Compressed Sensing, Sparsity, and Dimensionality in Neuronal Information Processing and Data Analysis

• Published in: Annual review of neuroscience 2012-01, Vol.35 (1), p.485-508
• Main Authors: GANGULI, Surya, SOMPOLINSKY, Haim
• Format: Article
• Language: English
• Subjects: Biological and medical sciences; Brain; Brain - physiology; Cognitive ability; Data analysis; Data Interpretation, Statistical; Fundamental and applied biological sciences. Psychology; General aspects. Models. Methods; Humans; Information processing; Learning - physiology; Mathematical models; Memory, Short-Term - physiology; Mental Processes - physiology; Models, Statistical; Neural Networks (Computer); Neurons - physiology; Neurosciences; Nonlinear Dynamics; Vertebrates: nervous system and sense organs
• ISSN: 0147-006X; 1545-4126
• DOI: 10.1146/annurev-neuro-062111-150410

The curse of dimensionality poses severe challenges to both technical and conceptual progress in neuroscience. In particular, it plagues our ability to acquire, process, and model high-dimensional data sets. Moreover, neural systems must cope with the challenge of processing data in high dimensions to learn and operate successfully within a complex world. We review recent mathematical advances that provide ways to combat dimensionality in specific situations. These advances shed light on two dual questions in neuroscience. First, how can we as neuroscientists rapidly acquire high-dimensional data from the brain and subsequently extract meaningful models from limited amounts of these data? And second, how do brains themselves process information in their intrinsically high-dimensional patterns of neural activity as well as learn meaningful, generalizable models of the external world from limited experience?