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AI artificial intelligence brings about new quantitative techniques to assess the state of an economy. Here, we describe a new measure for systemic risk: the Financial Risk Meter (FRM). This measure is based on the penalization parameter (λ) of a linear quantile lasso regression. The FRM is calculated by taking the average of the penalization parameters over the 100 largest US publicly-traded financial institutions. We demonstrate the suitability of this AI-based risk measure by comparing the proposed FRM to other measures for systemic risk, such as VIX, SRISK and Google Trends. We find that mutual Granger causality exists between the FRM and these measures, which indicates the validity of the FRM as a systemic risk measure. The implementation of this project is carried out using parallel computing, the codes are published on www.quantlet.de with keyword  FRM. The R package RiskAnalytics is another tool with the purpose of integrating and facilitating the research, calculation and analysis methods around the FRM project. The visualization and the up-to-date FRM can be found on hu.berlin/frm.

The naïve Bayes model is a simple but often satisfactory supervised classification method. The original naïve Bayes scheme, does, however, have a serious weakness, namely, the harmful effect of redundant predictors. In this paper, we study how to apply a regularization technique to learn a computationally efficient classifier that is inspired by naïve Bayes. The proposed formulation, combined with an L₁-penalty, is capable of discarding harmful, redundant predictors. A modification of the LARS algorithm is devised to solve this problem. We tackle both real-valued and discrete predictors, assuring that our method is applicable to a wide range of data. In the experimental section, we empirically study the effect of redundant and irrelevant predictors. We also test the method on a high dimensional data set from the neuroscience field, where there are many more predictors than data cases. Finally, we run the method on a real data set than combines categorical with numeric predictors. Our approach is compared with several naïve Bayes variants and other classification algorithms (SVM and kNN), and is shown to be competitive.

There are about 1 billion hypertensives patients on a global scale. Hypertension has become the main cause of shorter lifespan and disability for humans worldwide. In this essay, we constructed a new model based on hybrid feature selection and the standard XGBoost for hypertension detection and prediction. After having successfully utilized Lasso regression to identify hypertension-related factors, we used the standard XGBoost model for hypertension prediction. The result from the experiments conducted on the data from the BRFSS shows that proposed model can achieve 77.2% accuracy and 84.6% AUC, both about 7% higher than that without the nonoptimized model. Our proposed model can not only be used to predict the risk of hypertension, but also provide customers with suggestions on how to lead a healthy lifestyle.

A sparse Bayesian linear regression model is proposed that generalizes the Bayesian Lasso to a class of Bayesian models with scale mixtures of normal distributions as priors for the regression coefficients. We assume a hierarchical Bayesian model with a binary indicator for whether a predictor variable is included in the model, a generalized normal prior distribution for the coefficients of the included variables, and a Student-t error model for robustness to heavy tailed noise. Our model out-performs other popular sparse regression estimators on synthetic and real data.

Heteroscedasticity often appears in the high-dimensional data analysis. In order to achieve a sparse dimension reduction direction for high-dimensional data with heteroscedasticity, we propose a new sparse sufficient dimension reduction method, called Lasso-PQR. From the candidate matrix derived from the principal quantile regression (PQR) method, we construct a new artificial response variable which is made up from top eigenvectors of the candidate matrix. Then we apply a Lasso regression to obtain sparse dimension reduction directions. While for the “large $p$ small $n$” case that $p\ge n$, we use principal projection to solve the dimension reduction problem in a lower-dimensional subspace and projection back to the original dimension reduction problem. Theoretical properties of the methodology are established. Compared with several existing methods in the simulations and real data analysis, we demonstrate the advantages of our method in the high dimension data with heteroscedasticity.

Pancreatic cancer is the fourth leading cause of cancer deaths in the United States with five-year survival rates less than 5% due to rare detection in early stages. Identification of genes that are directly correlated to pancreatic cancer survival is crucial for pancreatic cancer diagnostics and treatment. However, no existing GWAS or transcriptome studies are available for addressing this problem. We apply lasso penalized Cox regression to a transcriptome study to identify genes that are directly related to pancreatic cancer survival. This method is capable of handling the right censoring effect of survival times and the ultrahigh dimensionality of genetic data. A cyclic coordinate descent algorithm is employed to rapidly select the most relevant genes and eliminate the irrelevant ones. Twelve genes have been identified and verified to be directly correlated to pancreatic cancer survival time and can be used for the prediction of future patient's survival.

Microarray data profiles gene expression on a whole genome scale, and provides a good way to study associations between gene expression and occurrence or progression of cancer disease. Many researchers realized that microarray data is useful to predict cancer cases. However, the high dimension of gene expressions, which is significantly larger than the sample size, makes this task very difficult. It is very important to identify the significant genes causing cancer. Many feature selection algorithms have been proposed focusing on improving cancer predictive accuracy at the expense of ignoring the correlations between the features. In this work, a novel framework (named by SGS) is presented for significant genes selection and efficient cancer case classification. The proposed framework first performs a clustering algorithm to find the gene groups where genes in each group have higher correlation coefficient, and then selects (1) the significant (2) genes in each group using the Bayesian Lasso method and important gene groups using the group Lasso method, and finally builds a prediction model based on the shrinkage gene space with efficient classification algorithm (such as support vector machine (SVM), 1NN, and regression). Experimental results on public available microarray data show that the proposed framework often outperforms the existing feature selection and prediction methods such as SAM, information gain (IG), and Lasso-type prediction models.

We propose a statistical method based on graphical Gaussian models for estimating large gene networks from DNA microarray data. In estimating large gene networks, the number of genes is larger than the number of samples, we need to consider some restrictions for model building. We propose weighted lasso estimation for the graphical Gaussian models as a model of large gene networks. In the proposed method, the structural learning for gene networks is equivalent to the selection of the regularization parameters included in the weighted lasso estimation. We investigate this problem from a Bayes approach and derive an empirical Bayesian information criterion for choosing them. Unlike Bayesian network approach, our method can find the optimal network structure and does not require to use heuristic structural learning algorithm. We conduct Monte Carlo simulation to show the effectiveness of the proposed method. We also analyze Arabidopsis thaliana microarray data and estimate gene networks.

Xia, Tong, Li and Zhu (2002) proposed a general estimation method termed minimum average variance estimation (MAVE) for semiparametric models. The method has been found very useful in estimating complicated semiparametric models (Xia, Zhang and Tong, 2004; Xia and Härdle, 2006) and general dimension reduction (Xia, 2008; Wang and Xia, 2008). The method is also convenient to combine with other methods in order to incorporate additional statistical requirements (Wang and Yin, 2007). In this paper, we give a general review on the method and discuss some issues arising in estimating semiparametric models and dimension reduction (Li, 1991 and Cook, 1998) when complicated statistical requirements are imposed, including quantile regression, sparsity of variables and censored data.

Recent interest in the application of microarray technology focuses on relating gene expression profiles to censored survival outcome such as patients' overall survival time or time to cancer relapse. Due to the high-dimensional nature of the gene expression data, regularization becomes an effective approach for such analyses. In this chapter, we review several aspects of the recent development of penalized regression models for censored survival data with high-dimensional covariates, e.g. gene expressions. We first discuss the Cox proportional hazards model (Cox 1972) as the primary example and then the accelerated failure time model (Kalbfleisch and Prentice 2002) for further consideration.

In this paper, we suggest the pretest estimation strategy for variable selection and estimating the regression parameters using quasi-likelihood method when uncertain prior information (UPI) exist. We also apply the lasso-type estimation and variable selection strategy and compare the relative performance of lasso with the pretest and quasi-likelihood estimators. The performance of each estimator is evaluated in terms of the simulated mean square error. Further, we develop the asymptotic properties of pretest estimator (PTE) using the notion of asymptotical distributional risk, and compare it with the unrestricted quasi-likelihood estimator (UE) and restricted quasi-likelihood estimator (RE), respectively. The asymptotic result demonstrates the superiority of pretest strategy over the UE and RE in meaningful part of the parameter space. The simulation results show that when UPI is correctly specified the PTE outperforms lasso.