Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count Data via Data Augmentation
- URL: http://arxiv.org/abs/2405.11683v1
- Date: Sun, 19 May 2024 21:53:36 GMT
- Title: Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count Data via Data Augmentation
- Authors: Yididiya Y. Nadew, Xuhui Fan, Christopher J. Quinn,
- Abstract summary: Recently, GPFA has been extended to model spike count data.
We propose a conditionally-conjugate Gaussian process factor analysis (ccGPFA) resulting in both analytically and computationally tractable inference.
- Score: 8.114880112033644
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Gaussian process factor analysis (GPFA) is a latent variable modeling technique commonly used to identify smooth, low-dimensional latent trajectories underlying high-dimensional neural recordings. Specifically, researchers model spiking rates as Gaussian observations, resulting in tractable inference. Recently, GPFA has been extended to model spike count data. However, due to the non-conjugacy of the likelihood, the inference becomes intractable. Prior works rely on either black-box inference techniques, numerical integration or polynomial approximations of the likelihood to handle intractability. To overcome this challenge, we propose a conditionally-conjugate Gaussian process factor analysis (ccGPFA) resulting in both analytically and computationally tractable inference for modeling neural activity from spike count data. In particular, we develop a novel data augmentation based method that renders the model conditionally conjugate. Consequently, our model enjoys the advantage of simple closed-form updates using a variational EM algorithm. Furthermore, due to its conditional conjugacy, we show our model can be readily scaled using sparse Gaussian Processes and accelerated inference via natural gradients. To validate our method, we empirically demonstrate its efficacy through experiments.
Related papers
- von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
We explore a family of expressive and interpretable distributions over circle-valued random functions.
The resulting probability model has connections with continuous spin models in statistical physics.
For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
arXiv Detail & Related papers (2024-06-19T01:57:21Z) - Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation.
In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model.
We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
arXiv Detail & Related papers (2024-04-11T09:23:36Z) - Sparse Variational Contaminated Noise Gaussian Process Regression with Applications in Geomagnetic Perturbations Forecasting [4.675221539472143]
We propose a scalable inference algorithm for fitting sparse Gaussian process regression models with contaminated normal noise on large datasets.
We show that our approach yields shorter prediction intervals for similar coverage and accuracy when compared to an artificial dense neural network baseline.
arXiv Detail & Related papers (2024-02-27T15:08:57Z) - Neural Operator Variational Inference based on Regularized Stein
Discrepancy for Deep Gaussian Processes [23.87733307119697]
We introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes.
NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior.
We demonstrate that the bias introduced by our method can be controlled by multiplying the divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm.
arXiv Detail & Related papers (2023-09-22T06:56:35Z) - Data-driven Modeling and Inference for Bayesian Gaussian Process ODEs
via Double Normalizing Flows [28.62579476863723]
We introduce normalizing flows to re parameterize the ODE vector field, resulting in a data-driven prior distribution.
We also apply normalizing flows to the posterior inference of GP ODEs to resolve the issue of strong mean-field assumptions.
We validate the effectiveness of our approach on simulated dynamical systems and real-world human motion data.
arXiv Detail & Related papers (2023-09-17T09:28:47Z) - Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood
Estimation for Latent Gaussian Models [69.22568644711113]
We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversions.
Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation.
In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.
arXiv Detail & Related papers (2023-06-05T21:08:34Z) - Score-based Diffusion Models in Function Space [140.792362459734]
Diffusion models have recently emerged as a powerful framework for generative modeling.
We introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space.
We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
arXiv Detail & Related papers (2023-02-14T23:50:53Z) - Scalable mixed-domain Gaussian process modeling and model reduction for longitudinal data [5.00301731167245]
We derive a basis function approximation scheme for mixed-domain covariance functions.
We show that we can approximate the exact GP model accurately in a fraction of the runtime.
We also demonstrate a scalable model reduction workflow for obtaining smaller and more interpretable models.
arXiv Detail & Related papers (2021-11-03T04:47:37Z) - Scalable Variational Gaussian Processes via Harmonic Kernel
Decomposition [54.07797071198249]
We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability.
We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections.
Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
arXiv Detail & Related papers (2021-06-10T18:17:57Z) - SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for
Gaussian Process Regression with Derivatives [86.01677297601624]
We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features.
We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
arXiv Detail & Related papers (2020-03-05T14:33:20Z)
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.