Edgeworth Expansion by Stein's Method

Edgeworth expansion provides higher-order corrections to the normal approximation for a probability distribution. The classical proof of Edgeworth expansion is via characteristic functions. As a powerful method for distributional approximations, Stein's method has also been used to prove Edgeworth expansion results. However, these results assume that either the test function is smooth (which excludes indicator functions of the half line) or that the random variables are continuous (which excludes random variables having only a continuous component). Thus, how to recover the classical Edgeworth expansion result using Stein's method has remained an open problem. In this paper, we develop Stein's method for two-term Edgeworth expansions in a general case. Our approach involves repeated use of Stein equations, Stein identities via Stein kernels, and a replacement argument.Comment: 22 page

Cervical Cancer-Associated Human Papillomavirus 16 E7 Oncoprotein Inhibits Induction of Anti-Cancer Immunity by a CD4+ T Cell Dependent Mechanism

Attempts to develop therapeutic vaccines against cervical cancer have been proven difficult. One of the major causes of the failure is due to the use of the wrong mouse models based on transplantable tumours in testing the efficacy of vaccines. Now that a transgenic epithelial mouse model has been developed to closely mimic cervical cancer, the mechanisms needed to eliminate this type of cancer could be studied. The E7 oncoprotein of Human Papillomavirus (HPV) is the most expressed HPV protein in cervical cancers and its continuous production is essential to maintain the cancerous state and therefore the obvious target in the development of vaccines. Skin grafts expressing the HPV 16 E7 protein (E7 autografts) are not spontaneously rejected from an MHC matched immunocompetent host. Interestingly, simultaneous placement of an MHC mismatched skin (allograft) next to an E7 autograft results in the E7 autograft rejection. However when the allograft also expresses E7, the E7 autograft is rejected more slowly. Autograft rejection requires CD8+ T cells, and is accelerated by removal of CD4+ T cells after placement of the E7 expressing allograft, suggesting induction of an E7 specific CD4+ regulatory T cell population by the E7 expressing allograft. This observation may have implications in designing effective vaccines and immunotherapy against cervical cancers in women

Efficient Path Prediction for Semi-Supervised and Weakly Supervised Hierarchical Text Classification

Hierarchical text classification has many real-world applications. However, labeling a large number of documents is costly. In practice, we can use semi-supervised learning or weakly supervised learning (e.g., dataless classification) to reduce the labeling cost. In this paper, we propose a path cost-sensitive learning algorithm to utilize the structural information and further make use of unlabeled and weakly-labeled data. We use a generative model to leverage the large amount of unlabeled data and introduce path constraints into the learning algorithm to incorporate the structural information of the class hierarchy. The posterior probabilities of both unlabeled and weakly labeled data can be incorporated with path-dependent scores. Since we put a structure-sensitive cost to the learning algorithm to constrain the classification consistent with the class hierarchy and do not need to reconstruct the feature vectors for different structures, we can significantly reduce the computational cost compared to structural output learning. Experimental results on two hierarchical text classification benchmarks show that our approach is not only effective but also efficient to handle the semi-supervised and weakly supervised hierarchical text classification.Comment: Aceepted by 2019 World Wide Web Conference (WWW19