王學(xué)欽教授在廈門(mén)大學(xué)經(jīng)濟(jì)學(xué)院舉行了有條件的相關(guān)距離講座。在職研究生講座的主要內(nèi)容如下：

　　有條件依賴(lài)的統(tǒng)計(jì)推斷在許多領(lǐng)域，包括遺傳關(guān)聯(lián)研究和圖形模型至關(guān)重要。經(jīng)典的措施側(cè)重于線性條件相關(guān)，并不能表征非線性條件的關(guān)系，包括非單調(diào)的關(guān)系。為了克服這種局限性，我們引入了多元隨機(jī)變量任意尺寸的條件依賴(lài)的非參數(shù)度量。我們的措施具有必要的和直觀的屬性作為相關(guān)指數(shù)。簡(jiǎn)單地說(shuō)，它是零幾乎肯定，當(dāng)且僅當(dāng)兩個(gè)多元隨機(jī)變量條件獨(dú)立給出一個(gè)第三隨機(jī)變量。更重要的是，這一措施的樣品版本可以?xún)?yōu)雅表示為V或U形的過(guò)程與隨機(jī)內(nèi)核的根，并具有理想的理論特性。根據(jù)樣品的版本中，我們提出了一個(gè)測(cè)試條件獨(dú)立性，這被證明是比一些通過(guò)我們的數(shù)值模擬新近開(kāi)發(fā)的測(cè)試功能更強(qiáng)大。我們的試驗(yàn)的優(yōu)點(diǎn)是更大時(shí)給出的第三隨機(jī)變量的多元隨機(jī)變量之間的關(guān)系，不能表示在一個(gè)隨機(jī)變量與其它的線性或單調(diào)函數(shù)。我們還表明，樣本的措施是一致的和弱收斂，并檢驗(yàn)統(tǒng)計(jì)是漸近正常。通過(guò)應(yīng)用我們的測(cè)試在真實(shí)的數(shù)據(jù)分析，我們能夠識(shí)別兩種條件相關(guān)的基因表達(dá)，否則不能透露。因此，我們的測(cè)量條件的依賴(lài)不僅是一個(gè)理想的概念，同時(shí)也具有重要的實(shí)用價(jià)值。

　　原文：Statistical inference on conditional dependence is essential in many fields including genetic association studies and graphical models. The classic measures focus on linear conditional correlations, and are incapable of characterizing non-linear conditional relationship including non-monotonic relationship. To overcome this limitation, we introduces a nonparametric measure of conditional dependence for multivariate random variables with arbitrary dimensions. Our measure possesses the necessary and intuitive properties as a correlation index. Briefly, it is zero almost surely if and only if two multivariate random variables are conditionally independent given a third random variable. More importantly, the sample version of this measure can be expressed elegantly as the root of a V or U-process with random kernels and has desirable theoretical properties. Based on the sample version, we propose a test for conditional independence, which is proven to be more powerful than some recently developed tests through our numerical simulations. The advantage of our test is even greater when the relationship between the multivariate random variables given the third random variable cannot be expressed in a linear or monotonic function of one random variable versus the other. We also show that the sample measure is consistent and weakly convergent, and the test statistic is asymptotically normal. By applying our test in a real data analysis, we are able to identify two conditionally associated gene expressions, which otherwise cannot be revealed. Thus, our measure of conditional dependence is not only an ideal concept, but also has important practical utility.