Title: | Efficient Estimation for Semiparametric Structural Equation Models With Censored Data |
Speaker: | Mr Wong Kin Yau, Department of Biostatistics, University of North Carolina at Chapel Hill, NC, USA |
Time/Place: | 11:30 - 12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | Structural equation modeling is commonly used to capture complex structures of relationships among multiple variables, both latent and observed. In this talk, I describe a general class of structural equation models with a semiparametric component for potentially censored survival times. I consider nonparametric maximum likelihood estimation and propose a combined Expectation-Maximization and Newton-Raphson algorithm for its computation. I discuss conditions for model identifiability and present results on the consistency, asymptotic normality, and semiparametric efficiency of the estimators. Finally, I demonstrate the satisfactory performance of the proposed methods through simulation studies and provide applications to a motivating cancer study from The Cancer Genome Atlas that contains a variety of genomic variables. |
Title: | Spectrum slicing for sparse Hermitian definite matrices based on Zolotarev's functions |
Speaker: | Dr. Haizhao YANG, Department of Mathematics, Duke University, USA |
Time/Place: | 11:30 - 12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil (A, B). Based on Zolotarev’s best rational function approximations of the signum function and conformal maps, we construct the best rational function approximation of a rectangular function supported on an arbitrary interval. This new best rational function approximation is applied to construct spectrum filters of (A, B). Combining fast direct solvers and the shift-invariant GMRES, a hybrid fast algorithm is proposed to apply spectral filters efficiently. Assuming that the sparse Hermitian matrices A and B are of size N × N with O(N) nonzero entries, the computational cost for computing O(1) interior eigenpairs is bounded by that of solving a shifted linear system (A − σB)x = b. Utilizing the spectrum slicing idea, the proposed method computes the full eigenvalue decomposition of a sparse Hermitian definite matrix pencil via solving O(N) linear systems. The efficiency and stability of the proposed method are demonstrated by numerical examples of a wide range of sparse matrices. Compared with existing spectrum slicing algorithms based on contour integrals, the proposed method is faster and more reliable. |
Title: | Goodness-of-Fit Tests for Semiparametric and Parametric Hypotheses Based on The Probability Weighted Characteristic Function |
Speaker: | Prof. Simos G. MEINTANIS, Department of Economics, National and Kapodistrian University of Athens, Greece |
Time/Place: | 11:30 - 12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | We consider the novel notion of the probability weighted characteristic function (PWCF) and the corresponding empirical counterpart, the probability weighted empirical characteristic function (PWECF). The properties of both these quantities are presented and their application in goodness-of-fit testing (parametric and non-parametric) is considered. The asymptotic null distribution and consistency of the new tests is discussed. As an example we revisit the case of testing for multivariate normality. Tests for symmetry and for the two-sample problem are also illustrated. |
Title: | Asymptotically compatible discretizations for nonlocal models and their applications |
Speaker: | Dr. Jiang YANG, Applied Physics and Applied Mathematics, Columbia University, USA |
Time/Place: | 15:00 - 16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | Many problems in nature, being characterized by a parameter, are of interests both with a fixed parameter value and with the parameter approaching an asymptotic limit. Numerical schemes that are convergent in both regimes offer robust discretizations which can be highly desirable in practice. The asymptotically compatible schemes discussed here meet such objectives for a class of parametrized problems. In this talk, we will present two asymptotically compatible discretizations for nonlocal models, including specially designed quadrature based finite difference methods and Fourier spectral methods. In particular, we will discuss the efficient implementation of these two asymptotically compatible for nonlocal models. In the end, we will apply these asymptotically compatible discretizations for a robust a posteriori stress analysis, as well as some nonlocal gradient flows including nonlocal Allen-Cahn equations, nonlocal Cahn-Hilliard equations and nonlocal phase-field models. |
Title: | Deep Learning Approach for Model Learning in Image Processing and Analysis |
Speaker: | Dr. Jian SUN, Xi'an Jiaotong University, China |
Time/Place: | 16:00 - 17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In this talk, I will show that many iterative optimization algorithms in image processing and analysis can be modeled as deep networks, by which the parameters in energy function and the corresponding optimization algorithm can be discriminatively learned for specific task. I will show that the iterative shrinkage in signal processing, ADMM (Alternating Direction Method of Multipliers) algorithm optimizing a compressive sensing model, a multi-atlas organ segmentation method in medical image analysis can be formulated as deep networks. These networks are non-conventional, task-specific and achieved state-of-the-art results in image restoration, compressive sensing MRI and cardiac MR image segmentation. |
We organize conferences and workshops every year. Hope we can see you in future.
Learn MoreProf. M. Cheng, Dr. Y. S. Hon, Dr. K. F. Lam, Prof. L. Ling, Dr. T. Tong and Prof. L. Zhu have been awarded research grants by Hong Kong Research Grant Council (RGC) — congratulations!
Learn MoreFollow HKBU Math