Unsupervised Learning Techniques for Large-Scale, Multi-Trial Neural Data
An increasingly common paradigm in neuroscience is to simultaneously record the activity of many neurons over repeated experimental trials (e.g., multiple presentations of a sensory stimulus, or a repeated motor action). The resulting datasets can be very large, potentially containing recordings from thousands of neurons over thousands of experimental trials. I'm interested in finding general statistical approaches for understanding datasets of this form.
Tensor Components Analysis (TCA)
Commonly used methods for dimensionality reduction (such as PCA) identify low-dimensional features of within-trial neural dynamics, but do not model changes in neural activity across trials. To better understand processes like learning and trial-to-trial variability, I'm exploring tensor decomposition methods to find reduced representations of multi-trial datasets.
My Python toolbox for fitting tensor decompositions to neural data.
Time Warped Dimensionality Reduction
Analysis of neural data often relies on a strict alignment of neural activity to a stimulus or behavioral event on each trial. However, alignment to external events is not always possible (e.g., in cases where neural activity is locked to internal cognitive states or decisions or other unobserved latent factors). I've developed a method to align trials by time warping, while jointly fitting a dimensionality reduction model. This was done in close collaboration with Ben Poole and Niru Maheswaranathan.
Theoretical Molecular Neurobiology
Biology computes with both electrical and biochemical signals. I'm interested in modeling the interface of these two substrates of computation.
Neurons alter ion channel and synaptic receptor expression/activity to maintain activity levels in physiologically stable regimes. This can be modeled from a control theoretic perspective, which provides perspectives on how noisy molecular processes can nevertheless support reliable physiological behaviors.
Microtubular Transport in Complex Dendritic Trees
Neurons are remarkably complex cells. Given this, it seems an almost insurmountable challenge to transport molecular cargo reliably. I've studied a few simple models of how reliable transport can be accomplished.