Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking (Fan and Lv, 2008) or feature selection using a two-sample t-test in high-dimensional classification (Tibshirani et al., 2003). Within the context of the linear model, Fan and Lv (2008) showed that this simple correlation ranking possesses a sure independence screening property under certain conditions and that its revision, called iteratively sure independent screening (ISIS), is needed when the features are marginally unrelated but jointly related to the response variable. In this paper, we extend ISIS, without explicit definition of residuals, to a general pseudo-likelihood framework, which includes generalized linear models as a special case. Even in the least-squares setting, the new method improves ISIS by allowing variable deletion in the iterative process. Our technique allows us to select important features in high-dimensional classification where the popularly used two-sample t-method fails. A new technique is introduced to reduce the false discovery rate in the feature screening stage. Several simulated and two real data examples are presented to illustrate the methodology.

We propose a semiparametric latent Gaussian copula model for modelling mixed multivariate data, which contain a combination of both continuous and binary variables. The model assumes that the observed binary variables are obtained by dichotomizing latent variables that satisfy the Gaussian copula distribution. The goal is to infer the conditional independence relationship between the latent random variables, based on the observed mixed data. Our work has two main contributions: we propose a unified rankbased approach to estimate the correlation matrix of latent variables; we establish the concentration inequality of the proposed rankbased estimator. Consequently, our methods achieve the same rates of convergence for precision matrix estimation and graph recovery, as if the latent variables were observed. The methods proposed are numerically assessed through extensive simulation studies, and real

We present a novel variation of the well-known infomax algorithm of blind source separation. Under natural gradient descent, the infomax algorithm converges to a stationary point of a limiting ordinary differential equation. However, due to the presence of saddle points or local minima of the corresponding likelihood function, the algorithm may be trapped around these bad stationary points for a long time, especially if the initial data are near them. To speed up convergence, we propose to add a sequence of random perturbations to the infomax algorithm to shake the iterating sequence so that it is captured by a path descending to a more stable stationary point. We analyze the convergence of the randomly perturbed algorithm, and illustrate its fast convergence through numerical examples on blind demixing of stochastic signals. The examples have analytical structures so that saddle points or local minima of the likelihood functions are explicit. The results may have implications for online learning algorithms in dissimilar problems.

Kernel density estimates are frequently used, based on a second order kernel. Thus, the bias inherent to the estimates has an order of O(<i>h</i>²_<i>n</i>). In this note, a method of correcting the bias in the kernel density estimates is provided, which reduces the bias to a smaller order. Effectively, this method produces a higher order kernel based on a second order kernel. For a kernel function <i>K</i>, the functions W_k(x)=^k-1₁₌₀(^k_l+1)x^lK^(l)(x)/l! and [1/<i>K</i>^{(<i>k</i> 1)}(<i>x</i>)/<i>x</i> d <i>x</i>]<i>K</i>^{(<i>k</i> 1)}(<i>x</i>)/<i>x</i> are kernels of order <i>k</i>, under some mild conditions.

We develop an expectation-maximization algorithm with local adaptivity for image segmentation and classification. The key idea of our approach is to combine global statistics extracted from the Gaussian mixture model or other proper statistical models with local statistics and geometrical information, such as local probability distribution, orientation, and anisotropy. The combined information is used to design an adaptive local classification strategy that improves the robustness of the algorithm and also keeps fine features in the image. The proposed methodology is flexible and can be easily generalized to deal with other inferred information/quantities and statistical methods/models.

When people in a society want to make inference about some parameter, each person may want to use data collected by other people. Information (data) exchange in social networks is usually costly, so to make reliable statistical decisions, people need to weigh the benefits and costs of information acquisition. Conflicts of interests and coordination problems will arise in the process. Classical statistics does not consider peoples incentives and interactions in the data-collection process. To address this imperfection, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Motivated by our interest in aggregate inference at the societal level, we propose a new concept, <i>finite population learning</i>, to address whether with high probability, a large fraction of people in a given finite population network can make good inference. Serving as a foundation, this concept enables

Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries by such data mining approaches be spurious due to high dimensionality and limited sample size? Can our fundamental assumptions on exogeneity of covariates needed for such variable selection be validated with the data? To answer these questions, we need to derive the distributions of the maximum spurious correlations given certain number of predictors, namely, the distribution of the correlation of a response variable Y with the best s linear combinations of p covariates X, even when X and Y are independent. When the covariance matrix of X possesses the restricted eigenvalue property, we derive such distributions for both finite s and diverging s, using Gaussian approximation and empirical process

This paper considers a proportional hazards model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of lifetime data. A local partial-likelihood technique is proposed to estimate nonlinear interactions. Asymptotic normality of the proposed estimator is established. The baseline hazard function, the bias and the variance of the local likelihood estimator are consistently estimated. In addition, a one-step local partial-likelihood estimator is presented to facilitate the computation of the proposed procedure and is demonstrated to be as efficient as the fully iterated local partial-likelihood estimator. Furthermore, a penalized local likelihood estimator is proposed to select important risk variables in the model. Numerical examples are used to illustrate the effectiveness of the proposed procedures.

No abstract uploaded!

We study the estimation of the additive components in additive regression models, based on the weighted sample average of regression surface, for stationary <i></i>-mixing processes. Explicit expression of this method makes possible a fast computation and allows an asymptotic analysis. The estimation procedure is especially useful for additive modeling. In this paper, it is shown that the average surface estimator shares the same optimality as the ideal estimator and has the same ability to estimate the additive component as the ideal case where other components are known. Formulas for the asymptotic bias and normality of the estimator are established. A small simulation study is carried out to illustrate the performance of the estimation and a real example is also used to demonstrate our methodology.