It is well known that collaborative filtering (CF) based recommender systems provide better modeling of users and items associated with considerable rating history. The lack of historical ratings results in the user and the item coldstart problems. The latter is the main focus of this work. Most of the current literature addresses this problem by integrating content-based recommendation techniques to model the new item. However, in many cases such content is not available, and the question arises is whether this problem can be mitigated using CF techniques only. We formalize this problem as an optimization problem: given a new item, a pool of available users, and a budget constraint, select which users to assign with the task of rating the new item in order to minimize the prediction error of our model. We show that the objective function is monotone-supermodular, and propose efficient optimal design based algorithms that attain an approximation to its optimum. Our findings are verified by an empirical study using the Netflix dataset, where the proposed algorithms outperform several baselines for the problem at hand.
Abstract. Let N * (m) be the minimal length of a polynomial with ±1 coefficients divisible by (x − 1) m . Byrnes noted that N * (m) ≤ 2 m for each m, and asked whether in fact N * (m) = 2 m . Boyd showed that N * (m) = 2 m for all m ≤ 5, but N * (6) = 48. He further showed that N * (7) = 96, and that N * (8) is one of the 5 numbers 96, 144, 160, 176, or 192. Here we prove that N * (8) = 144. Similarly, let m * (N ) be the maximal power of (x − 1) dividing some polynomial of degree N − 1 with ±1 coefficients. Boyd was able to find m * (N ) for N < 88. In this paper we determine m * (N ) for N < 168.
Many real-world graphs have complex labels on the nodes and edges. Mining only exact patterns yields limited insights, since it may be hard to find exact matches. However, in many domains it is relatively easy to define a cost (or distance) between different labels. Using this information, it becomes possible to mine a much richer set of approximate subgraph patterns, which preserve the topology but allow bounded label mismatches. We present novel and scalable methods to efficiently solve the approximate isomorphism problem. We show that approximate mining yields interesting patterns in several real-world graphs ranging from IT and protein interaction networks to protein structures.
Abstract. Let N * q (m) be the minimal positive integer N , for which there exists a splitting of the set [0, N − 1] into q subsets, S 0 , S 1 , . . . , S q−1 , whose first m moments are equal. Similarly, let m * q (N ) be the maximal positive integer m, such that there exists a splitting of [0, N − 1] into q subsets whose first m moments are equal. For q = 2, these functions were investigated by several authors, and the values of N * 2 (m) and m * 2 (N ) have been found for m ≤ 8 and N ≤ 167, respectively. In this paper, we deal with the problem for any prime q. We demonstrate our methods by finding m * 3 (N ) for any N < 90 and N * 3 (m) for m ≤ 6.
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