arXiv subjects

Christy Anna Hipsley

Publications and source records attributed to Christy Anna Hipsley.

3 recordsLinked to original sources

arXiv2025

Infinite-dimensional Diffusion Bridge Simulation via Operator Learning

The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling natural data can be challenging due to both the intractability of the drift term and continuous representations of the data. Although several methods are available to simulate finite-dimensional diffusion bridges, infinite-dimensional cases remain under explored. This paper presents a method that merges score matching techniques with operator learning, enabling a direct approach to learn the infinite-dimensional bridge and achieving a discretization equivariant bridge simulation. We conduct a series of experiments, ranging from synthetic examples with closed-form solutions to the stochastic nonlinear evolution of real-world biological shape data. Our method demonstrates high efficacy, particularly due to its ability to adapt to any resolution without extra training.

cs.LG↗

arXiv2024

Parameter Inference via Differentiable Diffusion Bridge Importance Sampling

We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including ancestral state reconstruction. Estimation is performed by utilising score matching to approximate diffusion bridges, which are subsequently used in an importance sampler to estimate log-likelihoods. The entire setup is differentiable, allowing gradient ascent on approximated log-likelihoods. This allows both parameter inference and diffusion mean estimation. This novel, numerically stable, score matching-based parameter inference framework is presented and demonstrated on biological two- and three-dimensional morphometry data.

stat.ML↗

arXiv2024

Conditioning non-linear and infinite-dimensional diffusion processes

Generative diffusion models and many stochastic models in science and engineering naturally live in infinite dimensions before discretisation. To incorporate observed data for statistical and learning tasks, one needs to condition on observations. While recent work has treated conditioning linear processes in infinite dimensions, conditioning non-linear processes in infinite dimensions has not been explored. This paper conditions function valued stochastic processes without prior discretisation. To do so, we use an infinite-dimensional version of Girsanov's theorem to condition a function-valued stochastic process, leading to a stochastic differential equation (SDE) for the conditioned process involving the score. We apply this technique to do time series analysis for shapes of organisms in evolutionary biology, where we discretise via the Fourier basis and then learn the coefficients of the score function with score matching methods.

stat.ML↗