Collaborative Research: Small-Sample Error Estimation for Classification with Application to Genomic Signal Processing

DNA微阵列芯片和其他用于测量基因组变量的高通量技术的可用性，为工程能够成功解决翻译基因组学的一个关键问题带来了希望：利用基因组信号对疾病进行分类。分类可以用于诊断特定病理的存在或分类，也可以用于预测治疗的效果。在癌症中，诊断可以在肿瘤发展的不同阶段之间进行，而预后可以预测药物相对于个体特定基因组成的毒性或益处，这是个性化医疗的一个例子。误差估计是至关重要的，因为分类器的误差决定了它的价值。基于基因的分类通常涉及小样本（微阵列的数量），因此必须使用相同的数据来训练和测试分类器。在训练数据上工作的误差估计器往往受到低偏差或高方差的影响。该研究提高了最近提出的三种小样本估计范式的性能并扩大了适用范围：(1)增强误差估计器在每个样本点放置一个核，然后将设计的分类器应用于由增强核形成的分布来估计其误差；(2)由低偏估计量和高偏估计量的最优加权平均形成凸误差估计量；(3)利用数据对标准误差估计量进行最优校准，形成校准误差估计量。本研究推广了估计规则，提供了估计器参数的获取方法，并将估计器应用于基因组诊断和预后。性质主要通过模拟研究：然而，分析结果是在已知误差估计量分布的情况下得出的。

The availability of DNA microarray chips and other high-throughput technologies for measuring genomic variables fosters the hope that engineering can successfully address a key problem of translational genomics: using genomic signals to classify disease. Classification can serve to diagnosis the existence or category of a particular pathology or it can be used to prognosticate the effect of a treatment. In cancer, diagnosis can be between different stages of tumor development, and prognosis can be to predict the toxicity or benefit of a drug relative to the particular genetic make-up of an individual an example of personalized medicine. Error estimation is critical because the error of a classifier determines its worth. Gene-based classification typically involves small samples (numbers of microarrays), so that the same data must be used to train and test a classifier. Error estimators that work on the training data tend to suffer from low bias or high variance. This research improved the performance and widens the range of applicability of three recently proposed small-sample estimation paradigms: (1) bolstered error estimators place a kernel at each sample point and then apply the designed classifier to the distribution formed from the bolstering kernels to estimate its error; (2) convex error estimators are formed by an optimal weighted average of low- and high-biased estimators; and (3) calibrated error estimators are formed by using the data to optimally calibrate standard error estimators. This research generalizes the estimation rules, provides methods to obtain estimator parameters, and applies the estimators to genomic diagnosis and prognosis. Properties are mainly studied via simulation: however, analytic results are derived in cases where the error-estimator distributions are known.