Thresholded Graphical Lasso Adjusts for Latent Variables: Application to Functional Neural Connectivity

Emerging neuroscience technologies such as electrophysiology and calcium imaging can record from tens-of-thousands of neurons in the live animal brain while the animal is responding to stimuli and behaving freely. Scientists often seek to understand how neurons are communicating during certain stimuli or activities, something termed functional neural connectivity. To learn functional connections from large-scale neuroscience data, many have proposed using probabilistic graphical models (Yatsenko et al. 2015; Narayan et al. 2015; Chang et al. 2019), where each edge denotes conditional dependencies between nodes. Yet, applying such models in neuroscience poses a major challenge as only a small subset of neurons in the animal brain can be recorded at once, leading to abundant latent variables. Chandrasekaran et al. (2012) termed this the latent variable graphical model problem and proposed a convex program to solve this. While conceptually attractive, this approach poses several statistical, computational and practical challenges, discussed subsequently, for the task of learning functional neural connectivity from large-scale neuroscience data. Because of this, we are motivated to consider an incredibly simple solution to the latent variable graphical model problem: apply a hard thresholding operator to existing graph selection estimators. In this paper, we study this approach showing that thresholding has more desirable theoretical properties as well as superior empirical performance.