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