Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive representations of graphs as Gaussian mixture models, fitted to distributions of sampled node embeddings over the same space. The Wasserstein distance between these Gaussian mixture distributions then yields an interpretable and easily computable distance measure, which can further be tailored for the comparison at hand by choosing appropriate embeddings. We propose two embeddings for this framework and show that under certain assumptions about the shape of the resulting Gaussian mixture components, further computational improvements of this Wasserstein distance can be achieved. An empirical validation of our find- ings on synthetic data and real-world Functional Brain Connectivity networks shows promising performance compared to existing em- bedding methods.

Widefield calcium imaging enables recording of large-scale neural activity across the mouse dorsal cortex. In order to examine the relationship of these neural signals to the resulting behavior, it is critical to demix the recordings into meaningful spatial and temporal components that can be mapped onto well-defined brain regions. However, no current tools satisfactorily extract the activity of the different brain regions in individual mice in a data-driven manner, while taking into account mouse-specific and preparation-specific differences. Here, we introduce Localized semi-Nonnegative Matrix Factorization (LocaNMF), a method that efficiently decomposes widefield video data and allows us to directly compare activity across multiple mice by outputting mouse-specific localized functional regions that are significantly more interpretable than more traditional decomposition techniques. Moreover, it provides a natural subspace to directly compare correlation maps and neural dynamics across different behaviors, mice, and experimental conditions, and enables identification of task- and movement-related brain regions.

A fundamental goal of systems neuroscience is to understand the relationship between neural activity and behavior. Behavior has traditionally been characterized by low-dimensional, task-related variables such as movement speed or response times. More recently, there has been a growing interest in automated analysis of high-dimensional video data collected during experiments. Here we introduce a probabilistic framework for the analysis of behavioral video and neural activity. This framework provides tools for compression, segmentation, generation, and decoding of behavioral videos. Compression is performed using a convolutional autoencoder (CAE), which yields a low-dimensional continuous representation of behavior. We then use an autoregressive hidden Markov model (ARHMM) to segment the CAE representation into discrete "behavioral syllables." The resulting generative model can be used to simulate behavioral video data. Finally, based on this generative model, we develop a novel Bayesian decoding approach that takes in neural activity and outputs probabilistic estimates of the full-resolution behavioral video. We demonstrate this framework on two different experimental paradigms using distinct behavioral and neural recording technologies.