Year | Month |
2024 | Jan Feb Mar May Jun Jul |
2023 | Jan Feb Mar Apr May Jun Jul Aug Oct Nov Dec |
2022 | Oct Nov Dec |
Title: | Component Selection and Variable Selection for Mixture Regression Models |
Speaker: | Dr. FENG Zhenghui, School of Science, Harbin Institute of Technology |
Time/Place: | 10:00 - 11:00 FSC1217 |
Abstract: | Finite mixture regression models are commonly used to account for heterogeneity in populations and situations where the assumptions required for standard regression models may not hold. To expand the range of applicable distributions for components beyond the Gaussian distribution, other distributions, such as the exponential power distribution, the skew-normal distribution, and so on, are explored. To enable simultaneous model estimation, order selection, and variable selection, a penalized likelihood estimation approach that imposes penalties on both the mixing proportions and regression coefficients, which we call the double-penalized likelihood method is proposed in this paper. Four double-penalized likelihood functions and their performance are studied. The consistency of estimators, order selection, and variable selection are investigated. A modified expectation--maximization algorithm is proposed to implement the double-penalized likelihood method. Numerical simulations demonstrate the effectiveness of our proposed method and algorithm. Finally, the results of real data analysis are presented to illustrate the application of our approach. Overall, our study contributes to the development of mixture regression models and provides a useful tool for model and variable selection. |
Title: | Privacy-Preserving Community Detection for Locally Distributed Multiple Networks |
Speaker: | Professor Shujie Ma, Department of Statistics, University of California, Riverside, CA, USA |
Time/Place: | 11:00 - 12:00 FSC1217 |
Abstract: | In this talk, I will introduce a new efficient and scalable consensus community detection approach and distributed learning algorithm in a multi-layer stochastic block model using locally stored network data with privacy-preserving. Specifically, we develop a spectral clustering-based algorithm named ppDSC. To reduce the bias incurred by the randomized response (RR) mechanism for achieving differential privacy, we develop a two-step bias adjustment procedure. To reduce the communication cost encountered in distributed learning, we perform the eigen-decomposition locally and then aggregate the local eigenvectors using an orthogonal Procrustes transformation. We establish a novel bound on the misclassification rate of ppDSC. The new bound reveals the asymmetric roles of the two edge-flipping probabilities of the RR in the misclassification rate. Through the bound, we can also find the optimal choices for the flipping probabilities given a fixed privacy budget. Moreover, we show that ppDSC enjoys the same statistical error rate as its centralized counterpart, when the number of machines satisfies a polynomial order with the sample size on each local machine and the effective heterogeneity is well controlled. |
Title: | Inverse Optimal Transport (IOT) - Learning Cost Functions for Optimal Transport |
Speaker: | Prof. Haomin Zhou, School of Mathematics, Georgia Institute of Technology, Atlanta, USA |
Time/Place: | 16:30 - 17:30 FSC1217 |
Abstract: | The inverse problem of optimal transport (OT) aims at recovering the ground cost function from observed transport plan or its samples. It has been cast as a bi-level optimization problem in the literature, where each iteration requires solving a forward OT problem and causes substantial computational cost overall. In this work, we derive an equivalent but much simpler unconstrained and convex optimization formulation of the inverse OT problem, which can be further augmented by customizable regularization and solved efficiently. We provide a complete characterization of the new optimization problem and its solution space. To validate the effectiveness of this framework, we present a deep learning based method that trains the cost function as a deep neural network using the samples of transport plan for the continuous case. Numerical results demonstrate promising efficiency and accuracy advantages of the proposed methods. This is based on joint work with Shaojun Ma (Goldman-Sacks), Haodong Sun (Wells Fargo), Xiaojing Ye (GSU, Math) and Hongyuan Zha (CUHK, Shenzhen). |
Title: | Box-Cox Model Revisited |
Speaker: | Hui Zou, Dr. Lynn Y.S. Lin Professor, University of Minnesota |
Time/Place: | 11:00 - 12:00 FSC1217 |
Abstract: | The famous Box-Cox model is a must-taught idea even in an undergraduate regression class. However, its real application does not reflect its theoretical importance due to many serious issues in the model and the inference theory. We argue that the fundamental idea behind the Box-Cox model is still very useful and introduce a nonparametric and high-dimensional Box-Cox model to over its major drawbacks. We develop new inference method and theory that make the new Box-Cox model a better tool for high dimensional data analysis than the typical high-dimensional regression model. |
The Department has a distinguished record in teaching and research. A number of faculty members have been recipients of relevant awards.
Learn MoreDr S. Hon recevied the Early Career Award (21/22) from the Research Grants Council.
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