The task of inertial sensor calibration has required the development of various techniques to take into account the sources of measurement error coming from such devices. The calibration of the stochastic errors of these sensors has been the focus of increasing amount of research in which the method of reference has been the so-called "Allan variance slope method" which, in addition to not having appropriate statistical properties, requires a subjective input which makes it prone to mistakes. To overcome this, recent research has started proposing "automatic" approaches where the parameters of the probabilistic models underlying the error signals are estimated by matching functions of the Allan variance or Wavelet Variance with their modelimplied counterparts. However, given the increased use of such techniques, there has been no study or clear direction for practitioners on which approach is optimal for the purpose of sensor calibration. This paper formally defines the class of estimators based on this technique and puts forward theoretical and applied results that, comparing with estimators in this class, suggest the use of the Generalized Method of Wavelet Moments as an optimal choice.
Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. To do so, many of the recently proposed classification methods require some form of dimension-reduction of the problem which finally provide a single model as an output and, in most cases, rely on the likelihood function in order to achieve variable selection. We propose a new prediction-based objective function that can be tailored to the requirements of practitioners and can be used to assess and interpret a given problem. Based on cross-validation techniques and the idea of importance sampling, our proposal scans low-dimensional models under the assumption of sparsity and, for each of them, estimates their objective function to assess their predictive power in order to select. Two applications on cancer data sets and a simulation study show that the proposal compares favorably with competing alternatives such as, for example, Elastic Net and Support Vector Machine. Indeed, the proposed method not only selects smaller models for better, or at least comparable, classification errors but also provides a set of selected models instead of a single one, allowing to construct a network of possible models for a target prediction accuracy level.
Cutaneous melanoma is a highly aggressive skin cancer whose treatment and prognosis are critically affected by the presence of metastasis. In this study, we address the following issue: which gene transcripts and what kind of interactions between them can allow to predict nonmetastatic from metastatic melanomas with a high level of accuracy? We carry out a meta-analysis on the first gene expression set of the Leeds melanoma cohort, as made available online on 11 May 2016 through the ArrayExpress platform with MicroArray Gene Expression number 4725. According to the authors, primary melanoma mRNA expression was measured in 204 tumours using an illumina DASL HT12 4 whole-genome array. The tumour transcripts were selected through a recently proposed predictive-based regression algorithm for gene-network selection. A set of 64 equivalent models, each including only two gene transcripts, were each sufficient to accurately classify primary tumours into metastatic and nonmetastatic melanomas. The sensitivity and specificity of the genomic-based models were, respectively, 4% (95% confidence interval: 0.11-21.95%) and 99% (95% confidence interval: 96.96-99.99%). The very high specificity coupled with a significantly large positive likelihood ratio leads to a conclusive increase in the likelihood of disease when these biomarkers are present in the primary tumour. In conjunction with other highly sensitive methods, this approach can aspire to be part of the future standard diagnosis methods for the screening of metastatic cutaneous melanoma. The small dimension of the selected transcripts models enables easy handling of large-scale genomic testing procedures. Moreover, some of the selected transcripts have an understandable link with what is known about cutaneous melanoma oncogenesis, opening a window on the molecular pathways underlying the metastatic process of this disease.
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