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.

我们提出了一种条件共轭高斯过程因子分析 (ccGPFA) 方法，它能够在建模神经活动的脉冲计数数据时进行解析和计算上可行的推断。通过引入新颖的数据增强方法，使模型在条件上具有共轭性，从而在变分 EM 算法中获得简单的闭式更新。通过稀疏高斯过程和自然梯度加速推断，我们的模型能够轻松扩展，并通过实验证明了其有效性。

通过数据增强的条件共轭高斯过程因子分析用于脉冲计数数据

Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count  Data via Data Augmentation

Characterizing the relationship between neural population activity and
behavioral data is a central goal of neuroscience. While latent variable models
(LVMs) are successful in describing high-dimensional time-series data, they are
typically only designed for a single type of data, making it difficult to
identify structure shared across different experimental data modalities. Here,
we address this shortcoming by proposing an unsupervised LVM which extracts
temporally evolving shared and independent latents for distinct, simultaneously
recorded experimental modalities. We do this by combining Gaussian Process
Factor Analysis (GPFA), an interpretable LVM for neural spiking data with
temporally smooth latent space, with Gaussian Process Variational Autoencoders
(GP-VAEs), which similarly use a GP prior to characterize correlations in a
latent space, but admit rich expressivity due to a deep neural network mapping
to observations. We achieve interpretability in our model by partitioning
latent variability into components that are either shared between or
independent to each modality. We parameterize the latents of our model in the
Fourier domain, and show improved latent identification using this approach
over standard GP-VAE methods. We validate our model on simulated multi-modal
data consisting of Poisson spike counts and MNIST images that scale and rotate
smoothly over time. We show that the multi-modal GP-VAE (MM-GPVAE) is able to
not only identify the shared and independent latent structure across modalities
accurately, but provides good reconstructions of both images and neural rates
on held-out trials. Finally, we demonstrate our framework on two real world
multi-modal experimental settings: Drosophila whole-brain calcium imaging
alongside tracked limb positions, and Manduca sexta spike train measurements
from ten wing muscles as the animal tracks a visual stimulus.

我们提出了一种无监督的潜在变量模型，可以从不同的实验数据模态中提取演化的共享和独立的潜变量，通过结合高斯过程因子分析和高斯过程变分自编码器的方法，我们在傅里叶域中参数化模型的潜变量，并在两个真实的多模态实验设置上验证了模型的有效性。