Abstract Boosting has proven its superiority by increasing the diversity of base classifiers, mainly in various classification problems. In reality, target variables in classification often are formed by numerical variables, in possession of ordinal information. However, existing boosting algorithms for classification are unable to reflect such ordinal target variables, resulting in non‐optimal solutions. In this paper, we propose a novel algorithm of ordinal encoding adaptive boosting (AdaBoost) using a multi‐dimensional encoding scheme for ordinal target variables. Extending an original binary‐class AdaBoost, the proposed algorithm is equipped with a multi‐class exponential loss function. We show that it achieves the Bayes classifier and establishes forward stagewise additive modeling. We demonstrate the performance of the proposed algorithm with a base learner as a neural network. Our experiments show that it outperforms existing boosting algorithms in various ordinal datasets.

Abstract We study the problem of robust subspace learning when there is an adversary who can attack the data to increase the projection error. By deriving the adversarial projection risk when data follows the multivariate Gaussian distribution with the spiked covariance, or so‐called the Spiked Covariance model, we propose to use the empirical risk minimization method to obtain the optimal robust subspace. We then find a non‐asymptotic upper bound of the adversarial excess risk, which implies the empirical risk minimization estimator is close to the optimal robust adversarial subspace. The optimization problem can be solved easily by the projected gradient descent algorithm for the rank‐one spiked covariance model. However, in general, it is computationally intractable to solve the empirical risk minimization problem. Thus, we propose to minimize an upper bound of the empirical risk to find the robust subspace for the general spiked covariance model. Finally, we conduct numerical experiments to show the robustness of our proposed algorithms.

Gene-environment (G-E) interaction analysis plays a critical role in understanding and modeling complex diseases. Compared to main-effect-only analysis, it is more seriously challenged by higher dimensionality, weaker signals, and the unique "main effects, interactions" variable selection hierarchy. In joint G-E interaction analysis under which a large number of G factors are analysed in a single model, effort tailored to rare features (e.g., SNPs with low minor allele frequencies) has been limited. Existing investigations on rare features have been mostly focused on marginal analysis, where various data aggregation techniques have been developed, and hypothesis testings have been conducted to identify significant aggregated features. However, such techniques cannot be extended to joint G-E interaction analysis. In this study, building on a very recent tree-based data aggregation technique, which has been developed for main-effect-only analysis, we develop a new G-E interaction analysis approach tailored to rare features. The adopted data aggregation technique allows for more efficient information borrowing from neighboring rare features. Similar to some existing state-of-the-art ones, the proposed approach adopts penalization for variable selection, regularized estimation, and respect of the variable selection hierarchy. Simulation shows that it has more accurate identification of important interactions and main effects than several competing alternatives. In the analysis of NFBC1966 study, the proposed approach leads to findings different from the alternatives and with satisfactory prediction and stability performance.

Abstract Sliced average third‐moment estimation (SATME) is a typical method for sufficient dimension reduction (SDR) based on high‐order conditional moment. It is useful, particularly in the scenarios of regression mixtures. However, as SATME uses the third‐order conditional moment of the predictors given the response, it may not as robust as some other SDR methods that use lower order moments, say, sliced inverse regression (SIR) and slice average variance estimation (SAVE). Based on the space displacement function, a local influence analysis framework of SATME is constructed including a statistic of influence assessment for the observations. Furthermore, a data‐trimming strategy is suggested based on the above influence assessment. The proposed methodologies solve a typical issue that also exists in some other SDR methods. A real‐data analysis and simulations are presented.

Abstract In this work, we develop a method namedTwinningfor partitioning a dataset into statistically similar twin sets.Twinningis based onSPlit, a recently proposed model‐independent method for optimally splitting a dataset into training and testing sets.Twinningis orders of magnitude faster than theSPlitalgorithm, which makes it applicable to Big Data problems such as data compression.Twinningcan also be used for generating multiple splits of a given dataset to aid divide‐and‐conquer procedures andk‐fold cross validation.

Abstract While many survival models have been invented, the Cox model and the proportional odds model are among the most popular ones. Both models are special cases of the linear transformation model. The linear transformation model typically assumes a linear function on covariates, which may not reflect the complex relationship between covariates and survival outcomes. Nonlinear functional form can also be specified in the linear transformation model. Nonetheless, the underlying functional form is unknown and mis‐specifying it leads to biased estimates and reduced prediction accuracy of the model. To address this issue, we develop a neural‐network transformation model. Similar to neural networks, the neural‐network transformation model uses its hierarchical structure to learn complex features from simpler ones and is capable of approximating the underlying functional form of covariates. It also inherits advantages from the linear transformation model, making it applicable to both time‐to‐event analyses and recurrent event analyses. Simulations demonstrate that the neural‐network transformation model outperforms the linear transformation model in terms of estimation and prediction accuracy when the covariate effects are nonlinear. The advantage of the new model over the linear transformation model is also illustrated via two real applications.