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学术报告

A Unified Analysis of Multi-task Functional Linear Regression Models with Manifold Constraint and Composite Quadratic Penalty

贺诗源 助理教授

（中国人民大学）

报告时间： 2022年11月18日 (星期五) 下午2：00-3：00

腾讯会议 ID：602-239-486

线下报告地点：沙河校区E404（由于疫情原因转线上）

报告摘要：
This work studies the multi-task functional linear regression models where both the covariates and the unknown regression coefficients (called slope functions) are curves. For slope function estimation, we employ penalized splines to balance bias, variance, and computational complexity. The power of multi-task learning is brought in by imposing additional structures over the slope functions. We propose a general model with double regularization over the spline coefficient matrix: i) a matrix manifold constraint, and ii) a composite penalty as a summation of quadratic terms. Many multi-task learning approaches can be treated as special cases of this proposed model, such as a reduced-rank model and a graph Laplacian regularized model. We show the composite penalty induces a specific norm, which helps to quantify the manifold curvature and determine the corresponding proper subset in the manifold tangent space. The complexity of tangent space subset is then bridged to the complexity of geodesic neighbor via generic chaining. A unified convergence upper bound is obtained and specifically applied to the reduced-rank model and the graph Laplacian regularized model. The phase transition behaviors for the estimators are examined as we vary the configurations of model parameters.

报告人简介：
贺诗源，中国人民大学统计与大数据研究院助理教授，博士生导师。贺诗源的研究领域包括统计函数数据分析、贝叶斯计算等，并将统计学方法与天文相结合，研究超新星、Mira变星等光谱和光面曲线拟合，进而测量宇宙尺度。已在Journal of the American Statistical Association、The Annals of Applied Statistics、The Astrophysical Journal等统计学、天文学一流期刊发表多篇论文。

邀请人： 罗雪