The integration of high-dimensional genomic data and clinical data into time-to-event prediction models has gained significant attention due to the growing availability of these datasets. Traditionally, a Cox regression model is employed, concatenating various covariate types linearly. Given that much of the data may be redundant or irrelevant, feature selection through penalization is often desirable. A notable characteristic of these datasets is their organization into blocks of distinct data types, such as methylation and clinical predictors, which requires selecting a subset of covariates from each group due to high intra-group correlations. For this reason, we propose utilizing Exclusive Lasso regularization in place of standard Lasso penalization. We apply our methodology to a real-life cancer dataset, demonstrating enhanced survival prediction performance compared to the conventional Cox regression model.

While achieving high prediction accuracy is a fundamental goal in machine learning, an equally important task is finding a small number of features with high explanatory power. One popular selection technique is permutation importance, which assesses a variable's impact by measuring the change in prediction error after permuting the variable. However, this can be problematic due to the need to create artificial data, a problem shared by other methods as well. Another problem is that variable selection methods can be limited by being model-specific. We introduce a new model-independent approach, Variable Priority (VarPro), which works by utilizing rules without the need to generate artificial data or evaluate prediction error. The method is relatively easy to use, requiring only the calculation of sample averages of simple statistics, and can be applied to many data settings, including regression, classification, and survival. We investigate the asymptotic properties of VarPro and show, among other things, that VarPro has a consistent filtering property for noise variables. Empirical studies using synthetic and real-world data show the method achieves a balanced performance and compares favorably to many state-of-the-art procedures currently used for variable selection.

When there are signals and noises, physicists try to identify signals by modeling them, whereas statisticians oppositely try to model noise to identify signals. In this study, we applied the statisticians' concept of signal detection of physics data with small-size samples and high dimensions without modeling the signals. Most of the data in nature, whether noises or signals, are assumed to be generated by dynamical systems; thus, there is essentially no distinction between these generating processes. We propose that the correlation length of a dynamical system and the number of samples are crucial for the practical definition of noise variables among the signal variables generated by such a system. Since variables with short-term correlations reach normal distributions faster as the number of samples decreases, they are regarded to be ``noise-like'' variables, whereas variables with opposite properties are ``signal-like'' variables. Normality tests are not effective for data of small-size samples with high dimensions. Therefore, we modeled noises on the basis of the property of a noise variable, that is, the uniformity of the histogram of the probability that a variable is a noise. We devised a method of detecting signal variables from the structural change of the histogram according to the decrease in the number of samples. We applied our method to the data generated by globally coupled map, which can produce time series data with different correlation lengths, and also applied to gene expression data, which are typical static data of small-size samples with high dimensions, and we successfully detected signal variables from them. Moreover, we verified the assumption that the gene expression data also potentially have a dynamical system as their generation model, and found that the assumption is compatible with the results of signal extraction.

Technological advances have enabled the generation of unique and complementary types of data or views (e.g. genomics, proteomics, metabolomics) and opened up a new era in multiview learning research with the potential to lead to new biomedical discoveries. We propose iDeepViewLearn (Interpretable Deep Learning Method for Multiview Learning) for learning nonlinear relationships in data from multiple views while achieving feature selection. iDeepViewLearn combines deep learning flexibility with the statistical benefits of data and knowledge-driven feature selection, giving interpretable results. Deep neural networks are used to learn view-independent low-dimensional embedding through an optimization problem that minimizes the difference between observed and reconstructed data, while imposing a regularization penalty on the reconstructed data. The normalized Laplacian of a graph is used to model bilateral relationships between variables in each view, therefore, encouraging selection of related variables. iDeepViewLearn is tested on simulated and two real-world data, including breast cancer-related gene expression and methylation data. iDeepViewLearn had competitive classification results and identified genes and CpG sites that differentiated between individuals who died from breast cancer and those who did not. The results of our real data application and simulations with small to moderate sample sizes suggest that iDeepViewLearn may be a useful method for small-sample-size problems compared to other deep learning methods for multiview learning.

In recent years, a great deal of interest has focused on conducting inference on the parameters in a linear model in the high-dimensional setting. In this paper, we consider a simple and very na\"{i}ve two-step procedure for this task, in which we (i) fit a lasso model in order to obtain a subset of the variables; and (ii) fit a least squares model on the lasso-selected set. Conventional statistical wisdom tells us that we cannot make use of the standard statistical inference tools for the resulting least squares model (such as confidence intervals and $p$-values), since we peeked at the data twice: once in running the lasso, and again in fitting the least squares model. However, in this paper, we show that under a certain set of assumptions, with high probability, the set of variables selected by the lasso is deterministic. Consequently, the na\"{i}ve two-step approach can yield confidence intervals that have asymptotically correct coverage, as well as p-values with proper Type-I error control. Furthermore, this two-step approach unifies two existing camps of work on high-dimensional inference: one camp has focused on inference based on a sub-model selected by the lasso, and the other has focused on inference using a debiased version of the lasso estimator.

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the subproblems separately, obtaining a coefficient vector for each one. Then, it uses non-negative least squares to recombine the different vectors into a single solution. This step is useful in selecting and reweighting components that are correlated with the response. Simulated and real data examples show that the component lasso can outperform standard regression methods such as the lasso and elastic net, achieving a lower mean squared error as well as better support recovery.