{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/tensor-on-tensor-regression","title":"Tensor-on-tensor regression","arxiv_id":"1701.01037","date":"2017-01-04","proceeding":null,"authors":["Eric F. Lock"],"abstract":"We propose a framework for the linear prediction of a multi-way array (i.e.,\na tensor) from another multi-way array of arbitrary dimension, using the\ncontracted tensor product. This framework generalizes several existing\napproaches, including methods to predict a scalar outcome from a tensor, a\nmatrix from a matrix, or a tensor from a scalar. We describe an approach that\nexploits the multiway structure of both the predictors and the outcomes by\nrestricting the coefficients to have reduced CP-rank. We propose a general and\nefficient algorithm for penalized least-squares estimation, which allows for a\nridge (L_2) penalty on the coefficients. The objective is shown to give the\nmode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for\ninference. We illustrate the approach with an application to facial image data.\nAn R package is available at https://github.com/lockEF/MultiwayRegression .","url_abs":"http://arxiv.org/abs/1701.01037v2","url_pdf":"http://arxiv.org/pdf/1701.01037v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"tensor-on-tensor-regression","repo_url":"https://github.com/lockEF/MultiwayRegression","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1701.01037","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}