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The challenge in this problem lies in the domain difference, which could degrade the generalization ability of the prediction model. To tackle this challenge, we propose to learn a neural network representation function to align a joint distribution and a product distribution in the representation space, and show that such joint-product distribution alignment conveniently leads to the alignment of multiple domains. In particular, we align the joint distribution and the product distribution under the<jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{2}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>L<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-distance, and show that this distance can be analytically estimated by exploiting its variational characterization and a linear variational function. This allows us to comfortably align the two distributions by minimizing the estimated distance with respect to the network representation function. Our experiments on synthetic and real-world datasets for classification and regression demonstrate the effectiveness of the proposed solution. For example, it achieves the best average classification accuracy of 82.26% on the text dataset Amazon Reviews, and the best average regression error of 0.114 on the WiFi dataset UJIIndoorLoc.<\/jats:p>","DOI":"10.1007\/s00521-023-08520-1","type":"journal-article","created":{"date-parts":[[2023,4,23]],"date-time":"2023-04-23T13:01:41Z","timestamp":1682254901000},"page":"16509-16526","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Joint-product representation learning for domain generalization in classification and regression"],"prefix":"10.1007","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3692-0728","authenticated-orcid":false,"given":"Sentao","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,4,23]]},"reference":[{"key":"8520_CR1","doi-asserted-by":"crossref","unstructured":"Akuzawa K, Iwasawa Y, Matsuo Y (2019) Adversarial invariant feature learning with accuracy constraint for domain generalization. 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