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。