ﻻ يوجد ملخص باللغة العربية
High-dimensional, low sample-size (HDLSS) data problems have been a topic of immense importance for the last couple of decades. There is a vast literature that proposed a wide variety of approaches to deal with this situation, among which variable selection was a compelling idea. On the other hand, a deep neural network has been used to model complicated relationships and interactions among responses and features, which is hard to capture using a linear or an additive model. In this paper, we discuss the current status of variable selection techniques with the neural network models. We show that the stage-wise algorithm with neural network suffers from disadvantages such as the variables entering into the model later may not be consistent. We then propose an ensemble method to achieve better variable selection and prove that it has probability tending to zero that a false variable is selected. Then, we discuss additional regularization to deal with over-fitting and make better regression and classification. We study various statistical properties of our proposed method. Extensive simulations and real data examples are provided to support the theory and methodology.
Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate functions, t
This paper proposes a new robust smooth-threshold estimating equation to select important variables and automatically estimate parameters for high dimensional longitudinal data. A novel working correlation matrix is proposed to capture correlations w
We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can benefit fr
Yang et al. (2016) proved that the symmetric random walk Metropolis--Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high-dimensional assumptions. We propose a novel MCMC sampler using an informed proposal scheme, whic
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of penalized regr