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【2020.12.15-12.15 北京】概率统计学术报告会
2020-12-15 | 编辑:

Dec. 15th, 2020

 

Time & Place

Content

8:30-9:15

N202

陳松蹊 (北京大學)

Linear Regression Trees and Forrest

9:15-10:00

N202

朱利平 (中國人民大學)

非線性相依關系的度量以及獨立性檢驗

10:00-10:15

N202

Tea Break

10:15-11:00

N202

何輝 (北京師範大學)

分枝布朗運動極值的偏差概率

11:00-11:45

N202

許惟鈞 (北京大學)

On convergence of a class of wave equations and their invariant Gibbs measure

12:00-14:30

Lunch

14:30-15:15

N219

王若度 (加拿大滑鐵盧大學)

E-values and hypothesis testing

15:15-16:00

N219

傅雙雙 (北京科技大學)

Gaussian States as Minimum Uncertainty States

Abstract

陳松蹊

北京大學

Title: Linear Regression Trees and Forrest

Abstract: This paper proposes a tree-based estimator called linear regression trees (LRT) for segmented linear regression models which prescribe piecewise linear models over unknown domains determined by binary splits of unknown split variables. The proposed estimation is based on an adaptive split variable selection and level estimation algorithm that maximizes, at each internal node, a cumulative conditional Kendall's tau statistic that measures the rank dependence between the regressors and the estimated residuals. The algorithm provides a data-driven way for estimating the unknown segments. Theoretical analysis shows that the binary split selection algorithm leads to consistent identification and estimation of both the genuine split variables and the split levels. The split selection algorithm is then applied recursively to generate a tree. To obtain a right-sized tree, we provide a tree pruning algorithm for LRT with adaptively defined cost-complexity measure. We also propose a hypothesis testing based stopping rule to control the partitioning process, which is more efficient than pruning. We demonstrate theoretically that the number of the leaf nodes of the pruned tree converges to the underlying number of segments in probability. The practical performance of the proposed approach is evaluated via numerical simulations and case studies on nine well studied datasets. The latter shows advantageous predictive performance of the proposed methods over the CART (Classification And Regression Trees), GUIDE (for Generalized, Unbiased Interaction Detection and Estimation), MARS (Multivariate Adaptive Regression Splines) and Random Forests. This is a joint work with Xiangyu Zheng.

 

朱利平

中國人民大學

題目: 非線性相依關系的度量以及獨立性檢驗

摘要: 本報告將報告三個部分。

一、均值獨立:我們引入累積散度的概念,來刻畫均值獨立。

二、區間分位數獨立:我們介紹區間分位數獨立的思想,這是對統計獨立性這個基本概念的直接推廣。

三、分布獨立:我們對BKR相關系數進行適當的修改,並介紹投影相關系數來描述兩個隨機向量之間的非線性相依關系。

 

何輝

北京師範大學

題目: 分枝布朗運動極值的偏差概率

摘要: 分枝布朗運動是統計物理學中的基礎模型,其極值理論的研究在偏微分方程、自旋玻璃和廣義能量模型、對數相關的高斯場、生物數學等領域的研究中有著重要的應用。在這個報告中,我們會介紹相關的偏差概率的估計的一些進展。

 

許惟鈞

北京大學

Title: On convergence of a class of wave equations and their invariant Gibbs measure

Abstract: Motivated by weak universality problems in singular SPDEs, we consider a class of higher order nonlinear approximations to 2D cubic defocusing wave equation starting with their corresponding Gibbs measures. We give a sufficient and almost necessary condition for the convergence of the Gibbs measures within this class of approximation. Interestingly, this condition turns out to be strictly stronger than that for the global convergence of the wave dynamics. The main ingredient in treating these measures is a variational method recently developed by Barashkov and Gubinelli.

 

王若度

加拿大滑鐵盧大學

Title: E-values and hypothesis testing

Abstract: Testing statistical hypothesis is usually done in sciences using p-values. Recently, e-values have gained attention as potential alternatives to p-values as measures of uncertainty, significance, and evidence. We discuss three important issues on e-values.

1) Advantages and disadvantages of e-values versus p-values in single, multiple, online and collaborative hypothesis testing.

2) The e-BH procedure, a natural analog of the Benjamini-Hochberg (BH) procedure for false discovery rate (FDR) control. Unlike the usual BH procedure, the e-BH procedure controls the FDR at the desired level for any dependence structure between the e-values, which allows for wide applications.

3) Use e-values to construct a model-free backtest of the Expected Shortfall, the most important risk measure in finance and insurance.

 

傅雙雙

北京科技大學

Title: Gaussian States as Minimum Uncertainty States

Abstract: Gaussian distributions and Gaussian states are fundamental and ubiquitous in probability theory and quantum theory. In bosonic fields, Gaussian states constitute a rather wide family of states including coherent states, squeezed states, thermal states, etc., and have many classical-like features, which are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this work, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation. This characterization puts Gaussian states on a novel basis of physical significance.

 
 
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