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13 Feb 2023: Taskar et al., 2002). For exam-ple, hyper-linked web-documents are often about similar topics, even if their textual contents aredisparate when viewed as bags of words.

13 Feb 2023: For exam-ple, in supervised and unsupervised probabilistic modelingthe objective function may be the (conditional) data like-lihood or the posterior over parameters.

13 Feb 2023: 1 agreewith all the results from the real datasets. For exam-ple, in Fig.

27 Jan 2023: This setup is very closely related to the classicseemingly unrelated regressionmodel popular in economics [12].

27 Jan 2023: ple processes that add together (Figure 4). For exam-ple, if the first and second columns of A are identical(a1 = a2), then one would expect that data pointsthat simultaneously belong

27 Jan 2023: Taskar et al., 2002). For exam-ple, hyper-linked web-documents are often about similar topics, even if their textual contents aredisparate when viewed as bags of words.

13 Feb 2023: As another exam-ple, we can further decompose the energy function in (2).This results in two different types of factors: a) unary1 fac-tors connecting components of input and output

27 Jan 2023: We show some exam-ples of this in the Results section. 5.

27 Jan 2023: In both exam-ples, it is not fully known how to explicitly describeclasses of relations that are believed to exist (and itis a nuisance to select negative examples by hand tolearn ... analogical reasoningquestion from a SAT-like exam where for a given

13 Feb 2023: binary hash. In this setting, we want to extend the ob-served binary representations hn H (for each exam-ple xn) where H{0, 1}D with a latent binary featurezn,