Small nucleolar RNAs (snoRNAs) play crucial roles in a wide range of biological processes, and studying their association with diseases can enhance our understanding of disease pathogenesis. Nevertheless, current knowledge of these associations is limited traditional biological experiments are both costly and time-consuming. Consequently, developing efficient computational methods is essential for predicting potential snoRNA-disease associations. We propose a novel prediction method based on non-negative matrix factorization and graph convolution for predicting snoRNA-disease associations (GCNMF-SDA). First, five different types of similarity information from snoRNA and disease entities are introduced to fully mine and refine the feature information. Then the snoRNA and disease similarity networks are integrated using nonlinearity approach Similarity Network Fusion (SNF), while the weighted K nearest known neighbors (WKNKN) algorithm is applied to optimize the snoRNA-disease association matrix. Following this, the graph convolution module and the non-negative matrix factorization module extract disease features and snoRNA features, respectively. After extracting these features, they are combined into a composite feature vector for each snoRNA-disease pair. Finally, the composite feature vectors along with their corresponding labels, are input into a multilayer perceptron for training. Our experiments, conducted using a rigorous five-fold cross-validation approach, reveal that the GCNMF-SDA model achieves an impressive area under the receiver operating characteristic curve (AUC-ROC) of 0.9659 and an area under the precision-recall curve (AUC-PR) of 0.9522. Furthermore, most of the novel associations identified by GCNMF-SDA were validated through case studies, underscoring the method's reliability in predicting potential relationships between snoRNAs and diseases.

Measuring the nonlinear dependence between random vectors and testing for their statistical independence is a fundamental problem in statistics. One of the most popular dependence measures is the Hilbert-Schmidt independence criterion (HSIC), which has attracted increasing attention in recent years. However, most existing works have focused on either fixed or very high-dimensional covariates. In this work, we bridge the gap between these two scenarios and provide statistical insights into the performance of HSIC when the dimensions grow at different rates. We first show that, under the null hypothesis, the rescaled HSIC converges in distribution to a standard normal distribution. Then we provide a general condition for the HSIC based tests to have nontrivial power in high dimensions. By decomposing this condition, we illustrate how the ability of HSIC to measure nonlinear dependence changes with increasing dimensions. Moreover, we demonstrate that, depending on the sample size, the covariate dimensions and the dependence structures within covariates, the HSIC can capture different types of associations between random vectors. We also conduct extensive numerical studies to validate our theoretical results.

This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional dependence by quantifying the mutual dependence among the transformed variables. The proposed index has several appealing properties. (a) It is distribution free since the limiting null distribution of the proposed index does not depend on the population distributions of the data. Hence the critical values can be tabulated by simulations. (b) The proposed index ranges from zero to one, and equals zero if and only if the conditional independence holds. Thus, it has nontrivial power under the alternative hypothesis. (c) It is robust to outliers and heavy-tailed data since it is invariant to conditional strictly monotone transformations. (d) It has low computational cost since it incorporates a simple closed-form expression and can be implemented in quadratic time. (e) It is insensitive to tuning parameters involved in the calculation of the proposed index. (f) The new index is applicable for multivariate random vectors as well as for discrete data. All these properties enable us to use the new index as statistical inference tools for various data. The effectiveness of the method is illustrated through extensive simulations and a real application on causal discovery.

In this work, we propose a robust test for the multivariate two-sample problem through projective ensemble, which is a generalization of the Cramer-von Mises statistic. The proposed test statistic has a simple closed-form expression without any tuning parameters involved, it is easy to implement can be computed in quadratic time. Moreover, our test is insensitive to the dimension and consistent against all fixed alternatives, it does not require the moment assumption and is robust to the presence of outliers. We study the asymptotic behaviors of the test statistic under the null and two kinds of alternative hypotheses. We also suggest a permutation procedure to approximate critical values and employ its consistency. We demonstrate the effectiveness of our test through extensive simulation studies and a real data application.