Event(s) on July 2019

• Tuesday, 9th July, 2019

  Title:	PhD Oral Exam: Numerical Algorithms for Data Clustering
  Speaker:	Ms LIU Ye, Department of Mathematics, Hong Kong Baptist University, HKSAR
  Time/Place:	10:00  -  12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this presentation, we study several novel numerical algorithms for data clustering mainly applied on multi-view data and tensor data. For multi-view clustering, more accurate results can be achieved by integrating information from multiple sources. However, Most existing multi-view clustering method assume the degree of association among all the graphs are the same. One significant truth is some graphs may be strongly or weakly associated with other graphs in reality. We propose several methods to cluster multi-view data and determine the degree of association among graphs simultaneously. Another part of presentation is we propose an orthogonal nonnegative Tucker decomposition method to decompose high-dimensional nonnegative tensor into a tensor with smaller size for dimension reduction, and then perform clustering analysis. A convex relaxation algorithm of the augmented Lagrangian function is devoloped to solve the optimization problem and the convergence of the algorithm is discussed. We employ our proposed method on several real image data sets from different real world applications, including face recognition, image representation and hyperspectral unmixing problem to illustrate the effectiveness of proposed algorithm.

  
  

• Thursday, 11th July, 2019

  Title:	PhD Oral Exam: Convergence Analysis and Applications of Two optimization Algorithms
  Speaker:	Mr MA Yaonan, Department of Mathematics, Hong Kong Baptist University, HKSAR
  Time/Place:	10:30  -  12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We focus on two optimization algorithms for solving convex programs: the $theta$-scheme and a preconditioned primal-dual algorithm. For the $theta$-scheme, we first present an elaborative convergence analysis in Hilbert space and propose a general convergent inexact $theta$-scheme. Second, for unconstrained problems, we prove the convergence of the $theta$-scheme and show a sublinear convergence rate in terms of objective value. Furthermore, a practical inexact $theta$-scheme is derived to solve $l_2$-loss based problems and its convergence is proved. Third, for constrained problems, the convergence of the $theta$-scheme is available in the literature. However, its sublinear convergence rate is unknown until we provide one via a variational reformulation of the solution set. Besides, in order to relax the condition imposed on the $theta$-scheme, we propose a new variant and show its convergence. Finally, numerical experiments demonstrate the efficiency of all concerned algorithms. For the preconditioned primal-dual algorithm, noticing that a practical step size cannot lie in the theoretical region, we show that the range of dual step size can be enlarged by 1/3 at most and at the same time, the convergence and a sublinear convergence rate can be ensured. Therefore, this practical step size can indeed guarantee the convergence. Besides, if more regularity conditions are imposed on objective functions, we can obtain a linear convergence rate. Finally, some connection with ADMM is revealed.

  
  

• Friday, 12th July, 2019

  Title:	PhD Oral Exam: Determination of Random Schrodinger Operators
  Speaker:	Mr MA Shiqi, Department of Mathematics, Hong Kong Baptist University, HKSAR
  Time/Place:	10:30  -  12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Random inverse problem is a fascinating area studying how to extract useful statistical information from unknown object coming from real world. In this thesis, we focus on the study of inverse problem related to random Schrödinger operators. We are particularly interested in the case where both the source and the potential of the Schrödinger system are random. In our first topic, we are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schrödinger equation with unknown random random source and unknown potential. Our second topic also focuses on the case where only the source is random. But in the second topic, the random model is different from our first topic. Lastly, base on the previous two results, we study the case where both the source and the potential are random and unknown. Three major novelties of our works in this thesis are that, first, we studied the case where both the source and the potential are unknown; second, both passive and active scattering measurements are used for the recovery in different scenarios; finally, only a single realization of the random sample is required to establish the recovery of useful information.

  
  

• Wednesday, 17th July, 2019

  Title:	Fast convergent splitting algorithms for phase retrieval with/without sparse prior
  Speaker:	Prof Huibin Chang, Department of Mathematics, Tianjin University, China
  Time/Place:	10:00  -  10:45 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Phase retrieval plays an important role in vast industrial and scientific applications, which is essentially a non-convex and possible non-smooth optimization problem mathematically. In this talk, we mainly concern how to design convergent splitting algorithm and further improve the quality of reconstructed images driven by the sparse prior. We first consider the bind ptychography problem. We address a general least squares model by maximum likelihood estimation and adopt fast alternating direction method of multipliers to solve it. Under mild conditions, we establish the global convergence to stationary points. Numerically, the proposed algorithm outperforms the state-of-the-art algorithms in both speed and image quality. Then we consider a noisy phase retrieval problem with measured intensities corrupted by strong Gaussian or Poisson noises. Due to the non-convexity of established models, we also discuss how to design fast splitting algorithms with convergence guarantee. This is a joint work with Stefano Marchesini in LBNL, Yifei Lou in UT Dallas, M. K. Ng in HKBU, T. Zeng in HKCU and Y. Duan in Tianjin U .

  
  

• Wednesday, 17th July, 2019

  Title:	Spatially adapted first and second order regularization for image reconstruction: from an image surface perspective
  Speaker:	Prof Yuping Duan, Department of Mathematics, Tianjin University, China
  Time/Place:	11:00  -  11:45 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We propose a spatially adapted first and second order regularization for image reconstruction to better localize image features. More specifically, we derive the regularization by pursuing the total variation of the unit normal of the associated image surface for a given image, which is proven with good geometric attribute in preserving image contrast. In what follows, we present the numerical solution to the proposed model by employing the alternating direction method of multipliers (ADMM) and provide its analytical properties. Various numerical experiments on image denoising, deblurring and inpainting are implemented to demonstrate the effectiveness and efficiency of the proposed regularization scheme.

  
  

• Thursday, 25th July, 2019

  Title:	Information retrieval from electronic medical record
  Speaker:	Dr. Xiang WAN, Shenzhen Research Institute of Big Data, Shenzhen, China
  Time/Place:	15:00  -  15:45 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Information retrieval (IR) in natural language processing is a standard technique used for efficiently accessing information in large collections of texts. In this talk, I will first present how to improve information access in electronic medical record (EMR) with advanced natural language processing (NLP) techniques. We concentrate more specifically on the NLP tasks of named entity recognition (NER), relation extraction, and text classification. Second, we recently propose a flexible framework field embedding to jointly learn Chinese word embeddings, which incorporates morphological, phonetic and other linguistic information. Experiments demonstrate that our model can make use of multiple fields to extract semantic information while other existing methods cannot. Empirical results on the word similarity, word analogy, text classification tasks illustrate the proposed model outperforms state-of-the-art methods, such as word2vec, CWE, JWE, and cw2vec.

  
  

• Thursday, 25th July, 2019

  Title:	New HSIC-based tests for independence between two stationary multivariate time series
  Speaker:	Dr Guochang WANG, Department of Statistics, Jinan University, Guangzhou, China
  Time/Place:	15:45  -  16:15 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	This paper proposes some novel one-sided omnibus tests for independence between two multivariate stationary time series. These new tests apply the Hilbert-Schmidt independence criterion (HSIC) to test the independence between the innovations of both time series. Under regular conditions, the limiting null distributions of our HSIC-based tests are established. Next, our HSIC-based tests are shown to be consistent. Moreover, a residual bootstrap method is used to obtain the critical values for our HSIC-based tests, and its validity is justified. Compared with the existing cross-correlation-based tests for linear dependence, our tests examine the general (including both linear and non-linear) dependence to give investigators more complete information on the causal relationship between two multivariate time series. The merits of our tests are illustrated by some simulation results and a real example.

  
  

• Thursday, 25th July, 2019

  Title:	Encoding the category to select the feature genes for single-cell RNA-seq classification
  Speaker:	Dr Yan ZHOU, Department of Statistics, Shenzhen University, Shenzhen, China
  Time/Place:	16:15  -  17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	With the development of next-generation sequencing techniques, microRNA-seq or single-cell RNA-seq (scRNA-seq) data are becoming popular as an alternative for biology and medicine studies, such as different expressed (DE) genes detected or disease diagnosis. Using microRNA-seq or scRNA-seq data to diagnose the type of diseases is an effective way in medical research. For microRNA-seq or scRNA-seq data, several statistical methods have been developed for classification, including for example Poisson linear discriminant analysis (PLDA), negative binomial linear discriminant analysis (NBLDA) and zero-inflated Poisson logistic discriminant analysis (ZIPLDA). We know that the feature genes are vitally important for microRNA-seq or scRNA-seq data classification. In fact, the majority of genes are not differentially expressed and they are irrelevant for class distinction. To improve the classification performance and save the computation time, it is necessary to remove the irrelevant genes and detect the important feature genes is necessary. The widely used methods in the literature assume the data as normally distributed so that they may not be suitable for microRNA-seq and scRNA-seq data. In this paper, we propose an encoding the category (ENTC) method to select the feature genes for single-cell RNA-seq data classification. The novel method encodes the category again by employing the rank of samples for each gene in each class. We then consider the correlation coefficient of gene and class with rank of sample and new rank of category. The highest correlation coefficient genes are considered as the differentially expressed genes which are most effective to classify the samples. We also establish the sure screening and rank consistency properties of the proposed ENTC method. Simulation studies show that the classifier using the proposed ENTC method performs better than, or at least as well as, the existing methods in most settings. Two real datasets including a microRNA-seq dataset and a scRNA-seq dataset are also analyzed, and the results demonstrate the superior performance of the proposed method over the existing competitors. To cater for the demands of the application, we have also developed an R package called “ENTC” and have made it freely available for download. Availability: The R package named ”ENTC” is available at https://github.com/zhangli1109/ENTC.

  
  

• Monday, 29th July, 2019

  Title:	PhD Oral Exam: Stochastic Gradient Descent for Pairwise Learning: Stability and Optimization Error
  Speaker:	Mr SHEN Wei, Department of Mathematics, Hong Kong Baptist University, HKSAR
  Time/Place:	10:00  -  12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	n this presentation, we focus on the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learning setting. Pairwise learning refers to a learning task which involves a loss function depending on pairs of instances among which notable examples are bipartite ranking, metric learning, area under ROC curve (AUC) maximization and minimum error entropy (MEE) principle. Our contribution is twofold. Firstly, we establish the stability results for SGD for pairwise learning in the convex, strongly convex and non-convex settings, from which generalization errors can be naturally derived. Moreover, we also give the stability results of buffer-based SGD and projected SGD. Secondly, we establish the trade-off between stability and optimization error of SGD algorithms for pairwise learning. This is achieved by lower-bounding the sum of stability and optimization error by the minimax statistical error over a prescribed class of pairwise loss functions. From this fundamental trade-off, we obtain lower bounds for the optimization error of SGD algorithms and the excess expected risk over a class of pairwise losses. In addition, we illustrate our stability results by giving some specific examples and experiments of AUC maximization and MEE.

  
  

• Tuesday, 30th July, 2019

  Title:	PhD Oral Exam: Order Determination for Large matrices with Spiked Structure
  Speaker:	Mr ZENG Yicheng, Department of Mathematics, Hong Kong Baptist University, HKSAR
  Time/Place:	10:45  -  12:45 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We investigate order determination for large dimensional matrices with spiked structures in which the dimensions of the matrices are proportional to the sample sizes. Because the asymptotic behaviors of the estimated eigenvalues differ completely from those in fixed dimension scenarios, we then discuss the largest possible order, say q, we can identify and introduce criteria for different settings of q. When q is assumed to be fixed, we propose a “valley-cliff” criterion with two versions. This generic method is very easy to implement and computationally inexpensive, and it can be applied to various matrices. As examples, we focus on spiked population models, spiked Fisher matrices and factor models with auto-covariance matrices. For the case of divergent q, we propose a scale-adjusted truncated double ridge ratio (STDRR) criterion, where a scale adjustment is implemented to deal with the bias in scale parameter for large q. Again, examples include spiked population models, spiked Fisher matrices. Numerical studies are conducted to examine the finite sample performances of the method and to compare it with existing methods. As for theoretical contributions, we investigate the limiting properties, including convergence in probability and central limit theorems, for spiked eigenvalues of spiked Fisher matrices with divergent q.

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