In this paper, we propose a technique that leverages graph-based representation learning using the GraphSAGE algorithm to furnish diverse personalized communications tailored to each user's unique engagement patterns within the fantasy sports ecosystem.By curating such personalized user suggestions, we promote diverse user engagement that is more customer centric while maintaining business metrics.We perform offline and online experiments to evaluate the effectiveness of our approaches concerning their impact on different user engagement and business metrics.

Motivated by a network fault detection problem, we study how recall can be boosted in a decision tree classifier, without sacrificing too much precision. This problem is relevant and novel in the context of transfer learning(TL), in which few target domain training samples are available. We define a geometric optimization problem for boosting the recall of a decision tree classifier, and show it is NP-hard. To solve it efficiently, we propose several near-linear time heuristics, and experimentally validate these heuristics in the context of TL. Our evaluation includes 7 public datasets, as well as 6 network fault datasets, and we compare our heuristics with several existing TL algorithms, as well as exact mixed integer linear programming(MILP) solutions to our optimization problem. We find that our heuristics boost recall in a manner similar to optimal MILP solutions, yet require several orders of magnitude less compute time. In many cases the F1 score of our approach is competitive, and often better, than other TL algorithms. Moreover, our approach can be used as a building block to apply transfer learning to more powerful ensemble methods, such as random forests.

In this paper, we introduce a measure of Boolean functions we call diameter, that captures the relationship between certificate complexity and several other measures of Boolean functions. Our measure can be viewed as a variation on alternating number, but while alternating number can be exponentially larger than certificate complexity, we show that diameter is always upper bounded by certificate complexity. We argue that estimating diameter may help to get improved bounds on certificate complexity in terms of sensitivity, and other measures. Previous results due to Lin and Zhang [Krishnamoorthy Dinesh and Jayalal Sarma, 2018] imply that s(f) ≥ Ω(n^{1/3}) for transitive functions with constant alternating number. We improve and extend this bound and prove that s(f) ≥ √n for transitive functions with constant alternating number, as well as for transitive functions with constant diameter. {We also show that bs(f) ≥ Ω(n^{3/7}) for transitive functions under the weaker condition that the "minimum" diameter is constant.} Furthermore, we prove that the log-rank conjecture holds for functions of the form f(x ⊕ y) for functions f with diameter bounded above by a polynomial of the logarithm of the Fourier sparsity of the function f.

Nisan and Szegedy [Nisan and Szegedy, 1994] conjectured that block sensitivity is at most polynomial in sensitivity for any Boolean function. There is a huge gap between the best known upper bound on block sensitivity in terms of sensitivity - which is exponential, and the best known separating examples - which give only a quadratic separation between block sensitivity and sensitivity. In this paper we give various new constructions of families of Boolean functions that exhibit quadratic separation between sensitivity and block sensitivity. Our constructions have several novel aspects. For example, we give the first direct constructions of families of Boolean functions that have both 0-block sensitivity and 1-block sensitivity quadratically larger than sensitivity.