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To overcome these difficulties, we propose a hierarchical model designed to flexibly parameterize low-rank receptive fields. The model includes gaussian process priors over spatial and temporal components of the receptive field, encouraging smoothness in space and time. We also propose a new temporal prior, temporal relevance determination, which imposes a variable degree of smoothness as a function of time lag. We derive a scalable algorithm for variational Bayesian inference for both spatial and temporal receptive field components and hyperparameters. The resulting estimator scales to high-dimensional settings in which full-rank maximum likelihood or a posteriori estimates are intractable. We evaluate our approach on neural data from rat retina and primate cortex and show that it substantially outperforms a variety of existing estimators. Our modeling approach will have useful extensions to a variety of other high-dimensional inference problems with smooth or low-rank structure.<\/jats:p>","DOI":"10.1162\/neco_a_01584","type":"journal-article","created":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T21:02:45Z","timestamp":1681160565000},"page":"995-1027","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":4,"title":["Scalable Variational Inference for Low-Rank Spatiotemporal Receptive Fields"],"prefix":"10.1162","volume":"35","author":[{"given":"Lea","family":"Duncker","sequence":"first","affiliation":[{"name":"Wu Tsai Neurosciences Institute and Howard Hughes Medical Institute, Stanford University, Stanford, CA 94302, U.S.A. lduncker@stanford.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kiersten M.","family":"Ruda","sequence":"additional","affiliation":[{"name":"Beth Israel Deaconess Medical Center, Harvard University, Boston, MA 02115, U.S.A. kruda@bidmc.harvard.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Greg D.","family":"Field","sequence":"additional","affiliation":[{"name":"Department of Neurobiology, Duke University, Durham, NC 27708, U.S.A. field@neuro.duke.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonathan W.","family":"Pillow","sequence":"additional","affiliation":[{"name":"Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, U.S.A. pillow@princeton.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","published-online":{"date-parts":[[2023,5,12]]},"reference":[{"key":"2023050921091227800_B1","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1364\/JOSAA.2.000284","article-title":"Spatiotemporal energy models for the perception of motion","volume":"2","author":"Adelson","year":"1985","journal-title":"J. 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