Qian Yu

Peng Zhang, Qian Yu, Yuexian Hou et al.

Recently, a Distribution Separation Method (DSM) is proposed for relevant feedback in information retrieval, which aims to approximate the true relevance distribution by separating a seed irrelevance distribution from the mixture one. While DSM achieved a promising empirical performance, theoretical analysis of DSM is still need further study and comparison with other relative retrieval model. In this article, we first generalize DSM's theoretical property, by proving that its minimum correlation assumption is equivalent to the maximum (original and symmetrized) KL-Divergence assumption. Second, we also analytically show that the EM algorithm in a well-known Mixture Model is essentially a distribution separation process and can be simplified using the linear separation algorithm in DSM. Some empirical results are also presented to support our theoretical analysis.

Xiaozhao Zhao, Yuexian Hou, Qian Yu et al.

Typical dimensionality reduction methods focus on directly reducing the number of random variables while retaining maximal variations in the data. In this paper, we consider the dimensionality reduction in parameter spaces of binary multivariate distributions. We propose a general Confident-Information-First (CIF) principle to maximally preserve parameters with confident estimates and rule out unreliable or noisy parameters. Formally, the confidence of a parameter can be assessed by its Fisher information, which establishes a connection with the inverse variance of any unbiased estimate for the parameter via the Cramér-Rao bound. We then revisit Boltzmann machines (BM) and theoretically show that both single-layer BM without hidden units (SBM) and restricted BM (RBM) can be solidly derived using the CIF principle. This can not only help us uncover and formalize the essential parts of the target density that SBM and RBM capture, but also suggest that the deep neural network consisting of several layers of RBM can be seen as the layer-wise application of CIF. Guided by the theoretical analysis, we develop a sample-specific CIF-based contrastive divergence (CD-CIF) algorithm for SBM and a CIF-based iterative projection procedure (IP) for RBM. Both CD-CIF and IP are studied in a series of density estimation experiments.