Pb-Hash: Partitioned b-bit Hashing

Many hashing algorithms including minwise hashing (MinHash), one permutation hashing (OPH), and consistent weighted sampling (CWS) generate integers of $B$ bits. With $k$ hashes for each data vector, the storage would be $B\times k$ bits; and when used for large-scale learning, the model size would be $2^B\times k$, which can be expensive. A standard strategy is to use only the lowest $b$ bits out of the $B$ bits and somewhat increase $k$, the number of hashes. In this study, we propose to re-use the hashes by partitioning the $B$ bits into $m$ chunks, e.g., $b\times m =B$. Correspondingly, the model size becomes $m\times 2^b \times k$, which can be substantially smaller than the original $2^B\times k$. Our theoretical analysis reveals that by partitioning the hash values into $m$ chunks, the accuracy would drop. In other words, using $m$ chunks of $B/m$ bits would not be as accurate as directly using $B$ bits. This is due to the correlation from re-using the same hash. On the other hand, our analysis also shows that the accuracy would not drop much for (e.g.,) $m=2\sim 4$. In some regions, Pb-Hash still works well even for $m$ much larger than 4. We expect Pb-Hash would be a good addition to the family of hashing methods/applications and benefit industrial practitioners. We verify the effectiveness of Pb-Hash in machine learning tasks, for linear SVM models as well as deep learning models. Since the hashed data are essentially categorical (ID) features, we follow the standard practice of using embedding tables for each hash. With Pb-Hash, we need to design an effective strategy to combine $m$ embeddings. Our study provides an empirical evaluation on four pooling schemes: concatenation, max pooling, mean pooling, and product pooling. There is no definite answer which pooling would be always better and we leave that for future study

Building K-Anonymous User Cohorts with\\ Consecutive Consistent Weighted Sampling (CCWS)

To retrieve personalized campaigns and creatives while protecting user privacy, digital advertising is shifting from member-based identity to cohort-based identity. Under such identity regime, an accurate and efficient cohort building algorithm is desired to group users with similar characteristics. In this paper, we propose a scalable $K$-anonymous cohort building algorithm called {\em consecutive consistent weighted sampling} (CCWS). The proposed method combines the spirit of the ($p$-powered) consistent weighted sampling and hierarchical clustering, so that the $K$-anonymity is ensured by enforcing a lower bound on the size of cohorts. Evaluations on a LinkedIn dataset consisting of $>70$M users and ads campaigns demonstrate that CCWS achieves substantial improvements over several hashing-based methods including sign random projections (SignRP), minwise hashing (MinHash), as well as the vanilla CWS