Kun Yang

Haipeng Gao, Kun Yang, Yuxue Yang et al.

Knowledge graph embedding has been an active research topic for knowledge base completion (KGC), with progressive improvement from the initial TransE, TransH, RotatE et al to the current state-of-the-art QuatE. However, QuatE ignores the multi-faceted nature of the entity and the complexity of the relation, only using rigorous operation on quaternion space to capture the interaction between entitiy pair and relation, leaving opportunities for better knowledge representation which will finally help KGC. In this paper, we propose a novel model, QuatDE, with a dynamic mapping strategy to explicitly capture the variety of relational patterns and separate different semantic information of the entity, using transition vectors to adjust the point position of the entity embedding vectors in the quaternion space via Hamilton product, enhancing the feature interaction capability between elements of the triplet. Experiment results show QuatDE achieves state-of-the-art performance on three well-established knowledge graph completion benchmarks. In particular, the MR evaluation has relatively increased by 26% on WN18 and 15% on WN18RR, which proves the generalization of QuatDE.

Kun Yang, Hao Su, Wing Hung Wang

Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a binary split of $[0, 1]^d$ and built up sequentially according to discrepancy criteria; the key ingredient is to control the discrepancy adaptively in each sub-rectangle to achieve overall bound. We prove that the estimate, even though simple as it appears, preserves most of the estimation power. By exploiting its structure, it can be directly applied to some important pattern recognition tasks such as mode seeking and density landscape exploration. We demonstrate its applicability through simulations and examples.

Dangna Li, Kun Yang, Wing Hung Wong

Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $Ω$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function. Our density estimate is a piecewise constant function defined on a binary partition of $Ω$. The key ingredient of the algorithm is to use discrepancy, a concept originates from Quasi Monte Carlo analysis, to control the partition process. The resulting algorithm is simple, efficient, and has a provable convergence rate. We empirically demonstrate its efficiency as a density estimation method. We present its applications on a wide range of tasks, including finding good initializations for k-means.