A Quantum Many-body Wave Function Inspired Language Modeling Approach

The recently proposed quantum language model (QLM) aimed at a principled approach to modeling term dependency by applying the quantum probability theory. The latest development for a more effective QLM has adopted word embeddings as a kind of global dependency information and integrated the quantum-inspired idea in a neural network architecture. While these quantum-inspired LMs are theoretically more general and also practically effective, they have two major limitations. First, they have not taken into account the interaction among words with multiple meanings, which is common and important in understanding natural language text. Second, the integration of the quantum-inspired LM with the neural network was mainly for effective training of parameters, yet lacking a theoretical foundation accounting for such integration. To address these two issues, in this paper, we propose a Quantum Many-body Wave Function (QMWF) inspired language modeling approach. The QMWF inspired LM can adopt the tensor product to model the aforesaid interaction among words. It also enables us to reveal the inherent necessity of using Convolutional Neural Network (CNN) in QMWF language modeling. Furthermore, our approach delivers a simple algorithm to represent and match text/sentence pairs. Systematic evaluation shows the effectiveness of the proposed QMWF-LM algorithm, in comparison with the state of the art quantum-inspired LMs and a couple of CNN-based methods, on three typical Question Answering (QA) datasets.Comment: 10 pages,4 figures,CIK

Modeling Covariate Effects in Group Independent Component Analysis with Applications to Functional Magnetic Resonance Imaging

Independent component analysis (ICA) is a powerful computational tool for separating independent source signals from their linear mixtures. ICA has been widely applied in neuroimaging studies to identify and characterize underlying brain functional networks. An important goal in such studies is to assess the effects of subjects' clinical and demographic covariates on the spatial distributions of the functional networks. Currently, covariate effects are not incorporated in existing group ICA decomposition methods. Hence, they can only be evaluated through ad-hoc approaches which may not be accurate in many cases. In this paper, we propose a hierarchical covariate ICA model that provides a formal statistical framework for estimating and testing covariate effects in ICA decomposition. A maximum likelihood method is proposed for estimating the covariate ICA model. We develop two expectation-maximization (EM) algorithms to obtain maximum likelihood estimates. The first is an exact EM algorithm, which has analytically tractable E-step and M-step. Additionally, we propose a subspace-based approximate EM, which can significantly reduce computational time while still retain high model-fitting accuracy. Furthermore, to test covariate effects on the functional networks, we develop a voxel-wise approximate inference procedure which eliminates the needs of computationally expensive covariance estimation. The performance of the proposed methods is evaluated via simulation studies. The application is illustrated through an fMRI study of Zen meditation.Comment: 36 pages, 5 figure

Exploiting Low-dimensional Structures to Enhance DNN Based Acoustic Modeling in Speech Recognition

We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces. To that end, the training posteriors are used for dictionary learning and sparse coding. Sparse representation of the test posteriors using this dictionary enables projection to the space of training data. Relying on the fact that the intrinsic dimensions of the posterior subspaces are indeed very small and the matrix of all posteriors belonging to a class has a very low rank, we demonstrate how low-dimensional structures enable further enhancement of the posteriors and rectify the spurious errors due to mismatch conditions. The enhanced acoustic modeling method leads to improvements in continuous speech recognition task using hybrid DNN-HMM (hidden Markov model) framework in both clean and noisy conditions, where upto 15.4% relative reduction in word error rate (WER) is achieved