Let Cost(π) be the value of weak OT functional for a plan π, i.e., Cost( π) We are going to use our Theorem 3.1. As a result, every plan is optimal.Proof of Proposition 3.3. According to our Theorem 3.2, one only has to ensure that Anyway, this is indifferent for us. It remains to upper bound the first term in (23). Formula (12) for the optimal drift follows from [38, Proposition 4.1] From our Proposition 3.3 it follows that For other ϵ > 0, the analogous equivalence holds true.

Given a relational database (RDB), how can we predict missing column values in some target table of interest? Although RDBs store vast amounts of rich, informative data spread across interconnected tables, the progress of predictive machine learning models as applied to such tasks arguably falls well behind advances in other domains such as computer vision or natural language processing. This deficit stems, at least in part, from the lack of established/public RDB benchmarks as needed for training and evaluation purposes. As a result, related model development thus far often defaults to tabular approaches trained on ubiquitous single-table benchmarks, or on the relational side, graph-based alternatives such as GNNs applied to a completely different set of graph datasets devoid of tabular characteristics. To more precisely target RDBs lying at the nexus of these two complementary regimes, we explore a broad class of baseline models predicated on: (i) converting multi-table datasets into graphs using various strategies equipped with efficient subsampling, while preserving tabular characteristics; and (ii) trainable models with well-matched inductive biases that output predictions based on these input subgraphs. Then, to address the dearth of suitable public benchmarks and reduce siloed comparisons, we assemble a diverse collection of (i) large-scale RDB datasets and (ii) coincident predictive tasks.

Inspired by the neural mechanisms that may contribute to the brain's associative power, specifically the cortical modularization and hippocampal pattern completion, here we propose a self-supervised controllable generation (SCG) framework.

In real-world applications, event data is typically received in a streaming manner, where the distribution of patterns may shift over time. Additionally, privacy and memory constraints are commonly observed in practical scenarios, further compounding the challenges.