Parameter Inference via Differentiable Diffusion Bridge Importance Sampling

• URL: http://arxiv.org/abs/2411.08993v1
• Date: Wed, 13 Nov 2024 19:33:47 GMT
• Title: Parameter Inference via Differentiable Diffusion Bridge Importance Sampling
• Authors: Nicklas Boserup, Gefan Yang, Michael Lind Severinsen, Christy Anna Hipsley, Stefan Sommer,
• Abstract summary: 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. This novel, numerically stable, score matching-based parameter inference framework is presented and demonstrated on biological two- and three-dimensional morphometry data.
• Score: 1.747623282473278
• License:
• Abstract: 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.

Related papers

• Kinetic Interacting Particle Langevin Monte Carlo [0.0]
  This paper introduces and analyses interacting underdamped Langevin algorithms, for statistical inference in latent variable models. We propose a diffusion process that evolves jointly in the space of parameters and latent variables. We provide two explicit discretisations of this diffusion as practical algorithms to estimate parameters of statistical models.
  arXiv  Detail & Related papers  (2024-07-08T09:52:46Z)
• Nonparametric Automatic Differentiation Variational Inference with Spline Approximation [7.5620760132717795]
  We develop a nonparametric approximation approach that enables flexible posterior approximation for distributions with complicated structures. Compared with widely-used nonparametrical inference methods, the proposed method is easy to implement and adaptive to various data structures. Experiments demonstrate the efficiency of the proposed method in approximating complex posterior distributions and improving the performance of generative models with incomplete data.
  arXiv  Detail & Related papers  (2024-03-10T20:22:06Z)
• Heterogeneous Multi-Task Gaussian Cox Processes [61.67344039414193]
  We present a novel extension of multi-task Gaussian Cox processes for modeling heterogeneous correlated tasks jointly. A MOGP prior over the parameters of the dedicated likelihoods for classification, regression and point process tasks can facilitate sharing of information between heterogeneous tasks. We derive a mean-field approximation to realize closed-form iterative updates for estimating model parameters.
  arXiv  Detail & Related papers  (2023-08-29T15:01:01Z)
• Robust probabilistic inference via a constrained transport metric [8.85031165304586]
  We offer a novel alternative by constructing an exponentially tilted empirical likelihood carefully designed to concentrate near a parametric family of distributions. The proposed approach finds applications in a wide variety of robust inference problems, where we intend to perform inference on the parameters associated with the centering distribution. We demonstrate superior performance of our methodology when compared against state-of-the-art robust Bayesian inference methods.
  arXiv  Detail & Related papers  (2023-03-17T16:10:06Z)
• Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data [68.62134204367668]
  This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. The generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution.
  arXiv  Detail & Related papers  (2023-02-14T17:02:35Z)
• Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
  Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
  arXiv  Detail & Related papers  (2021-06-03T12:59:16Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• Learning Disentangled Representations with Latent Variation Predictability [102.4163768995288]
  This paper defines the variation predictability of latent disentangled representations. Within an adversarial generation process, we encourage variation predictability by maximizing the mutual information between latent variations and corresponding image pairs. We develop an evaluation metric that does not rely on the ground-truth generative factors to measure the disentanglement of latent representations.
  arXiv  Detail & Related papers  (2020-07-25T08:54:26Z)
• Posterior Ratio Estimation of Latent Variables [14.619879849533662]
  In some applications, we want to compare distributions of random variables that are emphinferred from observations. We study the problem of estimating the ratio between two posterior probability density functions of a latent variable.
  arXiv  Detail & Related papers  (2020-02-15T16:46:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.