共查询到20条相似文献,搜索用时 0 毫秒
1.
Wei Lan Hansheng Wang Chih-Ling Tsai 《Annals of the Institute of Statistical Mathematics》2014,66(2):279-301
In a high-dimensional linear regression model, we propose a new procedure for testing statistical significance of a subset of regression coefficients. Specifically, we employ the partial covariances between the response variable and the tested covariates to obtain a test statistic. The resulting test is applicable even if the predictor dimension is much larger than the sample size. Under the null hypothesis, together with boundedness and moment conditions on the predictors, we show that the proposed test statistic is asymptotically standard normal, which is further supported by Monte Carlo experiments. A similar test can be extended to generalized linear models. The practical usefulness of the test is illustrated via an empirical example on paid search advertising. 相似文献
2.
Yun-Long Feng 《Applicable analysis》2013,92(5):979-991
Least-squares regularized learning algorithms for regression were well-studied in the literature when the sampling process is independent and the regularization term is the square of the norm in a reproducing kernel Hilbert space (RKHS). Some analysis has also been done for dependent sampling processes or regularizers being the qth power of the function norm (q-penalty) with 0?q?≤?2. The purpose of this article is to conduct error analysis of the least-squares regularized regression algorithm when the sampling sequence is weakly dependent satisfying an exponentially decaying α-mixing condition and when the regularizer takes the q-penalty with 0?q?≤?2. We use a covering number argument and derive learning rates in terms of the α-mixing decay, an approximation condition and the capacity of balls of the RKHS. 相似文献
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For a constrained pseudoinverse problem whose operators satisfy the complementarity condition we propose a one-parameter continuous regularization method of the second order. This method is based on stabilization of solutions to Cauchy problems for a linear differential equation of the second order in a Hilbert space which is obtained from the heavy ball method. We establish requirements to the parametric regularization function and perturbation levels that ensure the stability of the method in the class of all possible bounded perturbations. 相似文献
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Heavy-tailed noise or strongly correlated predictors often go with the multivariate linear regression model. To tackle with these problems, this paper focuses on the matrix elastic-net regularized multivariate Huber regression model. This new model possesses the grouping effect property and the robustness to heavy-tailed noise. Meanwhile, it also has the ability of reducing the negative effect of outliers due to Huber loss. Furthermore, an accelerated proximal gradient algorithm is designed to solve the proposed model. Some numerical studies including a real data analysis are dedicated to show the efficiency of our method. 相似文献
7.
Tomohiro Ando Sadanori Konishi 《Annals of the Institute of Statistical Mathematics》2009,61(2):331-353
A flexible nonparametric method is proposed for classifying high- dimensional data with a complex structure. The proposed
method can be regarded as an extended version of linear logistic discriminant procedures, in which the linear predictor is
replaced by a radial-basis-expansion predictor. Radial basis functions with a hyperparameter are used to take the information
on covariates and class labels into account; this was nearly impossible within the previously proposed hybrid learning framework.
The penalized maximum likelihood estimation procedure is employed to obtain stable parameter estimates. A crucial issue in
the model-construction process is the choice of a suitable model from candidates. This issue is examined from information-theoretic
and Bayesian viewpoints and we employed Ando et al. (Japanese Journal of Applied Statistics, 31, 123–139, 2002)’s model evaluation criteria. The proposed method is available not only for the high-dimensional data but
also for the variable selection problem. Real data analysis and Monte Carlo experiments show that our proposed method performs
well in classifying future observations in practical situations. The simulation results also show that the use of the hyperparameter
in the basis functions improves the prediction performance. 相似文献
8.
Semi-supervised learning is an emerging computational paradigm for machine learning,that aims to make better use of large amounts of inexpensive unlabeled data to improve the learning performance.While various methods have been proposed based on different intuitions,the crucial issue of generalization performance is still poorly understood.In this paper,we investigate the convergence property of the Laplacian regularized least squares regression,a semi-supervised learning algorithm based on manifold regularization.Moreover,the improvement of error bounds in terms of the number of labeled and unlabeled data is presented for the first time as far as we know.The convergence rate depends on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers.Some new techniques are exploited for the analysis since an extra regularizer is introduced. 相似文献
9.
Selma Toker Gülesen Üstündağ Şiray Selahattin Kaçıranlar 《Statistics & probability letters》2013,83(10):2391-2398
We carry out the idea of inequality constrained least squares (ICLS) estimation of Liew (1976) to the inequality constrained ridge regression (ICRR) estimation. We propose ICRR estimator by reducing the primal–dual relation to the fundamental problem of Dantzig and Cottle, 1967, Cottle and Dantzig, 1974 with Lemke (1962) algorithm. Furthermore, we conduct a Monte Carlo experiment. 相似文献
10.
Yoshisuke Nonaka Sadanori Konishi 《Annals of the Institute of Statistical Mathematics》2005,57(4):617-635
We introduce a nonlinear regression modeling strategy, using a regularized local likelihood method. The local likelihood method
is effective for analyzing data with complex structure. It might be, however, pointed out that the stability of the local
likelihood estimator is not necessarily guaranteed in the case that the structure of system is quite complex. In order to
overcome this difficulty, we propose a regularized local likelihood method with a polynomial function which unites local likelihood
and regularization. A crucial issue in constructing nonlinear regression models is the choice of a smoothing parameter, the
degree of polynomial and a regularization parameter. In order to evaluate models estimated by the regularized local likelihood
method, we derive a model selection criterion from an information-theoretic point of view. Real data analysis and Monte Carlo
experiments are conducted to examine the performance of our modeling strategy. 相似文献
11.
Yuko Araki Sadanori Konishi Shuichi Kawano Hidetoshi Matsui 《Annals of the Institute of Statistical Mathematics》2009,61(4):811-833
We consider the problem of constructing functional regression models for scalar responses and functional predictors, using
Gaussian basis functions along with the technique of regularization. An advantage of our regularized Gaussian basis expansions
to functional data analysis is that it creates a much more flexible instrument for transforming each individual’s observations
into functional form. In constructing functional regression models there remains the problem of how to determine the number
of basis functions and an appropriate value of a regularization parameter. We present model selection criteria for evaluating
models estimated by the method of regularization in the context of functional regression models. The proposed functional regression
models are applied to Canadian temperature data. Monte Carlo simulations are conducted to examine the efficiency of our modeling
strategies. The simulation results show that the proposed procedure performs well especially in terms of flexibility and stable
estimates. 相似文献
12.
Science China Mathematics - Various forms of penalized estimators with good statistical and computational properties have been proposed for variable selection respecting the grouping structure in... 相似文献
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Ren Mingyang Zhang Sanguo Zhang Qingzhao 《Annals of the Institute of Statistical Mathematics》2021,73(4):703-736
Annals of the Institute of Statistical Mathematics - The accuracy of response variables is crucially important to train regression models. In some situations, including the high-dimensional case,... 相似文献
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Acta Mathematicae Applicatae Sinica, English Series - Recently, variable selection based on penalized regression methods has received a great deal of attention, mostly through frequentist’s... 相似文献
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In this paper, we study the consistency of the regularized least-square regression in a general reproducing kernel Hilbert space. We characterize the compactness of the inclusion map from a reproducing kernel Hilbert space to the space of continuous functions and show that the capacity-based analysis by uniform covering numbers may fail in a very general setting. We prove the consistency and compute the learning rate by means of integral operator techniques. To this end, we study the properties of the integral operator. The analysis reveals that the essence of this approach is the isomorphism of the square root operator. 相似文献
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Nonlinear regression modeling via regularized wavelets and smoothing parameter selection 总被引:1,自引:0,他引:1
Toru Fujii 《Journal of multivariate analysis》2006,97(9):2023-2033
We introduce regularized wavelet-based methods for nonlinear regression modeling when design points are not equally spaced. A crucial issue in the model building process is a choice of tuning parameters that control the smoothness of a fitted curve. We derive model selection criteria from an information-theoretic and also Bayesian approaches. Monte Carlo simulations are conducted to examine the performance of the proposed wavelet-based modeling technique. 相似文献
18.
This paper addresses the learning algorithm on the unit sphere. The main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics kernel. The excess error can be estimated by the sum of sample errors and regularization errors. Our study shows that by introducing a suitable spherical harmonics kernel, the regularization parameter can decrease arbitrarily fast with the sample size. 相似文献
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This paper presents learning rates for the least-square regularized regression algorithms with polynomial kernels. The target
is the error analysis for the regression problem in learning theory. A regularization scheme is given, which yields sharp
learning rates. The rates depend on the dimension of polynomial space and polynomial reproducing kernel Hilbert space measured
by covering numbers. Meanwhile, we also establish the direct approximation theorem by Bernstein-Durrmeyer operators in with Borel probability measure.
相似文献
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本文讨论样本依赖空间中无界抽样情形下最小二乘损失函数的系数正则化问题. 这里的学习准则与之前再生核Hilbert空间的准则有着本质差异: 核除了满足连续性和有界性之外, 不需要再满足对称性和正定性; 正则化子是函数关于样本展开系数的l2-范数; 样本输出是无界的. 上述差异给误差分析增加了额外难度. 本文的目的是在样本输出不满足一致有界的情形下, 通过l2-经验覆盖数给出误差的集中估计(concentration estimates). 通过引入一个恰当的Hilbert空间以及l2-经验覆盖数的技巧, 得到了与假设空间的容量以及与回归函数的正则性有关的较满意的学习速率. 相似文献