Neural Coding in Visual and Auditory Systems for Natural Stimuli: Mathematical Modeling based on Data

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Neuroscience is the study of the nervous system, including the brain, spinal cord, and peripheral nervous system. Its goal is to define and understand the continuum from molecule to cell to behavior. Neuroscience is especially important now because in addition to our intrinsic interest in the nervous system, the field has been collecting rich data at an unprecedented rate (e.g. fMRI, electrode measurements with natural stimuli), and can benefit from rigorous tools for mathematical and data analyses.The PI Dr. Yu is a Professor of Statistics at UC Berkeley which has a very strong neuroscience group atthe Helen Wills Neuroscience Institute. She recognizes the importance of data-driven mathematical modeling in neuroscience at this point in time, and is very experienced with mathematical modeling based on data.The hosts for the IGMS grant are Professors Jack Gallant and Frederic Theunissen at the Helen Willis Neuroscience Institute. They study the visual and auditory nervous systems of macaques and songbirds, respectively. The hosts will provide the invaluable neuron recording data with natural stimuli andprovide access to the data collection process for the IGMS research of the PI.The goal of the IGMS research is to acquire the indispensable neuroscience knowledge and understand available data from the host labs to construct biologically meaningfulmathematical models to relate natural stimuli and responses (neuron firing rates) at different layers of the visual and auditory pathways of animals and humans. It is well-known from physiological and psychophysical experiments that some cells at lower levels of the pathways are linear and other cells at higher levels of the pathways are non-linear. Hence both linear and nonlinear stimulus-response models are relevant. Based on data from the host labs, the PI plans to 1) apply model selection techniques such as gMDL in linear neural coding models, and compare with existing linear methods;2) construct biologically meaningful non-linearmodels in the frameworks of boosting and Support Vector Machines from machine learning;3) select biologically meaningful features based on Independent Component Analysis (ICA) using natural phase images and complex wavelet transforms, and use them in linear or non-linear models from parts(1) and (2).As a result of this IGMS grant, the PI will be able to provide a unique opportunity for students of statistics/mathematics to pursuit a Ph.D. with applications in computational neuroscience. UC Berkeley has an incredible potential for a program in computational neuroscience since it has very strong departments both in neuroscience and in the physical sciences. Members of the faculty from these departments want to develop a formal interdisciplinary graduate training program in theoretical/computational neuroscience.The IGMS grant will enable the PI to be part of this new program and therefore help train the next generation of researchers at the interface of neuroscience and mathematics, or computational neuroscience.The training of graduate students in computational neuroscience will benefit society both by advancing our understanding of the brain and by inspiring advanced engineering applications. In particular, the research results will give us insight on how natural stimuli are processed in the visual and auditory system of animals and humans. Understanding how biological systems process natural stimuli might inspire the development of novel algorithms in engineering applications for image/sound compression, speech recognition and image/sound pre-processing for hearing or vision aids and neural prosthetics.Moreover, the IGMS grant will open up the field of neuroscience for the PI to solve problems in the field on one hand and on the other hand infuse new ideas into the PI's research in machine learning and data mining.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).