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Daniel MacKinlay

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3 papers

2 author rows

ICLR Conference 2025 Conference Paper

Gaussian Ensemble Belief Propagation for Efficient Inference in High-Dimensional, Black-box Systems

Daniel MacKinlay
Russell Tsuchida
Daniel Edward Pagendam
Petra Kuhnert

Efficient inference in high-dimensional models is a central challenge in machine learning. We introduce the Gaussian Ensemble Belief Propagation (GEnBP) algorithm, which combines the strengths of the Ensemble Kalman Filter (EnKF) and Gaussian Belief Propagation (GaBP) to address this challenge. GEnBP updates ensembles of prior samples into posterior samples by passing low-rank local messages over the edges of a graphical model, enabling efficient handling of high-dimensional states, parameters, and complex, noisy, black-box generative processes. By utilizing local message passing within a graphical model structure, GEnBP effectively manages complex dependency structures and remains computationally efficient even when the ensemble size is much smaller than the inference dimension --- a common scenario in spatiotemporal modeling, image processing, and physical model inversion. We demonstrate that GEnBP can be applied to various problem structures, including data assimilation, system identification, and hierarchical models, and show through experiments that it outperforms existing belief propagation methods in terms of accuracy and computational efficiency. Supporting code is available at https://github.com/danmackinlay/GEnBP}{github.com/danmackinlay/GEnBP

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NeurIPS Conference 2025 Conference Paper

Variational Transdimensional Inference

Laurence Davies
Daniel MacKinlay
Rafael Oliveira
Scott SIsson

The expressiveness of flow-based models combined with stochastic variational inference (SVI) has expanded the application of optimization-based Bayesian inference to highly complex problems. However, despite the importance of multi-model Bayesian inference for problems defined on a transdimensional joint model and parameter space, such as Bayesian structure learning, flow-based SVI has been limited to problems defined on a fixed-dimensional parameter space. We introduce CoSMIC normalizing flows (COntextually-Specified Masking for Identity-mapped Components), an extension to neural autoregressive conditional normalizing flow architectures that enables use of a single flow-based variational density for inference over a transdimensional (multi-model) conditional target distribution. We propose a combined stochastic variational transdimensional inference (VTI) approach to training CoSMIC flows using ideas from Bayesian optimization and Monte Carlo gradient estimation. Numerical experiments show the performance of VTI on challenging problems that scale to high-cardinality model spaces.

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NeurIPS Conference 2022 Conference Paper

PDEBench: An Extensive Benchmark for Scientific Machine Learning

Makoto Takamoto
Timothy Praditia
Raphael Leiteritz
Daniel MacKinlay
Francesco Alesiani
Dirk Pflüger
Mathias Niepert

Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and repre- sentative of a wide range of problems. We introduce PDEBENCH, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs). PDEBENCH comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulations and machine learning baselines. Our proposed set of benchmark problems con- tribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more real- istic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of ini- tial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method). PDEBENCH allows researchers to extend the benchmark freely for their own pur- poses using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community. The code is available at https: //github. com/pdebench/PDEBench.

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