I tend to have a broad interest in various aspects of the mathematical and statistical foundations of machine learning and AI in general. In the limit of tending to praxis, I work on designing strategies to train and certify machine learning models. Previously, I have led or been a contributor to projects on offline reinforcement learning, generative models, PAC-Bayes bounds for deep learning and kernel classifiers, among other.

The field of machine learning research is fascinating! One of the things I enjoy most about my work being the confluence of maths and stats, and computer experiments with collaborators, to answer questions about the optimisation and certification of machine learning models. Besides statistical learning I am interested also in online learning and reinforcement learning. Of course I am interested in deep learning, which is quite popular these days. Optimisation is a pervasive theme across machine learning theory and practice, though it comes up in such a variety of flavours and colours that it isn't boring. It reminds of the least action principle of Maupertuis, saying that "everything happens as if some quantity was to be made as small as possible." (This principle has lead the optimists to believe that we live in the best possible world.) But just optimisation doesn't quite do it for machine learning... to really be talking about learning one has to pay attention to learner's performance beyond the data used for training; so certification is very important!

Affiliations with learned sociaties: I am a member of the European Laboratory for Learning and Intelligent Systems (ELLIS), based at the ELLIS Unit Manchester. I am member of the London Mathematical Society (LMS) and LMS Regional Representative for the North. Fellow of the Institute of Mathematics and its Applications (IMA). Fellow of the Royal Statistical Society (RSS), committee member of the RSS section on Computational Statistics and Machine Learning (CSML), and part of the RSS AI Task Force.

*Current Job*

Associate Professor (Senior Lecturer) in Machine Learning in the Department of Computer Science at the University of Manchester. Also, I am an academic staff in the Manchester Centre for AI Fundamentals and a supervisor in the UKRI AI CDT in Decision Making for Complex Systems.

Before

For a couple of years and a half I was a Senior Research Fellow in the Department of Statistical Science at UCL, where I created and led the research group DELTA. Mine was one of two departments of the upcoming Institute for Mathematical and Statistical Sciences, the other one being the Department of Mathematics.

My dissertation PAC-Bayesian Computation was the result of my research studies in statistical learning at the Department of Computer Science, University College London, which were sponsored by DeepMind. In parallel with my research studies at UCL, I had a fixed-term position with DeepMind for three years.

My journey into ML research started at the Department of Computing Science, University of Alberta, where I spent a year and two months. During this time I started building my mental model of the ML field and fine-tuning my hyperparameters. My host was Rich Sutton in theory, and in practice I was working with Csaba Szepesvári on theory.

Much Before

I spent postdoc time with Mauricio Sacchi's group looking at optimization problems related to seismic signal analysis.

My PhD dissertation Smallest singular value of sparse random matrices was the result of my work with Sasha Litvak and Nicole Tomczak-Jaegermann.

My MSc thesis was about characterizatinos of reversibility for Brownian motion with drift, supervised by Byron Schmuland.

My BSc thesis was a fun project about repeated two-player games with incomplete information on one side.

Talks (sample)

Tighter risk certificates for (probabilistic) neural networks. UCL Centre for AI. Slides Video
Statistical Learning Theory: A Hitchhiker's Guide. NeurIPS 2018 Tutorial. (with J. Shawe-Taylor) Slides Video

Preprints

Ioar Casado-Telletxea, Omar Rivasplata, Error Bounds for a Diffusion Model-Based Drift Estimator.

Conference & Journal Papers

Semi-pessimistic Reinforcement Learning (with collaborators) is now accepted in the Journal of the American Statistical Association (JASA), July 2026.

A. Zitouni, M. Hennequin, J. Agoun, R. Horache, N. Kabachi and O. Rivasplata, PAC-Bayesian Reinforcement Learning Trains Generalizable Policies. ICML, 2026.

M. Tucat, A. Mukherjee, M. Sun, P. Sen, O. Rivasplata, Regularized Gradient Clipping Provably Trains Wide and Deep Neural Networks. TMLR, 2025.

T. Silva, A. H. Souza, O. Rivasplata, V. Garg, S. Kaski, D. Mesquita, Generalization and Distributed Learning of GFlowNets. In ICLR, 2025. PDF

P. Blomstedt, D. Mesquita, O. Rivasplata et al. Meta-analysis of Bayesian Analyses. Bayesian Analysis, 2024.

S.D. Mbacke and O. Rivasplata, A Note on the Convergence of Denoising Diffusion Probabilistic Models. TMLR, 2024. PDF

B. Rodríguez Gálvez, O. Rivasplata, R. Thobaben, M. Skoglund, A note on generalization bounds for losses with finite moments. ISIT 2024. PDF

I. Kuzborskij, Cs. Szepesvári, O. Rivasplata, A. Rannen-Triki, R. Pascanu, On the Role of Optimization in Double Descent: A Least Squares Study. NeurIPS 2021. PDF

M. Pérez-Ortiz, O. Rivasplata, J. Shawe-Taylor, Cs. Szepesvári, Tighter Risk Certificates for Neural Networks. JMLR, 22, 227 (2021), 1-40. PDF

L. Orseau, M. Hutter, O. Rivasplata, Logarithmic Pruning is All You Need. NeurIPS 2020 . PDF

O. Rivasplata, I. Kuzborskij, Cs. Szepesvári, J. Shawe-Taylor, PAC-Bayes analysis beyond the usual bounds. NeurIPS 2020. PDF

O. Rivasplata, E. Parrado-Hernández, J. Shawe-Taylor, S. Sun, Cs. Szepesvári, PAC-Bayes bounds for stable algorithms with instance-dependent priors. NeurIPS 2018. PDF

A.E. Litvak, O. Rivasplata, Smallest singular value of sparse random matrices. Studia Math., 212, 3 (2012), 195-218. PDF

O. Rivasplata, J. Rychtar, B. Schmuland, Reversibility for diffusions via quasi-invariance. Acta Univ. Carolin. Math. Phys., 48, 1 (2007), 3-10. PDF

O. Rivasplata, J. Rychtar, C. Sykes, Evolutionary games in finite populations. Pro Mathematica, 20, 39/40 (2006), 147-164. PDF

O. Rivasplata, B. Schmuland, Invariant and reversible measures for random walks on Z. Pro Mathematica, 19, 37/38 (2005), 117-124. PDF

Workshop Papers

K. Novikava, A. Lytova, O. Rivasplata, δ-Regularized Gradient Clipping for Stable Optimization: Analysis and Empirical Evaluation. Presented at the ICML 2026 Workshop High-dimensional Learning Dynamics.

G. Aminian, R. Vega, O. Rivasplata, L. Toni, M. Rodrigues, Semi-Counterfactual Risk Minimization Via Neural Networks. Presented at the 15th European Workshop on Reinforcement Learning, EWRL 2022.

M. Pérez-Ortiz, O. Rivasplata, E. Parrado-Hernández, B. Guedj, J. Shawe-Taylor, Progress in Self-Certified Neural Networks. Presented at the NeurIPS 2021 Workshop - Bayesian Deep Learning.

A. Grabska-Barwińska, A. Rannen-Triki, O. Rivasplata, A. György, Towards better visual explanations for deep image classifiers. Presented at the NeurIPS 2021 Workshop - eXplainable AI.

M. Pérez-Ortiz, O. Rivasplata, J. Shawe-Taylor, Cs. Szepesvári, Towards self-certified learning: Probabilistic neural networks trained by PAC-Bayes with Backprop. Presented at the NeurIPS 2020 Workshop - Beyond BackPropagation.

O. Rivasplata, I. Kuzborskij, Cs. Szepesvári, J. Shawe-Taylor, PAC-Bayes analysis with stochastic kernels. Presented at the NeurIPS 2019 Workshop - Machine Learning with Guarantees.

Expository Notes

O. Rivasplata, A note on a confidence bound of Kuzborskij and Szepesvári. (2021) PDF

O. Rivasplata, Subgaussian random variables: An expository note. (2012) PDF

Utterly arXiv'ed

O. Rivasplata, V. Tankasali, Cs. Szepesvári, PAC-Bayes with Backprop. (2019) PDF

Machine Learning Links

What is machine learning?

Understanding Machine Learning

Rich Sutton's incomplete ideas (and RL resources)

Robert Duin's 37 steps (and PR tools and blog)

Advice for Machine Learning students

Math Links

What's new (Terry Tao's blog)

Maths Research Seminars (beta).

The complex number operations neatly visualised.

Advice for Math students

Probability Links (probably accessible)

Almost Sure

Research in Probability

The Gaussian Processes Website

Advice for Probability students

Stats Links (most significant)

Random stuff

Frequentism and Bayesianism

Advice for Stats students

Writing aids

How to Write Mathematics, tips from the Mathematics Student Handbook at Trent University.

A Guide to Writing Mathematics by Kevin Lee.

Writing Mathematics by Berry & Lawson.

The Underground Grammarian by Richard Mitchell.

Canadian Links

My Canadian home town is Edmonton, Alberta.

Not far from the beautiful Canadian Rocky Mountains.

Favourite spots in the Canadian Rockies are Jasper, Banff, Lake Louise, Emerald Lake.

Datasets CIFAR-10 and CIFAR-100 are named after the Canadian Institute For Advanced Research.

Peruvian Links

My birth town is Trujillo, the marinera dance town.

Sometimes people ask me about Machu Picchu, it's a great place to see.

They ask me less about Arequipa though it is also a great place to visit.

Last link, in case you care to know, is about Pisco.