We present Variational Bayesian Network (VBN) - a novel Bayesian entity representation learning model that utilizes hierarchical and relational side information and is particularly useful for modeling entities in the "long-tail'', where the data is scarce. VBN provides better modeling for long-tail entities via two complementary mechanisms: First, VBN employs informative hierarchical priors that enable information propagation between entities sharing common ancestors. Additionally, VBN models explicit relations between entities that enforce complementary structure and consistency, guiding the learned representations towards a more meaningful arrangement in space. Second, VBN represents entities by densities (rather than vectors), hence modeling uncertainty that plays a complementary role in coping with data scarcity. Finally, we propose a scalable Variational Bayes optimization algorithm that enables fast approximate Bayesian inference. We evaluate the effectiveness of VBN on linguistic, recommendations, and medical inference tasks. Our findings show that VBN outperforms other existing methods across multiple datasets, and especially in the long-tail.

This paper presents the Bayesian Hierarchical Words Representation (BHWR) learning algorithm.BHWR facilitates Variational Bayes word representation learning combined with semantic taxonomy modeling via hierarchical priors.By propagating relevant information between related words, BHWR utilizes the taxonomy to improve the quality of such representations.Evaluation of several linguistic datasets demonstrates the advantages of BHWR over suitable alternatives that facilitate Bayesian modeling with or without semantic priors.Finally, we further show that BHWR produces better representations for rare words.

Top-$k$ Combinatorial Bandits generalize multi-armed bandits, where at each round any subset of $k$ out of $n$ arms may be chosen and the sum of the rewards is gained. We address the full-bandit feedback, in which the agent observes only the sum of rewards, in contrast to the semi-bandit feedback, in which the agent observes also the individual arms’ rewards. We present the Combinatorial Successive Accepts and Rejects (CSAR) algorithm, which generalizes SAR (Bubeck et al., 2013) for top-k combinatorial bandits. Our main contribution is an efficient sampling scheme that uses Hadamard matrices in order to estimate accurately the individual arms’ expected rewards. We discuss two variants of the algorithm, the first minimizes the sample complexity and the second minimizes the regret. We also prove a lower bound on sample complexity, which is tight for $k=O(1)$. Finally, we run experiments and show that our algorithm outperforms other methods.

Learning item representations is a key building block in recommender systems research. However, representations often suffer from the cold start problem - a well-known problem in which rare items in the tail of the distribution face insufficient data yielding inadequate representations. In this work, we present a novel hybrid recommender that supports the utilization of hierarchical content-based information to mitigate the cold start problem. In particular, we assume a taxonomy of item tags in which every item is associated with several `parent' tags and the tags themselves can be associated with several `parent' tags in a hierarchical manner. Our model learns item representations that are guided by the `parent' tags of each item which allows propagating relevant information between items sharing the same hierarchy. In addition, the tags are modeled using tag representations that allow propagating information between any two tags that share a common ancestor. Due to space limitation, we focus this work on a recommendations task, however the same approach can be utilized for general representation learning e.g. language models.