Besides the aim of identifying a subset of useful features, the stability of feature selection algorithms is also a critical topic in increasing the confidence of selected features, where an objective stability measure with required properties is expected. To this end, we herein propose a new stability measure simsnJRthat considers the feature correlations and possesses the desirable properties. Specifically, we first utilize the Pearson correlation coefficients and the false discovery rate control procedure to identify significantly correlated feature pairs that are not shared in two feature sets. A normalization step is then conducted to reduce the effects of the size of feature sets and of general feature correlations in the dataset. Finally, we consider two commonly used feature selectors (i.e., relief and mRMR) and conduct comparative experiments on several datasets under different hyperparameter values and the variation of train sets. Results show its effectiveness.

与线性因果相比, 非线性因果具有更复杂的特点和内涵. 本文主要讨论非线性因果中的若干个问题, 并着重强调因果域的概念. 本文基于广泛应用的计算模型和方法, 围绕非线性因果分析与计算以及因果域的识别问题提出相应观点和建议, 并通过几个具体案例揭示非线性因果在处理复杂因果推断问题中的重要性和现实意义.

Feature selection has been playing an important role in analyzing the high-dimension and low-sample-size gene expression profiles towards high classification performance of diseases and deep understanding of the underlying biological mechanisms. Besides classification performance, the stability of selected features is another non-ignorable factor in evaluating a feature selector, since stable feature selection results enhance the confidence of selected features for true biomarker discovery and further biological validation. In this study, we propose a novel feature selection method under the ensemble learning framework. Specifically, we take Fast Correlation Based Filter as the base feature selector to analyze subsamples of microarray data. We then present several aggregation methods to combine multiple feature subsets. Finally, two stability measures are used to quantify the robustness of feature selectors to data variations. Our comparative empirical study on publicly available datasets demonstrates the superiority of the proposed methods over its competitors in obtaining high stability scores and classification accuracy.

A fast sparse covariance-based fitting algorithm with the non-negative least squares (NNLS) form is proposed for the direction of arrival (DOA) estimation. The Khatri-Rao product of the array manifold of the uniform linear arrays is utilized to achieve the dimension reducing transformation after vectorizing the array covariance matrix. Furthermore, the DOA estimation problem is derived as a NNLS problem by using the non-negative property of the spatial spectrum, which can be solved by some efficient solvers. Numerical experiments show that the proposed method can obtain high resolution with a competitive computational complexity, as well as works in the presence of coherent sources.

Microarray experiments on gene expression inevitably generate missing values, which impedes further downstream biological analysis. Therefore, it is key to estimate the missing values accurately. Most of the existing imputation methods tend to suffer from the over-fitting problem. In this study, we propose two regularized local learning methods for microarray missing value imputation. Motivated by the grouping effect of $L_{2}$L2 regularization, after selecting the target gene, we train an $L_{2}$L2 Regularized Local Least Squares imputation model (RLLSimpute_L2) on the target gene and its neighbors to estimate the missing values of the target gene. Furthermore, RLLSimpute_L2 imputes the missing values in an ascending order based on the associated missing rate with each target gene. This contributes to fully utilizing the previously estimated values. Besides $L_{2}$L2, we further explore $L_{1}$L1 regularization and propose an $L_{1}$L1 Regularized Local Least Squares imputation model (RLLSimpute_L1). To evaluate their effectiveness, we conducted extensive experimental studies on six benchmark datasets covering both time series and non-time series cases. Nine state-of-the-art imputation methods are compared with RLLSimpute_L2 and RLLSimpute_L1 in terms of three performance metrics. The comparative experimental results indicate that RLLSimpute_L2 outperforms its competitors by achieving smaller imputation errors and better structure preservation of differentially expressed genes.

Wrapper based gene selection methods tend to obtain better classification accuracy than filter methods, while it is much more time consuming. Accelerating this process without degrading the high accuracy is of great value for researchers to better analyze gene expression profiles. In this paper, we explore to reduce the time complexity of wrapper based gene selection method with K-Nearest-Neighbor (KNN) classifier embedded. Instead of taking KNN as a black box, we incrementally construct and maintain a classifier distance matrix to speed up the gene selection process. Experiments on six publicly available microarrays were first conducted to show the effectiveness of incremental wrapper based gene selection method with KNN. Then, to demonstrate the performance gain in time cost reduction, we analyzed the time complexity and experimentally evaluated it. Both theoretical analysis and experimental results prove that the proposed approach greatly accelerates the gene selection process without degrading the classification accuracy.

Gene selection plays a crucial role in the analysis of microarray data with high dimensionality and small sample size. Incremental wrapper based feature subset selection (FSS) methods, among various feature selection approaches, tend to obtain high quality feature subset and better classification accuracy than filter methods, while it is much more time consuming since the interdependence and redundancy between features is evaluated in a wrapper way. In this paper, we explore to introduce Markov Blanket (MB) into incremental wrapper based FSS process. Rather than evaluate the quality of all the features ranked by a filter method, our proposal eliminates features that are redundant to the newly selected one via MB during the wrapper evaluation process to reduce the number of wrappers, enabling us to select the relevant features and eliminate redundant ones efficiently. To verify the effectiveness and efficiency of the proposed approach, experimental comparisons on six publicly available microarray data are conducted with two typical classifiers with different metrics, Naïve Bayes and 1-Nearest-Neighbor. Experimental results demonstrate that our approach greatly speeds up the feature selection process, obtains more compact feature subset and achieves better classification accuracy compared to that without MB for both two-category and multi-category problems.

Correctly discovering causal relations from healthcare information can help people to understand disease mechanisms and discover disease causes. In some cases, the healthcare data do not follow a multivariate Gaussian distribution. We design a new causal structure learning algorithm. The algorithm can effectively combines ideas from local learning with simultaneous equations models techniques. In the first phase of the algorithm we select potential neighbors for each variable based on simultaneous equations models, and then perform a constrained hill-climbing search to orient the edges. Using the algorithm without prior knowledge, we analyze causal relations in the real data from the National Health and Nutrition Examination Survey.