This paper develops smooth-threshold estimating equations that can automatically eliminate irrelevant parameters by setting them as zero. The resulting estimator enjoys the oracle property in the sense of Fan & Li (2001), even in estimators for which the covariance assumption of Wang & Leng (2007) is violated, such as the Buckley–James estimator. Furthermore, the estimator can be obtained without solving a convex optimization problem. A bic-type criterion for tuning parameter selection is also proposed. It is shown that the criterion achieves consistent model selection. A numerical study confirms the performance of the method.

Genome-wide gene-gene interaction analysis using single nucleotide polymorphisms (SNPs) is an attractive way for identification of genetic components that confers susceptibility of human complex diseases. Individual hypothesis testing for SNP-SNP pairs as in common genome-wide association study (GWAS) however involves difficulty in setting overall p-value due to complicated correlation structure, namely, the multiple testing problem that causes unacceptable false negative results. A large number of SNP-SNP pairs than sample size, so-called the large p small n problem, precludes simultaneous analysis using multiple regression. The method that overcomes above issues is thus needed.

The fused lasso penalizes a loss function by the L₁ norm for both the regression coefficients and their successive differences to encourage sparsity of both. In this paper, we propose a Bayesian generalized fused lasso modeling based on a normal-exponential-gamma (NEG) prior distribution. The NEG prior is assumed into the difference of successive regression coefficients. The proposed method enables us to construct a more versatile sparse model than the ordinary fused lasso using a flexible regularization term. Simulation studies and real data analyses show that the proposed method has superior performance to the ordinary fused lasso.

Functional connectivity (FC) and neural excitability may interact to affect symptoms of autism spectrum disorder (ASD). We tested this hypothesis with neural network simulations, and applied it with functional magnetic resonance imaging (fMRI). A hierarchical recurrent neural network embodying predictive processing theory was subjected to a facial emotion recognition task. Neural network simulations examined the effects of FC and neural excitability on changes in neural representations by developmental learning, and eventually on ASD-like performance. Next, by mapping each neural network condition to subject subgroups on the basis of fMRI parameters, the association between ASD-like performance in the simulation and ASD diagnosis in the corresponding subject subgroup was examined. In the neural network simulation, the more homogeneous the neural excitability of the lower-level network, the more ASD-like the performance (reduced generalization and emotion recognition capability). In addition, in homogeneous networks, the higher the FC, the more ASD-like performance, while in heterogeneous networks, the higher the FC, the less ASD-like performance, demonstrating that FC and neural excitability interact. As an underlying mechanism, neural excitability determines the generalization capability of top-down prediction, and FC determines whether the model’s information processing will be top-down prediction-dependent or bottom-up sensory-input dependent. In fMRI datasets, ASD was actually more prevalent in subject subgroups corresponding to the network condition showing ASD-like performance. The current study suggests an interaction between FC and neural excitability, and presents a novel framework for computational modeling and biological application of a developmental learning process underlying cognitive alterations in ASD.

Gene-environment (GxE) interaction is one potential explanation for the missing heritability problem. A popular approach to genome-wide environment interaction studies (GWEIS) is based on regression models involving interactions between genetic variants and environment variables. Unfortunately, GWEIS encounters systematically inflated (or deflated) test statistics more frequently than a marginal association study. The problematic behavior may occur due to poor specification of the null model (i.e. the model without genetic effect) in GWEIS. Improved null model specification may resolve the problem, but the investigation requires many time-consuming analyses of genome-wide scans, e.g. by trying out several transformations of the phenotype. It is therefore helpful if we can predict such problematic behavior beforehand. We present a simple closed-form formula to assess problematic behavior of GWEIS under the null hypothesis of no genetic effects. It requires only phenotype, environment variables, and covariates, enabling quick identification of systematic test statistic inflation or deflation. Applied to real data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), our formula identified problematic studies from among hundreds GWEIS considering each metabolite as the environment variable in GxE interaction. Our formula is useful to quickly identify problematic GWEIS without requiring a genome-wide scan.