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多核学习中的稀疏性AI 解读

The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical L2 norms and the reproducing kernel Hilbert space (RKHS) norms induced by the kernels with a data-driven choice of regularization parameters. The main focus is on the case when the total number of kernels is large, but only a relatively small number of them is needed to represent the target function, so that the…

函数型线性回归的再生核希尔伯特空间方法AI 解读

We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive definite kernels, we obtain shaper results on the minimax rates of convergence and show that smoothness regularized estimators achieve the optimal rates of convergence for both prediction and estimation under conditions weaker than those…

广义非线性 ℓ1 正则化解路径的高效全局近似及应用AI 解读

We consider efficient construction of nonlinear solution paths for general ℓ1-regularization. Unlike the existing methods that incrementally build the solution path through a combination of local linear approximation and recalibration, we propose an efficient global approximation to the whole solution path. With the loss function approximated by a quadratic spline, we show that the solution path can be computed using a generalized Lars algorithm. The proposed methodology…

复合分位数回归与模型选择的预言机理论AI 解读

Coefficient estimation and variable selection in multiple linear regression is routinely done in the (penalized) least squares (LS) framework. The concept of model selection oracle introduced by Fan and Li [J. Amer. Statist. Assoc. 96 (2001) 1348–1360] characterizes the optimal behavior of a model selection procedure. However, the least-squares oracle theory breaks down if the error variance is infinite. In the current paper we propose a new regression method called…

多元线性回归中的降维与系数估计AI 解读

Summary We introduce a general formulation for dimension reduction and coefficient estimation in the multivariate linear model. We argue that many of the existing methods that are commonly used in practice can be formulated in this framework and have various restrictions. We continue to propose a new method that is more flexible and more generally applicable. The method proposed can be formulated as a novel penalized least squares estimate. The penalty that we employ is the…

非负Garrotte估计量研究AI 解读

Summary We study the non-negative garrotte estimator from three different aspects: consistency, computation and flexibility. We argue that the non-negative garrotte is a general procedure that can be used in combination with estimators other than the original least squares estimator as in its original form. In particular, we consider using the lasso, the elastic net and ridge regression along with ordinary least squares as the initial estimate in the non-negative garrotte.…

多种生物条件下微阵列时间序列数据的隐马尔可夫模型AI 解读

Among the first microarray experiments were those measuring expression over time, and time course experiments remain common. Most methods to analyze time course data attempt to group genes sharing similar temporal profiles within a single biological condition. However, with time course data in multiple conditions, a main goal is to identify differential expression patterns over time. An intuitive approach to this problem would be to apply at each time point any of the many…

分组变量回归中的模型选择与估计AI 解读

Summary We consider the problem of selecting grouped variables (factors) for accurate prediction in regression. Such a problem arises naturally in many practical situations with the multifactor analysis-of-variance problem as the most important and well-known example. Instead of selecting factors by stepwise backward elimination, we focus on the accuracy of estimation and consider extensions of the lasso, the LARS algorithm and the non-negative garrotte for factor selection.…

线性模型中的高效经验贝叶斯变量选择与估计AI 解读

We propose an empirical Bayes method for variable selection and coefficient estimation in linear regression models. The method is based on a particular hierarchical Bayes formulation, and the empirical Bayes estimator is shown to be closely related to the LASSO estimator. Such a connection allows us to take advantage of the recently developed quick LASSO algorithm to compute the empirical Bayes estimate, and provides a new way to select the tuning parameter in the LASSO…