Methodology (stat.ME)

Abstract: We investigate the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. We achieve such a goal by theoretically studying the feature selection performance of a practically implemented knockoffs algorithm, which we name as the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and family wise error rate (FWER). The approximate knockoffs procedure differs from the model-X knockoffs procedure only in that the former uses the misspecified or estimated feature distribution. A key technique in our theoretical analyses is to couple the approximate knockoffs procedure with the model-X knockoffs procedure so that random variables in these two procedures can be close in realizations. We prove that if such coupled model-X knockoffs procedure exists, the approximate knockoffs procedure can achieve the asymptotic FDR or FWER control at the target level. We showcase three specific constructions of such coupled model-X knockoff variables, verifying their existence and justifying the robustness of the model-X knockoffs framework.

Abstract: In this paper,firstly,to overcome the shortcoming of traditional ARX model, a new operator between an interval number and a real matrix is defined, and then it is applied to the traditional ARX model to get a new type of structure interval ARX model that can deal with interval data, which is defined as interval ARX model (IARX). Secondly,the IARX model is applied to moving pattern-based modeling. Finally,to verify the validity of the proposed modeling method,it is applied to a sintering process. The simulation results show the moving pattern-based modeling using the new type of interval ARX model is robust to variation in parameters of the model, and the performance of the modeling using the proposed IARX is superior to that of the previous work.

Abstract: High-dimensional spectral data -- routinely generated in dairy production -- are used to predict a range of traits in milk products. Partial least squares regression (PLSR) is ubiquitously used for these prediction tasks. However PLSR is not typically viewed as arising from statistical inference of a probabilistic model, and parameter uncertainty is rarely quantified. Additionally, PLSR does not easily lend itself to model-based modifications, coherent prediction intervals are not readily available, and the process of choosing the latent-space dimension, $\mathtt{Q}$, can be subjective and sensitive to data size. We introduce a Bayesian latent-variable model, emulating the desirable properties of PLSR while accounting for parameter uncertainty. The need to choose $\mathtt{Q}$ is eschewed through a nonparametric shrinkage prior. The flexibility of the proposed Bayesian partial least squares regression (BPLSR) framework is exemplified by considering sparsity modifications and allowing for multivariate response prediction. The BPLSR framework is used in two motivating settings: 1) trait prediction from mid-infrared spectral analyses of milk samples, and 2) milk pH prediction from surface-enhanced Raman spectral data. The prediction performance of BPLSR at least matches that of PLSR. Additionally, the provision of correctly calibrated prediction intervals objectively provides richer, more informative inference for stakeholders in dairy production.

Abstract: In this paper we address the problem of bias in machine learning of parameters following covariate shifts. Covariate shift occurs when the distribution of input features change between the training and deployment stages. Regularization and model selection associated with machine learning biases many parameter estimates. In this paper, we propose an automatic debiased machine learning approach to correct for this bias under covariate shifts. The proposed approach leverages state-of-the-art techniques in debiased machine learning to debias estimators of policy and causal parameters when covariate shift is present. The debiasing is automatic in only relying on the parameter of interest and not requiring the form of the form of the bias. We show that our estimator is asymptotically normal as the sample size grows. Finally, we evaluate the method using a simulation.

Abstract: The two-trials rule for drug approval requires "at least two adequate and well-controlled studies, each convincing on its own, to establish effectiveness". This is usually employed by requiring two significant pivotal trials and is the standard regulatory requirement to provide evidence for a new drug's efficacy. However, there is need to develop suitable alternatives to this rule for a number of reasons, including the possible availability of data from more than two trials. I consider the case of up to 3 studies and stress the importance to control the partial Type-I error rate, where only some studies have a true null effect, while maintaining the overall Type-I error rate of the two-trials rule, where all studies have a null effect. Some less-known $p$-value combination methods are useful to achieve this: Pearson's method, Edgington's method and the recently proposed harmonic mean $\chi^2$-test. I study their properties and discuss how they can be extended to a sequential assessment of success while still ensuring overall Type-I error control. I compare the different methods in terms of partial Type-I error rate, project power and the expected number of studies required. Edgington's method is eventually recommended as it is easy to implement and communicate, has only moderate partial Type-I error rate inflation but substantially increased project power.