Flexible combination of multiple diagnostic biomarkers to improve diagnostic accuracy

In medical research, it is common to collect information of multiple continuous biomarkers to improve the accuracy of diagnostic tests. Combining the measurements of these biomarkers into one single score is a popular practice to integrate the collected information, where the accuracy of the resultant diagnostic test is usually improved. To measure the accuracy of a diagnostic test, the Youden index has been widely used in literature. Various parametric and nonparametric methods have been proposed to linearly combine biomarkers so that the corresponding Youden index can be optimized. Yet there seems to be little justification of enforcing such a linear combination. This paper proposes a flexible approach that allows both linear and nonlinear combinations of biomarkers. The proposed approach formulates the problem in a large margin classification framework, where the combination function is embedded in a flexible reproducing kernel Hilbert space. Advantages of the proposed approach are demonstrated in a variety of simulated experiments as well as a real application to a liver disorder study

The Garden Hose Complexity for the Equality Function

The garden hose complexity is a new communication complexity introduced by H. Buhrman, S. Fehr, C. Schaffner and F. Speelman [BFSS13] to analyze position-based cryptography protocols in the quantum setting. We focus on the garden hose complexity of the equality function, and improve on the bounds of O. Margalit and A. Matsliah[MM12] with the help of a new approach and of our handmade simulated annealing based solver. We have also found beautiful symmetries of the solutions that have lead us to develop the notion of garden hose permutation groups. Then, exploiting this new concept, we get even further, although several interesting open problems remain.Comment: 16 page

Augmented Lagrangian Algorithms under Constraint Partitioning

We present a novel constraint-partitioning approach for solving continuous nonlinear optimization based on augmented Lagrange method. In contrast to previous work, our approach is based on a new constraint partitioning theory and can handle global constraints. We employ a hyper-graph partitioning method to recognize the problem structure. We prove global convergence under assumptions that are much more relaxed than previous work and solve problems as large as 40,000 variables that other solvers such as IPOPT [11] cannot solve

Explainable Reasoning over Knowledge Graphs for Recommendation

Incorporating knowledge graph into recommender systems has attracted increasing attention in recent years. By exploring the interlinks within a knowledge graph, the connectivity between users and items can be discovered as paths, which provide rich and complementary information to user-item interactions. Such connectivity not only reveals the semantics of entities and relations, but also helps to comprehend a user's interest. However, existing efforts have not fully explored this connectivity to infer user preferences, especially in terms of modeling the sequential dependencies within and holistic semantics of a path. In this paper, we contribute a new model named Knowledge-aware Path Recurrent Network (KPRN) to exploit knowledge graph for recommendation. KPRN can generate path representations by composing the semantics of both entities and relations. By leveraging the sequential dependencies within a path, we allow effective reasoning on paths to infer the underlying rationale of a user-item interaction. Furthermore, we design a new weighted pooling operation to discriminate the strengths of different paths in connecting a user with an item, endowing our model with a certain level of explainability. We conduct extensive experiments on two datasets about movie and music, demonstrating significant improvements over state-of-the-art solutions Collaborative Knowledge Base Embedding and Neural Factorization Machine.Comment: 8 pages, 5 figures, AAAI-201