Title: | PhD Oral Defense: Communication-efficient Distributed Optimization and Federated Learning |
Speaker: | Mr NI Renyuan, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
Time/Place: | 14:00 - 16:00 FSC1217, or Zoom (Meeting ID: 973 5544 4200 Password: 528692) |
Abstract: | We propose efficient methods for distributed machine learning, using gradient compression to tackle communication and bandwidth constraints. The FEDPEQ approach combines gradient compression, partial participation, and error compensation to significantly reduce communication costs in centralized stochastic optimization. Rigorous analysis of the method's convergence properties reveals a direct link between convergence rates and client engagement. Experimental results demonstrate its effectiveness in solving logistic regression and neural network tasks on MNIST and NIST datasets. Moreover, we introduce a novel quantized dual averaging technique for decentralized stochastic optimization. This technique maintains convergence properties while achieving competitive convergence rates, as confirmed through theoretical analysis and numerical experiments on logistic regression and LASSO problems. |
Title: | A fast algorithm for the quadratic optimization problem with inequality quadratic constraints |
Speaker: | Dr. LI Siqing, College of Mathematics Taiyuan University of Technology |
Time/Place: | 15:00 - 16:00 FSC1110, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | The least-squares quadratic optimization problems with quadratic inequality constraints (LSQI) are applicable in various research fields, including the inverse problem and the wave equations with energy preservation. In this talk, we introduce a fast algorithm for solving this kind of LSQI problem. The proposed algorithm begins by simplifying the original LSQI problem through the the Generalized Singular Value Decomposition (GSVD) of matrices in the objective function and inequality constraint function. This step helps to transform the problem into an equivalent LSQI problem which is easier to solve. Next, the Lagrange multiplier and Lagrange function are introduced to formulate the optimization problem which incorporate the inequality constraints into the objective function. The proposed algorithm computes the Lagrange parameter by solving a scalar secular equation using Newton iteration with a Hebden model. We will show the performance of the proposed fast algorithm by applying it to two specific problems: the inverse Cauchy problem and Hamiltonian wave equations with energy preservation. These examples demonstrate the effectiveness and applicability of the proposed algorithm in real-world scenarios. |
Title: | Tensor Decompositions by Generating Polynomials and Their Applications |
Speaker: | Dr. Zi YANG, Department of Mathematics and Statistics, State University of New York, Albany |
Time/Place: | 10:30 - 11:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | Tensors are multi-dimensional data arrays, widely used in data science. The tensor decomposition is to write a tensor into a sum of rank-one tensors. Given a tensor, finding its tensor decomposition is a fundamentally challenging problem. In this talk, we will discuss how the generating polynomials are related to the tensor decomposition problem and how we can efficiently obtain the tensor decomposition using the generating polynomials. Specifically, we will talk about the symmetric tensor decompositions with applications to Gaussian mixture models and general nonsymmetric tensor decompositions. |
Title: | PhD Oral Defense: Quasisymmetric Functions in Partially Commuting Variables under Hivert’s Local Action |
Speaker: | Mr LAZZERONI JR Anthony Aurthur, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
Time/Place: | 09:00 - 11:00 FSC1217, or Zoom (Meeting ID: 910 8134 6622 Password: 599578) |
Abstract: | We introduce the Hopf algebra of r-quasisymmetric functions in s-partially commuting variables, denoted PCQSym(r,s). This Hopf algebra generalizes the Hopf algebra of symmetric functions in commuting and noncommuting variables and the Hopf algebra of quasisymmetric functions in commuting and noncommuting variables. The space PCQSym(r,s) is defined by an equivalence relation on r-set compositions, which is a generalization of set partitions and set compositions. This ideal makes use of the powersum basis of symmetric functions in commuting and noncommuting variables as well as the powersum basis of quasisymmetric functions in commuting variables and noncommuting variables. |
Title: | Parallel-in-Time Iterative Methods for Pricing American Options |
Speaker: | Prof. Jun Liu, Department of Mathematics and Statistics, Southern Illinois University Edwardsville |
Time/Place: | 09:30 - 10:30 Zoom, Meeting ID: 977 5587 0594 |
Abstract: | In finance, American options allow holders to exercise the option rights at any time before and including the day of expiration. For pricing such American options by PDE models, a sequence of linear complementarity problems (LCPs) need to be solved at each time step sequentially. We can reformulate LCPs as HJB equations, which can be then solved by the popular policy iteration. We propose to solve an “all-at-once” form of HJB equations simultaneously by the policy iteration, which can be accelerated by our designed parallel-in-time (PinT) preconditioners. Numerical examples are presented to confirm the effectiveness of our proposed methods. |
Title: | Nonstandard inference for mortality models and momentum trade |
Speaker: | Prof Liang Peng, Georgia State University |
Time/Place: | 16:00 - 17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | Mortality models have been critical in pricing life insurance products, and trading momentum is popular in finance. The employed mortality models in the literature of actuarial science involve unobserved mortality indexes and use estimated mortality indexes to fit a time series model for forecasting mortality risk and hedging longevity risk. The estimated mortality index approximates the random mortality index with measurement error. A recent study of trading momentum involves measurement errors for a time series model too. Standard statistical methods without taking the measurement errors into account often lead to biased inferences. This talk will discuss some nonstandard inferences in these two situations. |
Title: | Adaptive distributed learning system with privacy preservation |
Speaker: | Prof Shao-Bo Lin, Xi’an Jiaotong University |
Time/Place: | 16:00 - 17:00 FSC1110, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In this talk, we propose a novel adaptive distributed learning system based on divide-and-conquer and local average regression for prediction and privacy preservation simultaneously. Different from the classical distributed learning strategy whose algorithmic parameters and patterns are given by the central agent, our approach provides autonomy to each local agent in terms of parameter selection, algorithm designation and data perturbation. Such an adaptive manner significantly enhances the privacy preservation of the system. Our theoretical results demonstrate that the novel adaptive distributed learning system does not degrade the prediction performance of classical systems via presenting optimal learning rates in the framework of statistical learning theory. Our theoretical assertions are verified via numerous numerical experiments including both toy simulations and real data study. In our analysis, the new system also admits a certain perturbation of the test data via showing an almost comparable accuracy to that of the original data, which provides a realistic possibility for protecting privacy from both training and testing sides. |
Title: | Learning theory of spectral algorithms under covariate shift |
Speaker: | Prof Zheng-Chu Guo, Zhejiang University |
Time/Place: | 17:00 - 18:00 FSC1110, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In machine learning, it is commonly assumed that the training and test samples are drawn from the same underlying distribution. However, this assumption may not always hold true in practice. In this talk, we delve into a scenario where the distribution of the input variables (also known as covariates), differs between the training and test phases. This situation is referred to as covariate shift. To address the challenges posed by covariate shift, various techniques have been developed, such as importance weighting, domain adaptation, and reweighting methods. In this talk, we specifically focus on the weighted spectral algorithm. Under mild conditions imposed on the weights, we demonstrate that this algorithm achieves satisfactory convergence rates. |
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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!
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