Efficient dependency models for some distributions

The BP Dependency Function: a Generic Measure of Dependence between Random Variables

Measuring and quantifying dependencies between random variables (RV's) can give critical insights into a data-set. Typical questions are: `Do underlying relationships exist?', `Are some variables redundant?', and `Is some target variable $Y$ highly or weakly dependent on variable $X$?' Interestingly, despite the evident need for a general-purpose measure of dependency between RV's, common practice of data analysis is that most data analysts use the Pearson correlation coefficient (PCC) to quantify dependence between RV's, while it is well-recognized that the PCC is essentially a measure for li…

Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures

Combining individual p-values to aggregate multiple small effects has a long-standing interest in statistics, dating back to the classic Fisher's combination test. In modern large-scale data analysis, correlation and sparsity are common features and efficient computation is a necessary requirement for dealing with massive data. To overcome these challenges, we propose a new test that takes advantage of the Cauchy distribution. Our test statistic has a very simple form and is defined as a weighted sum of Cauchy transformation of individual p-values. We prove a non-asymptotic result that the tai…

对输入过程序列相关性的敏感性：一种鲁棒方法

Sensitivity to Serial Dependency of Input Processes: A Robust Approach

评估序列依赖性对性能分析影响的程序通常建立在参数化指定模型上。在本文中，我们提出了一个强大的，非参数的方法来进行这种评估，通过计算最坏情况下的偏差的性能指标，由于任意依赖。该方法是基于优化，假设在模型空间，具有约束条件，指定的依赖程度的非参数距离测量到一些名义独立同分布。输入模型我们通过模拟和方差分析（ANOVA）研究这些优化的近似方法。数值实验表明，所提出的方法可以发现隐藏的影响的依赖超出了传统的参数建模和相关性研究。

句子理解中依赖补全的贝叶斯分层混合过程模型--以汉语关系从句为例

Modelling dependency completion in sentence comprehension as a Bayesian hierarchical mixture process: A case study involving Chinese relative clauses

我们提出了一个案例研究证明贝叶斯分层混合模型的有用性，调查认知过程。在句子理解中，人们普遍认为语言共同依存关系之间的距离影响依存关系解决的延迟：距离越长，检索时间越长（基于距离的帐户）。另一种理论，直接访问，假设检索时间是两个分布的混合：一个分布代表成功的检索（这些是独立的依赖距离），另一个代表一个初始的失败，以检索正确的依赖，其次是重新分析，导致成功的检索。我们将这两个模型作为贝叶斯层次模型来实现，结果表明，直接访问模型比距离帐户更好地解释了中文关系从句阅读时间数据。

Variational Bayes approach for model aggregation in unsupervised classification with Markovian dependency

We consider a binary unsupervised classification problem where each observation is associated with an unobserved label that we want to retrieve. More precisely, we assume that there are two groups of observation: normal and abnormal. The `normal' observations are coming from a known distribution whereas the distribution of the `abnormal' observations is unknown. Several models have been developed to fit this unknown distribution. In this paper, we propose an alternative based on a mixture of Gaussian distributions. The inference is done within a variational Bayesian framework and our aim is to…

Copula变分推断

Copula variational inference

我们开发了一个通用的变分推断方法，保留了潜在变量之间的依赖关系。我们的方法使用Copula来增加平均场和结构近似中使用的分布族。Copulas模型的依赖性，没有被捕获的原始变分分布，因此，增强变分家庭保证更好的近似后验。利用随机最优化，对增广分布的推断是可扩展的。此外，我们的策略是通用的：它可以适用于任何推理过程，目前使用的平均场或结构化的方法。Copula变分推断具有许多优点：它减少了偏差;它对局部最优值不太敏感;它对超参数不太敏感;它有助于表征和解释潜在变量之间的依赖关系。