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含时变协变量的非参数风险函数提升估计AI 解读

Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient. From this we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard. The generic estimator is consistent…

L2 Boosting 的性质刻画AI 解读

We consider $L_{2}$Boosting, a special case of Friedman’s generic boosting algorithm applied to linear regression under $L_{2}$-loss. We study $L_{2}$Boosting for an arbitrary regularization parameter and derive an exact closed form expression for the number of steps taken along a fixed coordinate direction. This relationship is used to describe $L_{2}$Boosting’s solution path, to describe new tools for studying its path, and to characterize some of the algorithm’s unique…

生存数据的高维变量选择AI 解读

The minimal depth of a maximal subtree is a dimensionless order statistic measuring the predictiveness of a variable in a survival tree. We derive the distribution of the minimal depth and use it for high-dimensional variable selection using random survival forests. In big p and small n problems (where p is the dimension and n is the sample size), the distribution of the minimal depth reveals a “ceiling effect” in which a tree simply cannot be grown deep enough to properly…

最高后验概率模型选择的深入考察AI 解读

We consider the properties of the highest posterior probability model in a linear regression setting. Under a spike and slab hierarchy we find that although highest posterior model selection is total risk consistent, it possesses hidden undesirable properties. One such property is a marked underfitting in finite samples, a phenomenon well noted for Bayesian information criterion (BIC) related procedures but not often associated with highest posterior model selection. Another…

多组微阵列数据的尖峰与厚尾基因选择AI 解读

DNA microarrays can provide insight into genetic changes that characterize different stages of a disease process. Accurate identification of these changes has significant therapeutic and diagnostic implications. Statistical analysis for multistage (multigroup) data is challenging, however. ANOVA-based extensions of two-sample Z-tests, a popular method for detecting differentially expressed genes in two groups, do not work well in multigroup settings. False detection rates…

基于尖峰—平板先验的变量选择：频率学派与贝叶斯策略AI 解读

Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation. Specifically, we study the usefulness of continuous bimodal priors to model hypervariance parameters, and the…

基于加权伽马过程的乘法强度模型计算方法AI 解读

We develop computational procedures for a class of Bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures. A key feature of our approach is that explicit expressions for posterior distributions of these models share many common structural features with the posterior distributions of Bayesian hierarchical models using the Dirichlet process. Using this fact, along with an approximation for the…

利用贝叶斯模型选择识别微阵列中的差异表达基因AI 解读

DNA microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease. The high throughput nature of these arrays, where differential expression for thousands of genes can be measured simultaneously, creates an enormous wealth of information, but also poses a challenge for data analysis because of the large multiple testing problem involved. The solution has generally been to focus on optimizing false-discovery rates while…

半参数线性混合模型的独立同分布蒙特卡洛算法AI 解读

Hybrid versions of independent and identically distributed weighted Chinese restaurant (WCR) algorithms are developed for inference in semiparametric linear mixed models under minimal assumptions for the random-effects distributions. The WCR method of working with the posterior partition structure leads to Rao–Blackwell estimates for higher-order moments of random effects, such as skewness and kurtosis, and can be used to estimate densities for random effects. A key feature…

通过边际密度分解进行有限混合模型的贝叶斯选择AI 解读

We consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture model, in which d is bounded by some fixed finite number N. Our approach relies on the use of a prior over the space of mixing distributions with at most N components. By decomposing the resulting marginal density under this prior, we discover a weighted Bayes factor method for consistently estimating d that can be implemented by an iid generalized…

折棍先验的 Gibbs 抽样方法AI 解读

A rich and flexible class of random probability measures, which we call stick-breaking priors, can be constructed using a sequence of independent beta random variables. Examples of random measures that have this characterization include the Dirichlet process, its two-parameter extension, the two-parameter Poisson–Dirichlet process, finite dimensional Dirichlet priors, and beta two-parameter processes. The rich nature of stick-breaking priors offers Bayesians a useful class…

指数族半参数混合模型中的信息AI 解读

Z In a class of semiparametric mixture models, the score function (and consequently the effective information) for a finite-dimensional parameter can be made arbitrarily small depending upon the direction taken in the parameter space. This result holds for a broad range of semiparametric mixtures over exponential families and includes examples such as the gamma semiparametric mixture, the normal mean mixture, the Weibull semiparametric mixture and the negative binomial…

有限半参数混合模型中广义Pólya urn方案的指数后验一致性AI 解读

Advances in Markov chain Monte Carlo MCMC methods now make it computationally feasible and relatively straightforward to apply the Dirichlet process prior in a wide range of Bayesian nonparametric problems. The feasibility of these methods rests heavily on the fact that the MCMC approach avoids direct sampling of the Dirichlet process and is instead based on sampling the finite-dimensional posterior which is obtained from marginalizing out the process. In application, it is…

半参数 Weibull 混合模型的一致估计速率AI 解读

This paper presents a uniform estimator for a finite-dimensional parameter in the semiparametric Weibull mixture model. The rates achieved by the estimator hold uniformly over shrinking sequences of models much more general than traditional sequences that are required to satisfy a Hellinger differentiable property. We show that these rates are optimal in a class of identified models constrained by a moment condition on the nonparametric mixing distribution.

位置混合模型中尺度参数的可识别性与估计速率AI 解读

In this paper we consider the problem of identifiability and estimation for the scale parameter $\theta$ in the location mixture model $\theta (X + Y)$, where X has a known distribution independent of the Y, whose distribution is unknown. Identification of $\theta$ is ensured by constraining Y based on the tail behavior of the distribution for X. Rates for estimation are described for those X which can be written as a square summable series of exponential variables. As a…