However, some critical aspects of it, such as the relationship between superconductivity and materials' chemical/structural features, still need to be understood. Recent successes of data-driven approaches in material science strongly inspire researchers to study this relationship with them, but a corresponding dataset is still lacking.

Molecular representation learning lays the foundation for drug discovery. However, existing methods suffer from poor out-of-distribution (OOD) generalization, particularly when data for training and testing originate from different environments.

Multilevel Monte-Carlo (MLMC) technique and establish its sample and computational complexities.

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Deep learning based neural decoding from stereotactic electroencephalography (sEEG) would likely benefit from scaling up both dataset and model size. To achieve this, combining data across multiple subjects is crucial.

Such embeddings induce the so-called maximum mean discrepancy (MMD; [Smola et al., 2007, Gretton et al., 2012]), which quantifies the discrepancy Many estimators for HSIC exist. The classical ones rely on U-statistics or V -statistics [Gretton et al., 2005, Quadrianto et al., 2009, Pfister et al., 2018] and are known to converge at a rate of Lower bounds for the related MMD are known [Tolstikhin et al., 2016], but the existing analysis considers radial kernels and relies on independent Gaussian distributions.

Here the concept of Granger causality is employed to propose a new criterion for unsupervised learning that is appropriate in the case of temporally-dependent source signals. The basic idea is to identify two projections of a multivariate time series such that the Granger causality among the resulting pair of components is maximized.